The document compares the performance of single stage and double stage interleavers in communication systems using turbo codes. A single stage interleaver uses one random interleaver between two convolutional encoders, while a double stage interleaver uses two interleavers in series. The document suggests that a double stage interleaver can improve the bit error rate (BER) of the system compared to a single stage interleaver by further scrambling the input bits. It also provides details on the components of a turbo code system such as convolutional encoders, interleavers, puncturing, and iterative decoding.
Design and Performance Analysis of Convolutional Encoder and Viterbi Decoder ...IJERA Editor
In digital communication forward error correction methods have a great practical importance when channel is
noisy. Convolutional error correction code can correct both type of errors random and burst. Convolution
encoding has been used in digital communication systems including deep space communication and wireless
communication. The error correction capability of convolutional code depends on code rate and constraint
length. The low code rate and high constraint length has more error correction capabilities but that also
introduce large overhead. This paper introduces convolutional encoders for various constraint lengths. By
increasing the constraint length the error correction capability can be increased. The performance and error
correction also depends on the selection of generator polynomial. This paper also introduces a good generator
polynomial which has high performance and error correction capabilities.
Noise Immune Convolutional Encoder Design and Its Implementation in Tanner ijcisjournal
With the rapid advances in integrated circuit(IC) technologies, number of functions on a chip was
increasing at a very fast rate, with which interconnect density is increasing especially in functional logic
chips. The on-chip noise affects are increasing and needs to be addressed. In this paper we have
implemented a convolution encoder using a technique that provides higher noise immunity. The encoder
circuit is simulated in Tanner 15.0 with data rate of 25Mbps and a clock frequency of 250MHz
NOISE IMMUNE CONVOLUTIONAL ENCODER DESIGN AND ITS IMPLEMENTATIONIN TANNERIJCI JOURNAL
With the rapid advances in integrated circuit(IC) technologies, number of functions on a chip was increasing at a very fast rate, with which interconnect density is increasing especially in functional logic chips. The on-chip noise affects are increasing and needs to be addressed. In this paper we have implemented a convolution encoder using a technique that provides higher noise immunity. The encoder circuit is simulated in Tanner 15.0 with data rate of 25Mbps and a clock frequency of 250MHz
Data detection with a progressive parallel ici canceller in mimo ofdmeSAT Publishing House
The document describes a progressive parallel interference canceller (PPIC) for use in a MIMO-OFDM system to suppress inter-carrier interference (ICI). PPIC is compared to parallel interference canceller (PIC) and shows lower complexity and better performance. PPIC architecture is simpler than PIC and more suitable for implementation in wireless communication systems requiring high data rates and mobility. Simulation results show that PPIC combined with LDPC coding achieves lower bit error rates than PIC combined with LDPC coding.
Error control coding using bose chaudhuri hocquenghem bch codesIAEME Publication
Information and coding theory has applications in telecommunication, where error detection
and correction techniques enable reliable delivery of data over unreliable communication channels.
Many communication channels are subject to noise. BCH technique is one of the most reliable error
control techniques and the most important advantage of BCH technique is both detection and
correction can be performed. The technique aims at detecting and correcting of two bit errors in a
code-word of length 15 bits. A seven bit message was specifically chosen so that ASCII characters
can be easily transmitted.
Error control coding using bose chaudhuri hocquenghem bch codesIAEME Publication
This document discusses error control coding using Bose-Chaudhuri-Hocquenghem (BCH) codes. It begins with an introduction to information and coding theory, describing how encoding and decoding are used to convey information reliably over noisy communication channels. It then provides details on BCH codes, including that they are a class of cyclic error-correcting codes constructed using finite fields that allow precise control over the number of errors corrected. The document presents the design and architecture of a specific (15,7) BCH code that can detect and correct up to two bit errors in a 15-bit codeword.
This document provides an overview and outline of a course on digital communications. It begins with background information on the course, including the textbook and references. The document then outlines the main topics to be covered in the course, including probability review, signal and spectra, modulation and demodulation techniques, channel coding, spread spectrum techniques, synchronization, source coding, and fading channels. It also provides brief descriptions of digital communication basics like source, transmitter, receiver, and channel components. Overall, the document introduces the key concepts and topics to be covered in a digital communications course.
The document compares the performance of single stage and double stage interleavers in communication systems using turbo codes. A single stage interleaver uses one random interleaver between two convolutional encoders, while a double stage interleaver uses two interleavers in series. The document suggests that a double stage interleaver can improve the bit error rate (BER) of the system compared to a single stage interleaver by further scrambling the input bits. It also provides details on the components of a turbo code system such as convolutional encoders, interleavers, puncturing, and iterative decoding.
Design and Performance Analysis of Convolutional Encoder and Viterbi Decoder ...IJERA Editor
In digital communication forward error correction methods have a great practical importance when channel is
noisy. Convolutional error correction code can correct both type of errors random and burst. Convolution
encoding has been used in digital communication systems including deep space communication and wireless
communication. The error correction capability of convolutional code depends on code rate and constraint
length. The low code rate and high constraint length has more error correction capabilities but that also
introduce large overhead. This paper introduces convolutional encoders for various constraint lengths. By
increasing the constraint length the error correction capability can be increased. The performance and error
correction also depends on the selection of generator polynomial. This paper also introduces a good generator
polynomial which has high performance and error correction capabilities.
