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T. Yasodha / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282
278 | P a g e
Decoding For 8x8 MIMO System Using Convolution Coding
Implemented In VLSI
T. Yasodha
Associate Professor, Department of ECE Christian College of Engineering and Technology Oddanchatram,
Tamil Nadu, India-624619
Abstract
The joint detection and decoding for
spatial multiplexing multiple- Input multiple-
output (MIMO) system which utilize
convolution Code is been proposed . The bit
error rate (BER) performance of the proposed
approach is significantly better than that of
systems which utilize separate detection and
decoding blocks. Formal algorithms with two
possible system setups are presented and their
performance. In particular, for a reference 8x8,
64-QAM System using a rate 1/2 convolution
code with generator polynomial [247, 371] and a
constraint length of 8, improves the Signal to
noise ratio (SNR) of 2.5 db and 3 db are
achieved over Conventional soft decoding at a
bit error ratio (BER) of 10 . The proof of
concept VLSI architecture for one algorithm is
provided and a novel way to reduce memory
usage is demonstrated. Results indicate that
better Performance over conventional systems is
achievable with comparable hardware
complexity. The proposed Design was
synthesized and layout with 65-nm at 334-
MHZ clock frequency. An average throughput
of 267.2 mbps at a SNR of 13 db with area
equivalent to 632 k gates was achieved.
1. INTRODUCTION
In Transmitter and receiver, the data rate
is increased by many techniques. One among them
is MIMO that uses multiple antennas to increase
the data rate. MIMO has the benefit of random
fading and BER Performance of MIMO-CDMA
Systems in Multi user Environment reduces the
multipath delay spread. MIMO systems must work
reliably in the noisy environment to be successful
[1]. CDMA systems are designed to operate in an
interference free environment and for this reason it
is used in modern cellular systems. The
combination of MIMO and CDMA can further
improve the system transmission rate over the
traditional CDMA system. Multiuser MIMO
CDMA systems are considered where each user has
multiple transmit antennas, different transmit
antennas of the same user use the same spreading
code. The developing wireless services require
higher data rates for future cellular wireless
communication systems [3]. However, new radio
frequency bands are very scarce if available at all.
CDMA is a promising technique for beyond 3G
wireless systems [2]. For the efficient bandwidth
utilization in both the network and physical layers,
some new solutions are necessary. The MIMO
systems provide efficient coding, modulation
methods, transmission adaptation schemes, and
antenna systems. Multiple-input multiple-output
(MIMO) communications based on multiple
transmit and receive antennae is a very promising
technique to increase bandwidth efficiency, and is
seen as a potential key solution for fading channels
with rich enough scattering. The frequency
selectivity challenge means that the multipath delay
spread of the channel is very large due to the large
bandwidth, causing very severe inter symbol
interference (ISI). Multiple-input and multiple-
output (MIMO) is a technique to increase data rate
significantly with multiple antennas at both the
transmitter and receiver [6]. In MIMO systems,
there are many spatial coding schemes including
space time codes with spatial code rate less than or
equal to 1 and spatial multiplexing with spatial
code rate > 1 [5]. Combining both CDMA and
MIMO will improve the system transmission
efficiency when compared to the traditional CDMA
system. Different modulation schemes are been
followed in MIMO-CDMA architecture. The
existing MIMO system using QPSK modulation is
studied in [4]. The proposed Convolutional coded
MIMO-CDMA system is compared with the
existing modulation scheme in this paper.
2. RELATED WORK
D’Amours [2005] suggested the idea of
using parity bit to be selected for spreading code
technique, based on systematic linear block codes
[7]. D’Amours et al., [2007] investigated the T-
designs to design the different spreading
permutations. In their work, they designed the
spreading code permutations based on Space-Time
Block Codes (STBC).They also showed that the
STBC-based design can improve the error rate of
the receiver over the flat fading channel without
increasing the system complexity [8].