Noise Immune Convolutional Encoder Design and Its Implementation in Tanner ijcisjournal
With the rapid advances in integrated circuit(IC) technologies, number of functions on a chip was
increasing at a very fast rate, with which interconnect density is increasing especially in functional logic
chips. The on-chip noise affects are increasing and needs to be addressed. In this paper we have
implemented a convolution encoder using a technique that provides higher noise immunity. The encoder
circuit is simulated in Tanner 15.0 with data rate of 25Mbps and a clock frequency of 250MHz
NOISE IMMUNE CONVOLUTIONAL ENCODER DESIGN AND ITS IMPLEMENTATIONIN TANNERIJCI JOURNAL
With the rapid advances in integrated circuit(IC) technologies, number of functions on a chip was increasing at a very fast rate, with which interconnect density is increasing especially in functional logic chips. The on-chip noise affects are increasing and needs to be addressed. In this paper we have implemented a convolution encoder using a technique that provides higher noise immunity. The encoder circuit is simulated in Tanner 15.0 with data rate of 25Mbps and a clock frequency of 250MHz
Data detection with a progressive parallel ici canceller in mimo ofdmeSAT Publishing House
The document describes a progressive parallel interference canceller (PPIC) for use in a MIMO-OFDM system to suppress inter-carrier interference (ICI). PPIC is compared to parallel interference canceller (PIC) and shows lower complexity and better performance. PPIC architecture is simpler than PIC and more suitable for implementation in wireless communication systems requiring high data rates and mobility. Simulation results show that PPIC combined with LDPC coding achieves lower bit error rates than PIC combined with LDPC coding.
Error control coding using bose chaudhuri hocquenghem bch codesIAEME Publication
Information and coding theory has applications in telecommunication, where error detection
and correction techniques enable reliable delivery of data over unreliable communication channels.
Many communication channels are subject to noise. BCH technique is one of the most reliable error
control techniques and the most important advantage of BCH technique is both detection and
correction can be performed. The technique aims at detecting and correcting of two bit errors in a
code-word of length 15 bits. A seven bit message was specifically chosen so that ASCII characters
can be easily transmitted.
Error control coding using bose chaudhuri hocquenghem bch codesIAEME Publication
This document discusses error control coding using Bose-Chaudhuri-Hocquenghem (BCH) codes. It begins with an introduction to information and coding theory, describing how encoding and decoding are used to convey information reliably over noisy communication channels. It then provides details on BCH codes, including that they are a class of cyclic error-correcting codes constructed using finite fields that allow precise control over the number of errors corrected. The document presents the design and architecture of a specific (15,7) BCH code that can detect and correct up to two bit errors in a 15-bit codeword.
This document provides an overview and outline of a course on digital communications. It begins with background information on the course, including the textbook and references. The document then outlines the main topics to be covered in the course, including probability review, signal and spectra, modulation and demodulation techniques, channel coding, spread spectrum techniques, synchronization, source coding, and fading channels. It also provides brief descriptions of digital communication basics like source, transmitter, receiver, and channel components. Overall, the document introduces the key concepts and topics to be covered in a digital communications course.
Channel coding adds redundancy to transmitted data to allow for error correction and detection. It is used to achieve reliable digital communication in the presence of noise and interference. There are two main types of channel coding: linear block codes and convolution codes. Linear block codes divide data into blocks and encode each block into a longer codeword. Convolution codes consider not only the current data but also previous data when encoding. Channel coding trades off bandwidth for improved error correction through the addition of redundant parity bits.
This document describes convolutional codes for channel coding in communication systems. Convolutional codes are represented by parameters like constraint length K, where K is the number of shift registers used. The convolutional encoder operates like a finite state machine, with the state defined by the most recent K-1 message bits. The trellis diagram provides an explicit representation of the convolutional encoder as a finite state machine. Convolutional codes are decoded using the Viterbi algorithm, which performs maximum likelihood decoding by selecting the most probable path through the trellis. Simulation results show the performance of the convolutional encoding and decoding system.
This document summarizes forward error correction techniques using convolutional encoders and Viterbi decoders. It first provides background on communication channels and the need for error correction when transmitting data. It then describes convolutional coding, a technique that maps a continuous stream of input bits to a continuous stream of encoded output bits using shift registers, with the encoded bits depending on current and past input bits. The key aspects of convolutional encoders are discussed, including parameters like the number of output bits, input bits, and shift registers. Generator polynomials are also introduced as characterizing the encoder connections. Viterbi decoding is highlighted as a maximum likelihood algorithm for decoding the trellis structure of convolutional codes based on soft decisions.
The document describes a lesson plan for a digital communication course at Matrusri Engineering College. The lesson plan covers linear block codes, including their description, generation, syndrome detection, minimum distance, error correction capabilities, and decoding using standard arrays and Hamming codes over 10 class periods. The objectives are to distinguish different error control coding techniques and their encoding/decoding algorithms. Textbooks and references are also listed.
The document describes a lesson plan for a digital communication course at Matrusri Engineering College. The lesson plan covers linear block codes, including their description, generation, syndrome detection, minimum distance, error correction capabilities, and decoding using standard arrays and Hamming codes over 10 class periods. The objectives are to distinguish different error control coding techniques and their encoding/decoding algorithms. Textbooks and references are also listed.
This document discusses various digital communication techniques including:
1. Pulse Code Modulation (PCM) which samples, quantizes, and encodes analog signals into digital pulses.
2. Differential PCM (DPCM) which encodes prediction errors rather than absolute samples to reduce bandwidth.
3. Delta Modulation (DM) which approximates signals as a staircase and quantizes the difference between samples.
4. Adaptive techniques like Adaptive DPCM (ADPCM) are also discussed which allow variable step sizes and filter coefficients to improve performance for different signal characteristics.
The proposed modulation technique employs
quadrature mixing to achieve transmission of high frequency
data over a narrow channel. In this modulation technique, the
phase of carrier is varied in accordance with the instantaneous
amplitude of the message signal. The message data bits are
transformed to an unintelligible form which then modulates a
carrier signal. The modulation technique induces probabilistic
characteristic over the entire process. The nondeterministic
nature of data is enhanced and thereby providing integrity and
confidentiality to the data which is transmitted across a channel.
Another important feature of this technique is that prediction of
the message data bits by observing the modulated signal is foiled
due to the use of different phase shifts for 40 symbols. In this
technique, the spectrum of modulated signal is translated to be
centered at 0 Hz. At the demodulator, the instantaneous
amplitude and phase can easily be determined. The major
advantage of this digital modulation technique is that, signaling
rate, requirement of high frequency carrier and transmission
channel bandwidth is reduced to a considerable extent without
compromising the transmission capacity and data rate.
The document discusses a study that implemented low density parity check (LDPC) decoding using a min sum algorithm with reduced complexity compared to existing methods. It used quadrature phase-shift keying (QPSK) modulation to improve bit error rate over previous approaches that used binary phase-shift keying (BPSK) modulation. The proposed method was able to achieve a lower bit error rate than other existing techniques using fewer iterations, improving performance flexibility by varying the code size. It implemented LDPC decoding on an irregular parity check matrix using a split row technique to reduce interconnect complexity and increase parallelism in the row processing stage compared to standard decoding algorithms.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
For ease of analog or digital information transmission and reception, modulation is the foremost important technique. In the present project, we’ll discuss about different modulation scheme in digital mode done by operating a switch/ key by the digital data. As we know, by modifying basic three parameters of the carrier signal, three basic modulation schemes can be obtained; generation and detection of these three modulations are discussed and compared with respect to probability of error or bit error rate (BER).
This document describes the implementation of a Viterbi decoder using VHDL. It begins with background on convolutional encoding, the Viterbi algorithm for decoding convolutional codes, and the basic structure of a Viterbi decoder. It then discusses the design and simulation of a rate 1/2 constraint length 3 Viterbi decoder in VHDL targeting the Spartan-3A FPGA. Simulation results and comparisons to other FPGA devices are presented.
The document provides information about the syllabus for the course "Information Theory & Error Correction Coding". It discusses the details of the final exam which has two parts worth 50 marks total. Part A is 20 marks and covers topics like channel capacity, coding models, error control types, and linear block codes. Part B is 30 marks and covers additional topics such as linear block codes, convolutional codes, decoding algorithms, and error correction capabilities. It also provides background information on discrete channels, channel capacity theorem, Shannon's channel coding theorem, and the purpose of channel coding. Key concepts discussed include linear codes, block codes, convolutional codes, encoding, decoding, and error detection/correction techniques.
The document discusses various digital communication techniques including:
- Elements of a digital communication system such as source encoding, channel encoding, modulation, and demodulation.
- Types of channels for digital communication including telephone channels, optical fiber channels, and satellite channels.
- Key aspects of telephone channels including a bandwidth of 300Hz to 3400Hz and support for transmission rates up to 16.8 kbps. Optical fiber channels use light signals transmitted through fiber optic cables while overcoming noise from photodiodes and amplifiers.
In digital communication system, the information bearing digital signal is processed such
that it can be represented by a sequence of binary digits (discrete messages). Then it is used for
ON/OFF keying of some characteristic of a high frequency sinusoidal carrier wave, such as
amplitude, phase or frequency. If the input message signal is in analog form, then it is converted
to digital form by the processes of sampling, quantizing and encoding. Computer data and
telegraph signals are some examples of digital signal. The key feature of a digital communication
system is that it deals with a finite set of discrete messages.
This document provides an overview of a communication systems course taught by Ass. Prof. Ibrar Ullah. The course objectives are to develop basic concepts of communication systems using the textbook "Modern Digital And Analog Communication Systems". Students will be evaluated based on homework, tests, quizzes, and a final exam. Key topics covered include analog versus digital communication, modulation techniques, and the relationship between signal-to-noise ratio, channel bandwidth, and rate of communication.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Estimation and design of mc ds-cdma for hybrid concatenated coding in high sp...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Estimation and design of mc ds-cdma for hybrid concatenated coding in high sp...eSAT Journals
Abstract The design of Multi Carrier Direct Sequence Code Division Multiple Access (MC-DS-CDMA) structure which generalizes serial and parallel concatenated code is investigated to this project. This model is ideal for designing various codes in the performance of both error floor and water floor region. We propose a concatenated code for transmitter block which is used for multi carrier direct sequence CDMA technique. Simulation results of MC-DS-CDMA uplink system using Cadence software shows the various parameters such as memory, Execution time and number of transient steps required for the Execution of MC-DS-CDMA uplink system was estimated and also power consumed was determined for each block in the transmitter. An improved concatenated code model is used for uplink mobile communication. Further system performance improvements can be obtained by concatenating inner code and outer code and the results of computer simulations demonstrate that the performance of the concatenated code was investigated. Keywords: Code Division Multiple Access, Concatenated code, inner code, outer code, interleaving and power analysis.
Performance Analysis of OSTBC MIMO Using Precoder with ZF & MMSE EqualizerIJERA Editor
In this paper, a bit error rate analysis is presented for multiple-input–multiple-output (MIMO) system with finite-bit feedback is considered in PSK modulation technique, where a transmit signal consists of a rotational precoder followed by an orthogonal space–time block code (OSTBC) which achieve full diversity when a linear receiver, such as, zeroforcing (ZF) or minimum mean square (MMSE), is used. By choosing different parameters, codes with different symbol rates and orthogonally can be obtained .In this paper, we compare the performance of a family of space-time codes. Simulations show how the precoders obtained by our proposed criterion and method perform better bit error rate reduction compared to the existing ones.
The document provides an overview of source coding in digital communication systems. It discusses the key elements of a communication system including the transmitter, receiver, and channel. It then describes how an analog information source is converted to a digital signal through sampling, quantization, and coding. Source coding aims to remove redundancy in the information so as to minimize the bandwidth required for transmission. Channel coding adds extra bits to help detect and correct errors. Line coding represents the digital bit stream as voltage or current variations suited for the transmission channel. Key techniques discussed include pulse code modulation (PCM), companding, and various line codes.