Z. Ding and M. Rice [2007] suggested the
HARQ techniques in the emerging wireless
systems that use bit-interleaved coded modulation
(BICM). The design of BICM-based wireless
systems involving HARQ is explained by a special
T. Yasodha / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282
279 | P a g e
case of IR-HARQ, where a different combination
of bits of a mother code is sent in each transmission
period. In optimal receiver implementations, IR-
HARQ out performs CC-HARQ because of its
coding gain. But in multiple-input multiple-output
(MIMO) systems, the performance of IR-HARQ
gets affected due to its sub optimal
implementations [9].
Jung-Fu and Cheng [2006] analyzed and
identified the performance of hybrid automatic
repeat request (HARQ) schemes over incremental
redundancy (IR) and Chase combining (CC). The
above cases are induced by fast time-variant fading
or long retransmission delays. The robust solution
for the above case is provided by the self-decodable
IR and the CC schemes. They evaluated and
offered solutions for the enhanced performance of
the conventional IR systems [10].
3. PROPOSED WORK
This design is targeted to process a system
using Algorithm I with 512 bits (i.e., 64 channel
realizations). The BER performance of such a
system was presented.
The channel entries are represented using
7 bits for the integral part and 7 bits for fractional
part and the path metrics are represented using 10
bits for the integral part and 5 bits for fractional
part. The proposed joint MIMO decoder was
designed and upgraded up to 8x8 for high data
transmission.
FIG 3.1 Block Diagram of 8x8 MIMO system
The above figure shows the proposed
MIMO-CDMA architecture. The 8x8 MIMO
systems have different blocks like QPSK
modulator, ideal channel, channel estimation block
and QPSK demodulation. QPSK modulator takes
the binary bits as input. Here the inputs bits are
taken as symbols. For example 00, 01, 10, 11 are 8
inputs symbols for QPSK. The symbols are
converted into complex values. The complex
output of the modulator is appended with the
training sequence at 2 transmitters. Here the
diversity technique is used to send the same data
with different training sequences. The channel
coefficients are multiplied with the modulated data.
Here 8 paths are considered for 8x8 channels. The
channel is an ideal channel i.e. the noise is not
considered. The reliability is increased by
employing the diversity technique i.e. transmitting
the same information across multiple channels. The
redundant data is transmitted so that the fading can
be reduced. If one of the channel is not used or if
the data is lost in space then the information/data
can still be recovered from redundant transmission
over the channels and hence the reliability of the
communication system is improved. The data
transmitted from transmitter tx1 across the
channels h11 and h12 and received by both the
receiver’s rx1 and rx2. Here the use of the available
channels is done to increase the capacity and
reliability. Then the received sequence is taken into
the channel estimation block to find the estimated
channel coefficients. The received data from LS
channel estimator block are the given to the
decision block in the QPSK demodulator block to
get back the sent binary sequence. The transmitted
sequence is then checked with the received
sequence at the QPSK modulator and the
Demodulator block respectively.
4. IMPLEMENTATION
8x8 MIMO system is designed using
VHDL and simulated in Modelsim. Each block
separately verified for its functionality. Each block
is synthesized and the integrated output is also
verified by implementing Xilinx FPGA.
T. Yasodha / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282
280 | P a g e
The top block of 8x8 MIMO system block
diagram from Xilinx is shown in Fig.3.1 All the
blocks in 8x8 MIMO system like QPSK
modulator/demodulator, ideal channel and the LS
channel estimation blocks are integrated and the
connections are shown in Fig.4.1, with inputs and
the outputs. The output of integrated 8x8 MIMO
system design is as shown in Fig.4.2 The fig.4.3
shows the 8x8 MIMO system output waveform.
FIG 4.1 MIMO System with QPSK Design
FIG 4.2 The 8X8 MIMO System output
The 8x8 MIMO system code is simulated
in Modelsim and synthesized using Xilinx before
giving to Design Compiler for timing analysis.