The CBC machine is a common diagnostic tool used by doctors to measure a patient's red blood cell count, white blood cell count and platelet count. The machine uses a small sample of the patient's blood, which is then placed into special tubes and analyzed. The results of the analysis are then displayed on a screen for the doctor to review. The CBC machine is an important tool for diagnosing various conditions, such as anemia, infection and leukemia. It can also help to monitor a patient's response to treatment.
Contenu connexe
Similaire à ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II Coding techniques
Channel coding adds redundancy to transmitted data to allow for error correction and detection. It is used to achieve reliable digital communication in the presence of noise and interference. There are two main types of channel coding: linear block codes and convolution codes. Linear block codes divide data into blocks and encode each block into a longer codeword. Convolution codes consider not only the current data but also previous data when encoding. Channel coding trades off bandwidth for improved error correction through the addition of redundant parity bits.
This document describes convolutional codes for channel coding in communication systems. Convolutional codes are represented by parameters like constraint length K, where K is the number of shift registers used. The convolutional encoder operates like a finite state machine, with the state defined by the most recent K-1 message bits. The trellis diagram provides an explicit representation of the convolutional encoder as a finite state machine. Convolutional codes are decoded using the Viterbi algorithm, which performs maximum likelihood decoding by selecting the most probable path through the trellis. Simulation results show the performance of the convolutional encoding and decoding system.
This document summarizes forward error correction techniques using convolutional encoders and Viterbi decoders. It first provides background on communication channels and the need for error correction when transmitting data. It then describes convolutional coding, a technique that maps a continuous stream of input bits to a continuous stream of encoded output bits using shift registers, with the encoded bits depending on current and past input bits. The key aspects of convolutional encoders are discussed, including parameters like the number of output bits, input bits, and shift registers. Generator polynomials are also introduced as characterizing the encoder connections. Viterbi decoding is highlighted as a maximum likelihood algorithm for decoding the trellis structure of convolutional codes based on soft decisions.
The document describes a lesson plan for a digital communication course at Matrusri Engineering College. The lesson plan covers linear block codes, including their description, generation, syndrome detection, minimum distance, error correction capabilities, and decoding using standard arrays and Hamming codes over 10 class periods. The objectives are to distinguish different error control coding techniques and their encoding/decoding algorithms. Textbooks and references are also listed.
The document describes a lesson plan for a digital communication course at Matrusri Engineering College. The lesson plan covers linear block codes, including their description, generation, syndrome detection, minimum distance, error correction capabilities, and decoding using standard arrays and Hamming codes over 10 class periods. The objectives are to distinguish different error control coding techniques and their encoding/decoding algorithms. Textbooks and references are also listed.
This document discusses various digital communication techniques including:
1. Pulse Code Modulation (PCM) which samples, quantizes, and encodes analog signals into digital pulses.
2. Differential PCM (DPCM) which encodes prediction errors rather than absolute samples to reduce bandwidth.
3. Delta Modulation (DM) which approximates signals as a staircase and quantizes the difference between samples.
4. Adaptive techniques like Adaptive DPCM (ADPCM) are also discussed which allow variable step sizes and filter coefficients to improve performance for different signal characteristics.
The proposed modulation technique employs
quadrature mixing to achieve transmission of high frequency
data over a narrow channel. In this modulation technique, the
phase of carrier is varied in accordance with the instantaneous
amplitude of the message signal. The message data bits are
transformed to an unintelligible form which then modulates a
carrier signal. The modulation technique induces probabilistic
characteristic over the entire process. The nondeterministic
nature of data is enhanced and thereby providing integrity and
confidentiality to the data which is transmitted across a channel.
Another important feature of this technique is that prediction of
the message data bits by observing the modulated signal is foiled
due to the use of different phase shifts for 40 symbols. In this
technique, the spectrum of modulated signal is translated to be
centered at 0 Hz. At the demodulator, the instantaneous
amplitude and phase can easily be determined. The major
advantage of this digital modulation technique is that, signaling
rate, requirement of high frequency carrier and transmission
channel bandwidth is reduced to a considerable extent without
compromising the transmission capacity and data rate.
The document discusses a study that implemented low density parity check (LDPC) decoding using a min sum algorithm with reduced complexity compared to existing methods. It used quadrature phase-shift keying (QPSK) modulation to improve bit error rate over previous approaches that used binary phase-shift keying (BPSK) modulation. The proposed method was able to achieve a lower bit error rate than other existing techniques using fewer iterations, improving performance flexibility by varying the code size. It implemented LDPC decoding on an irregular parity check matrix using a split row technique to reduce interconnect complexity and increase parallelism in the row processing stage compared to standard decoding algorithms.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
For ease of analog or digital information transmission and reception, modulation is the foremost important technique. In the present project, we’ll discuss about different modulation scheme in digital mode done by operating a switch/ key by the digital data. As we know, by modifying basic three parameters of the carrier signal, three basic modulation schemes can be obtained; generation and detection of these three modulations are discussed and compared with respect to probability of error or bit error rate (BER).
This document describes the implementation of a Viterbi decoder using VHDL. It begins with background on convolutional encoding, the Viterbi algorithm for decoding convolutional codes, and the basic structure of a Viterbi decoder. It then discusses the design and simulation of a rate 1/2 constraint length 3 Viterbi decoder in VHDL targeting the Spartan-3A FPGA. Simulation results and comparisons to other FPGA devices are presented.
The document provides information about the syllabus for the course "Information Theory & Error Correction Coding". It discusses the details of the final exam which has two parts worth 50 marks total. Part A is 20 marks and covers topics like channel capacity, coding models, error control types, and linear block codes. Part B is 30 marks and covers additional topics such as linear block codes, convolutional codes, decoding algorithms, and error correction capabilities. It also provides background information on discrete channels, channel capacity theorem, Shannon's channel coding theorem, and the purpose of channel coding. Key concepts discussed include linear codes, block codes, convolutional codes, encoding, decoding, and error detection/correction techniques.
The document discusses various digital communication techniques including:
- Elements of a digital communication system such as source encoding, channel encoding, modulation, and demodulation.
- Types of channels for digital communication including telephone channels, optical fiber channels, and satellite channels.
- Key aspects of telephone channels including a bandwidth of 300Hz to 3400Hz and support for transmission rates up to 16.8 kbps. Optical fiber channels use light signals transmitted through fiber optic cables while overcoming noise from photodiodes and amplifiers.
In digital communication system, the information bearing digital signal is processed such
that it can be represented by a sequence of binary digits (discrete messages). Then it is used for
ON/OFF keying of some characteristic of a high frequency sinusoidal carrier wave, such as
amplitude, phase or frequency. If the input message signal is in analog form, then it is converted
to digital form by the processes of sampling, quantizing and encoding. Computer data and
telegraph signals are some examples of digital signal. The key feature of a digital communication
system is that it deals with a finite set of discrete messages.
This document provides an overview of a communication systems course taught by Ass. Prof. Ibrar Ullah. The course objectives are to develop basic concepts of communication systems using the textbook "Modern Digital And Analog Communication Systems". Students will be evaluated based on homework, tests, quizzes, and a final exam. Key topics covered include analog versus digital communication, modulation techniques, and the relationship between signal-to-noise ratio, channel bandwidth, and rate of communication.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Estimation and design of mc ds-cdma for hybrid concatenated coding in high sp...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Estimation and design of mc ds-cdma for hybrid concatenated coding in high sp...eSAT Journals
Abstract The design of Multi Carrier Direct Sequence Code Division Multiple Access (MC-DS-CDMA) structure which generalizes serial and parallel concatenated code is investigated to this project. This model is ideal for designing various codes in the performance of both error floor and water floor region. We propose a concatenated code for transmitter block which is used for multi carrier direct sequence CDMA technique. Simulation results of MC-DS-CDMA uplink system using Cadence software shows the various parameters such as memory, Execution time and number of transient steps required for the Execution of MC-DS-CDMA uplink system was estimated and also power consumed was determined for each block in the transmitter. An improved concatenated code model is used for uplink mobile communication. Further system performance improvements can be obtained by concatenating inner code and outer code and the results of computer simulations demonstrate that the performance of the concatenated code was investigated. Keywords: Code Division Multiple Access, Concatenated code, inner code, outer code, interleaving and power analysis.
Performance Analysis of OSTBC MIMO Using Precoder with ZF & MMSE EqualizerIJERA Editor
In this paper, a bit error rate analysis is presented for multiple-input–multiple-output (MIMO) system with finite-bit feedback is considered in PSK modulation technique, where a transmit signal consists of a rotational precoder followed by an orthogonal space–time block code (OSTBC) which achieve full diversity when a linear receiver, such as, zeroforcing (ZF) or minimum mean square (MMSE), is used. By choosing different parameters, codes with different symbol rates and orthogonally can be obtained .In this paper, we compare the performance of a family of space-time codes. Simulations show how the precoders obtained by our proposed criterion and method perform better bit error rate reduction compared to the existing ones.
The document provides an overview of source coding in digital communication systems. It discusses the key elements of a communication system including the transmitter, receiver, and channel. It then describes how an analog information source is converted to a digital signal through sampling, quantization, and coding. Source coding aims to remove redundancy in the information so as to minimize the bandwidth required for transmission. Channel coding adds extra bits to help detect and correct errors. Line coding represents the digital bit stream as voltage or current variations suited for the transmission channel. Key techniques discussed include pulse code modulation (PCM), companding, and various line codes.
Similaire à ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II Coding techniques (20)
The CBC machine is a common diagnostic tool used by doctors to measure a patient's red blood cell count, white blood cell count and platelet count. The machine uses a small sample of the patient's blood, which is then placed into special tubes and analyzed. The results of the analysis are then displayed on a screen for the doctor to review. The CBC machine is an important tool for diagnosing various conditions, such as anemia, infection and leukemia. It can also help to monitor a patient's response to treatment.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
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ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II Coding techniques
1. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
UNIT – II
Coding Techniques
Errors are introduced in the data when it passes through the channel. The channel noise
interferes the signal. The signal power is also reduced. Hence errors are introduced.
In this chapter we will study various types of error detection and correction techniques.
The transmission of the data over the channel depends upon two parameters. They are
transmitted power and channel bandwidth. The power spectral density of channel
noise and these two parameters determine signal to noise power ratio.
The signal to noise power ratio determine the probability of error of the modulation
scheme.
For the given signal to noise ratio, the error probability can be reduced further by
using coding techniques. The coding techniques also reduce signal to noise power
ratio for fixed probability of error.
2. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Coding techniques play a crucial role in information transmission and storage systems,
enhancing reliability and efficiency.
One prominent approach is convolutional coding, a method widely used in digital
communication systems to add redundancy to data for error detection and correction.
Error Control Coding
Error control coding is a crucial aspect of digital communication systems, aiming to
detect and correct errors introduced during data transmission.
Redundancy bits are added to the original data to create a codeword, providing the
receiver with the means to identify and correct errors.
This process involves encoding at the transmitter and decoding at the receiver.
Channel Encoding
Channel encoding involves the addition of redundant information to the original data
before transmission, allowing for the detection and correction of errors at the receiver.
3. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Convolutional codes are one type of channel encoding technique. In a convolutional
encoder, input data is processed continuously, and the output is a coded sequence with
controlled redundancy.
Channel Decoding
Channel decoding is the process of reconstructing the original data at the receiver by
utilizing the redundant information added during encoding.
For convolutional codes, the Viterbi algorithm is a widely used decoding technique.
It involves traversing the trellis diagram to find the most likely path that corresponds to
the transmitted sequence.
Advantages of Coding Technique
1. Improved Transmission Efficiency:
Optimized Data Representation: Coding enhances data representation for
efficient use of available bandwidth.
Fast Encoding and Decoding: Efficient algorithms contribute to quicker
transmission rates, enabling more data transfer within a given timeframe.
2. Reduced Probability of Error and Error Correction:
Redundancy for Error Detection: Coding introduces redundancy for effective
error detection.
4. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Automatic Error Correction: Error correction codes automatically fix errors
during transmission, ensuring data integrity and reducing the probability of
errors.
3. Optimized Transmitted Power and Channel Bandwidth:
Minimized Transmission Power: Coding minimizes the required power for
transmission while maintaining reliability.
Bandwidth Efficiency: Carefully designed codes make effective use of
frequency spectrum, allowing for increased data transmission within allocated
bandwidth.
4. Signal-to-Noise Power Ratio Improvement:
Noise Combat: Coding techniques are designed to combat channel noise,
enhancing the signal-to-noise power ratio.
Distinguishing Signal from Noise: Error correction codes help distinguish the
actual signal from noise, improving overall data transmission reliability.
5. Reduction in Signal-to-Noise Power for Fixed Probability of Error:
Lower Signal-to-Noise Ratio: Coding allows achieving a lower signal-to-noise
power ratio for a fixed probability of error.
Robust Code Design: Careful code design enhances signal robustness,
enabling reliable communication even in the presence of noise.
Convolutional Encoding
Convolutional encoding is a powerful error-correcting technique employed in digital
communication systems to enhance the reliability of data transmission.
Unlike block codes, which operate on fixed-sized blocks of data, convolutional codes
process data in a continuous manner.
This approach is particularly advantageous in scenarios where the data stream is
continuous, such as in wireless communication, satellite communication, and digital
broadcasting.
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Convolutional Encoder Representation
The representation of a convolutional encoder through different methods:
i. Convolutional Encoder (Generator) Representation
ii. State Diagram
iii. Tree Diagram
iv. Trellis Diagram
i) Convolutional Encoder (Generator) Representation
A convolutional coding is done by combining the fixed number of input bits. The input
bits are stored in the fixed length shift register and they are combined with the help of
mod-2 adders.
This operation is equivalent to binary convolution and hence it is called convolutional
coding. This concept is illustrated with the help of simple example given below.
Operation
Whenever the message bit is shifted to position 'm', the new values of x1 and x2 are
generated depending upon in, ml and m2. ml and m2 store the previous two message
bits. The current bit is present in m. Thus we can write,
1 0 1 2
x m m m
and 2
2 0
x m m
The output switch first samples x1 and then x2. The shift register then shifts contents
of m 1 to m2 and contents of in to mi. Next input bit is then taken and stored in in.
Again x1 and x2 are generated according to this new combination m0, m1 and m2.
6. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
The output switch then samples x1 then x2. Thus the output bit stream for successive
input bits will be, 1 2 1 2 1 2 1 2.................
X=x x x x x x x x and so on ...
Here note that for every input message bit two encoded output bits x1 and x2 are
transmitted. In other words, for a single message bit, the encoded codeword is two bits.
Example:
Parameters of Convolutional Codes
Convolutional codes are characterized by several parameters that define their properties and
behavior. Let's discuss the key parameters associated with convolutional codes.
1) (n, k, K):
n: The number of output bits per input bit. It represents the rate of the convolutional
code. If n = 1, it's a rate-1 code. If n > 1, it's a rate-n code.
k: The number of input bits that affect the generation of one output bit
K: Constraint length, which is the number of bits in the shift register (excluding the
current input bit). It's the span over which the encoder has memory.
7. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Example: A convolutional code with (n=2, k=1, K=3) means it is a rate-1/2 code with
a constraint length of 2.
2) Code Rate (r):
The code rate, denoted as k
r =
n
, represents the ratio of the number of
information bits (k) to the total number of bits in the encoded sequence (n).
It provides information about the efficiency of the code.
Example: If a convolutional code has k=1 and n=2, then the code rate is
1
r =
2
3) Constraint Length (L):
The constraint length (L) of a convolutional code is the total number of shift register
stages involved in the encoding process.
It is directly related to k and K, where
L=K× n
( -1)+k
Example: For a convolutional code with k=1 and K=3, the constraint length would be
L=3× (2−1) +1=4.
4) Dimension of the Code (m):
The dimension of a convolutional code, denoted as m, represents the number of states
in the Sate/trellis diagram.
The dimension is related to the number of shift register states and is given by
K
m = 2 , where K is the constraint length.
Example: If a convolutional code has a constraint length of K=3, the dimension would
be 3
m = 2 = 8 .
8. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Types of Convolutional Encoding
The types of convolutional encoding methods can be categorized into analytical methods and
graphical methods.
a) Analytical Method:
1. Time Domain Approach:
a. Convolutional Method:
This approach involves defining convolutional codes directly in the time domain. It focuses
on the shift register operations and feedback connections that generate the encoded sequence.
Types of Convolutional Encoding
a)Analytical Method
1. Time Domain
Approach
a.Convoutional
Method
b.Matrix
Generator
Method
2. Transform
Domain
Approach
b)Graphical Method
a)State Diagram
b)Code Tree
Diagram
c)Trellis
Diagram
9. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Problems:
10. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
11. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
b. Matrix Generator Method:
In this method, matrices are used to represent the connections and operations of the
convolutional encoder. The generator matrix is a key component, and it allows for a concise
representation of the encoding process.
12. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
13. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
2. Transform Domain Approach:
This approach involves representing convolutional codes in a transformed domain, such as the
frequency domain.
14. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
15. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
16. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
b) Graphical Method:
1. State Diagram:
A state diagram is a graphical representation of a convolutional code. It illustrates the states of
the shift registers and the transitions between them based on the input symbols. Each state
represents a unique configuration of the shift registers.
17. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
2. Code Tree Diagram:
The code tree diagram is another graphical representation that shows the paths through the
encoder for all possible input sequences. It provides a visual way to understand how the
encoding process evolves based on different inputs.
18. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
3. Trellis Diagram:
The trellis diagram is a compact representation that combines elements of the state diagram
and the code tree. It visualizes the transitions between states for each input bit, allowing for an
efficient representation of the encoding process. The trellis diagram is particularly useful for
understanding and implementing the Viterbi algorithm for decoding.
19. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Formulation of the Convolutional Decoding Problem:
In convolutional coding, information bits are processed using convolutional encoders to
produce a coded sequence.
The convolutional decoding problem involves recovering the original information
bits from the received, possibly noisy, coded sequence.
This problem is typically solved using algorithms such as the Viterbi algorithm, which
searches for the most likely path through the trellis diagram representing the
convolutional code.
Properties of Convolutional Codes
1.Distance Property of Convolutional Codes
The distance properties of a convolutional code determine its ability to correct errors.
The minimum distance dmin of a code is defined as the smallest number of bit changes
required to convert one valid codeword into another.
Mathematically, it is expressed as min , (
, , )
j
i
c c ci cj
d min C HammingDistance ci cj
,whereC is the set of all valid codewords in the convolutional code.
For example, consider a convolutional code with two codewords C1=1101 and C2
=1010.
The Hamming distance between these codewords is
dmin=HammingDistance(1101,1010)=3, indicating that the minimum distance of the
code is 3.
2. Systematic Convolutional Codes
Systematic convolutional codes have a systematic encoder, which means that the
original data bits appear explicitly in the codeword.
The systematic form of a convolutional encoder is given by
)
c D
( ) ( )
= u ×g(
D D
where:
c(D) is the codeword polynomial,
20. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
u(D) is the information polynomial,
g(D) is the generator polynomial.
For example, let u(D)=1011 and g(D)=1+D+D2. The systematic convolutional
codeword is obtained by polynomial multiplication
2 2
2 3 4 5 6
( ) ( ) ( ) (
c D = 1+ D+ D × 1+ D+ D × 1 )
+ D
=1+D+D +D +D +D +D
So, the systematic convolutional codeword is 1011110010, where the original data
bits 10111011 are explicitly present.
3.Nonsystematic Convolutional Codes
Nonsystematic convolutional codes do not have a systematic structure, and the encoded
bits may not be the same as the original data bits.
The encoder is a general polynomial multiplication )
c D
( ) ( )
= u ×g(
D D
where u(D) is the information polynomial and g(D) is the generator polynomial.
For example, let u(D)=1011 and g(D)=1+D+D2. The nonsystematic convolutional
codeword is obtained by polynomial multiplication
2 2
2 3 4 5 6
( ) ( ) ( ) (
c D = 1+ D+ D × 1+ D+ D × 1 )
+ D
=1+D+D +D +D +D +D
So, the nonsystematic convolutional codeword is also 11011101101110, but in this
case, the original data bits are not explicitly present in the codeword.
4. Performance Bounds for Convolutional Codes
Coding Gain(G): Coding gain is a measure of the improvement in performance achieved by
using error-correcting codes. It is defined as the difference in signal-to-noise ratio (SNR)
between the uncoded system and the coded system required to achieve a certain error rate.
10
coded
1
)
G = 10log
BER
( where BER is the bit error rate.
Example:
Let's assume the following:
Uncoded System BER (BERuncoded): 10−3
(1 in 1000 bits is in error).
Coded System BER (BEBERcoded): 10−5
(1 in 100,000 bits is in error).
21. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
10 -5
5
10
1
G
0
(
1 )
= 0log
1
G =10log 10
G =10×5
G =50
( )
The coding gain, in this case, is 50 dB. This means that the coded system provides a 50 dB
improvement in signal-to-noise ratio (SNR) compared to the uncoded system for the same bit
error rate. In practical terms, the coded system achieves a significantly better performance,
allowing for more reliable communication in the presence of noise or interference.
A higher coding gain indicates a more robust and reliable communication system.
Convolutional codes, and error-correcting codes in general, are designed to provide substantial
coding gain, enhancing the system's ability to recover the transmitted information accurately.
Convolutional Decoding Algorithms
1. Sequential Decoding (Viterbi Algorithm):
Sequential decoding is commonly used in convolutional codes, and the Viterbi
algorithm is a popular method for implementing it.
Convolutional codes use shift registers to encode information, and the Viterbi
algorithm is employed to find the most likely sequence of transmitted bits
Viterbi decoding is a maximum likelihood decoding algorithm used for decoding
convolutional codes.
Choose the symbol or codeword with the highest likelihood as the estimated transmitted
message.
)
arg max (
x
x P x y
∣
where x^ is the estimated transmitted message, y is the received signal, and x
represents possible transmitted messages.
22. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Maximum Likelihood Decoding is widely used in various communication systems,
including those using error-correcting codes. It can be applied to different modulation
schemes, channel models, and coding techniques.
The Viterbi decoder traverses the trellis, calculating metrics for each path and selecting
the most likely path.
Example
Consider a rate-1/2, constraint length 3, convolutional code with the generator polynomials
g1 (D)=1+D2
and g2(D)=D+D2
. The trellis diagram for this code will have 2^2 = 4 states
since it's a rate-1/2 code.
Now, let's go through a Viterbi decoding example with a received sequence. Consider the
received sequence =110101010.
Path Metric Calculation:
For each state, calculate the path metrics for each incoming branch based on Hamming
distance:
State 00 to State 00: Path Metric = Hamming distance(00, 00) = 0
State 00 to State 01: Path Metric = Hamming distance(00, 01) = 1
State 01 to State 01: Path Metric = Hamming distance(01, 01) = 0
State 01 to State 10: Path Metric = Hamming distance(01, 10) = 2
State 10 to State 00: Path Metric = Hamming distance(10, 00) = 2
State 10 to State 01: Path Metric = Hamming distance(10, 01) = 1
State 11 to State 10: Path Metric = Hamming distance(11, 10) = 1
State 11 to State 11: Path Metric = Hamming distance(11, 11) = 0
23. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Survivor Path and Updated Metric: For each state, choose the incoming branch with
the minimum path metric and update the metric accordingly. Keep track of the survivor
path.
State 00: Choose State 00 to State 00 (Path Metric = 0)
State 01: Choose State 00 to State 01 (Path Metric = 1)
State 10: Choose State 00 to State 01 (Path Metric = 1)
State 11: Choose State 11 to State 11 (Path Metric = 0)
Repeat for the Next Set of Bits: Repeat the process for the next set of received bits until
the entire sequence is processed.
24. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
2.Feedback Decoding:
Feedback decoding involves using previously decoded bits to improve the decoding process.
This feedback information can come from known bits or estimated bits in earlier stages of
decoding.
25. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
3. Turbo codes
Turbo codes are a type of error-correcting code that uses multiple parallel convolutional
encoders and an iterative decoding process.
Turbo Encoder:
Turbo encoding relies on the use of two or more parallel convolutional encoders and an
interleaver to introduce redundancy and improve error correction capabilities.
Input Data Stream: The turbo encoder starts with the input data stream, which is the sequence of bits
that need to be transmitted.
Binary Data Stream (Input): 110101
Turbo Interleaver: A turbo interleaver is used to rearrange the input data bits in a systematic way. The
purpose of interleaving is to spread errors that may occur during transmission across different parts of
the encoded sequence. This helps the error correction decoder to better handle burst errors.
Assume a simple block interleaver where we rearrange the bits: 101101
Convolutional Encoder 1 - Parity Bits: The first convolutional encoder takes the interleaved data and
generates parity bits based on the convolutional encoding process. Convolutional encoding involves
using shift registers and exclusive OR (XOR) operations to produce additional bits (parity bits) that are
appended to the original data.
Assuming a simple convolutional code, let's say Conv Encoder 1 generates two parity bits:
11010110
Convolutional Encoder 2 - Parity Bits: Simultaneously, the second convolutional encoder takes the
same interleaved data and produces a different set of parity bits using a different set of shift registers
and XOR operations. The two sets of parity bits from Conv Encoder 1 and Conv Encoder 2 are then
combined with the interleaved data.
26. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Conv Encoder 2 produces a different set of parity bits:10101001
Combine the bits from Conv Encoder 1 and Conv Encoder 2 with the interleaved data:
1011011101010110100101
Puncturing and Mapping: Puncturing is a process of selectively discarding some of the parity bits to
reduce the overall redundancy and increase the data rate. The puncturing pattern is determined by a
puncture map. After puncturing, the remaining bits are mapped to a specific modulation scheme. This
step prepares the data for transmission.
Let's use a puncture map to remove some bits (represented by 'x'):
1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1
Encoder Output: The final output of the turbo encoder is the combination of the interleaved data,
punctured and mapped parity bits, and any remaining uncoded bits. This output is then transmitted over
the communication channel.
Turbo Decoder:
A turbo decoder is the counterpart to a turbo encoder and is designed to decode information
received over a noisy communication channel. It utilizes iterative decoding techniques and
multiple decoding stages to improve error correction performance.
Noisy Information and Parity Bits: The received signal contains both the original
information bits and additional parity bits. The information bits may be corrupted due to noise
during transmission.
27. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
Decoder 1 (Decoding Stage 1): The first decoding stage, often referred to as the soft-input
soft-output (SISO) decoder, processes the received information along with the parity bits. This
decoder produces a "soft" estimate of the likelihood (probability) of each bit being a 0 or a 1.
The output of this stage is used to inform the second decoding stage.
Deinterleaver: The output from the first decoder, which is the soft estimate of the information
bits, is deinterleaved to reorder the bits to their original sequence. This is the reverse process
of the interleaving applied by the turbo encoder.
Turbo Interleaver: The deinterleaved soft information is then interleaved again using the
turbo interleaver. This process prepares the data for the second decoding stage.
Decoder 2 (Decoding Stage 2): The second decoding stage, similar to the first stage, processes
the interleaved soft information along with the parity bits. This decoder takes into account both
the current soft information and the feedback from the first decoding stage. The output is
another set of soft estimates.
Deinterleaver (Reverse): The output from the second decoder is deinterleaved, again
reversing the interleaving process applied by the turbo encoder.
Hard Limiter: The deinterleaved soft estimates are then subjected to a "hard limiter"
operation. This involves making decisions to convert the soft estimates into hard decisions,
typically rounding to the nearest binary value (0 or 1).
Decoded Bits: The final output of the turbo decoder is the sequence of decoded bits obtained
after the hard limiter operation. These decoded bits represent the best estimate of the original
information bits.
28. ELH – 3.1: ADVANCED DIGITAL COMMUNICATION UNIT – II
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Notes by Mr. Chandrakantha T S, Dept.t of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri, Shankaraghatta,2023-24
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