Design compiler is tools which synthesize the
design using the user given constraints, libraries
and the RTL code. The clock is to be specified as a
constraint for which approximately the design work
is determined using Xilinx. A clock of 50-60%
from Xilinx is created for timing verification.
Clock network delay or min latency of 25% of the
clock, uncertainty for setup is given as 10% of the
clock, for hold 5% of the VLSI Implementation of
Least Square Channel Estimation and QPSK
Modulation Technique for 8x8 MIMO System.
T. Yasodha / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282
281 | P a g e
Table 4.1 Synthesis and Timing Verification of 8x8 MIMO system
Fig.4.3 Output wave form of 8x8 MIMO using convolutional code
T. Yasodha / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282
282 | P a g e
5. CONCLUSION
The simple working of a MIMO system is
carried till backend of the VLSI flow. The designs
simulated in to arrive at the specifications. The
RTL code is successfully simulated in Modelsim .
The design is synthesized and implemented on
board. The synthesis and timing is verified and the
timing is met for both setup and hold in DC and
PT. DFT is also carried without timing violation.
The top design takes about 3999 number of slices
out of 4928 slices i.e. in Virtex2Pro the device
selected is 2vp7ff896 at speed grade of 06 with
operating frequency 7.27MHz and minimum period
of 137.548ns. Timing verified is all met with
positive slack with zero violations .In the design
the channel is considered to be ideal. In the future
work the noise is to be added and the estimation of
channel using different channel models is to be
carried. Different channel estimation is to be
simulated in and then taken to the complete VLSI
flow. The frequency of the design is to be
optimized. The complete backend flow has to be
completed till the tape-out of the design.
Scope of the future work is to improve the
design further for the noise to be included in the
channel and use any improved matrix inversion
technique for improving the design frequency of
operation. This can be done using VHDL
algorithm. Iterative algorithm is applied for the
design so as to reduce the effect of noise on data.
The iterative algorithms like Recursive LS, Least
Mean Square,, etc. Channel estimation and
compensation for different channel models for
delays is to be implemented. Fixed point
implementation of the design is to be carried out by
obtaining the floating point values from because
the fixed- point representation will be more
efficient. MIMO performance can be improved by
using by incorporating the performance of the
overall system can be improved.
REFERENCES
[1] Joseph, W. Reynders, W. Debruyne, J. and
Martens, L., “Influence of Channel
Models and MIMO on the Performance of
a System based on IEEE 802.16”,Wireless
Communications and Networking
Conference, ISBN 1-4244-0659-5,
pp.1826-1830,11-15th March, 2007.
[2] Simon S Haykin and Michael
Moher,“Modern Wireless Communication,
Second Edition,Prentice-Hall publication
2004, ISBN-13: 9780130224729.
[3] George Tsoulos, “MIMO System
Technology For Wireless
Communications”,Revised Edition,CRC
Publisher, 2006.
[4] Chia-Liang Lui, “Impacts of I/Q Imbalance
on QPSK –OFDM-QAM Detection”, IEEE
Transactions on Consumer Electronics, vol.
44, no. 3, pp. (984-989), August, 1998.
MIMO Systems, Theory and Applications.
[5] Yantao Qiao, Songyu Yu, Pengcheng Su
and Lijun Zhang, “Research on an Iterative
Algorithm of LS Channel Estimation in
MIMO OFDM Systems”, IEEE
Transactions on Broadcasting, vol. 51, no.
1, pp. (149-153), March 2005.
[6] S.Cui, A.J.Goldsmith and A.Bahai,
“Energy Efficiency in MIMO and
cooperative MIMO techniques in Sensor
Networks”, IEEE Journal on Selective
Areas in Communication,vol. 22, no. 6, pp.
(1089-1098), August 2004.
[7] C. D’Amours, “Parity Bit Selected
Spreading Sequences: A Block Coding
Approach To Spread Spectrum,” IEEE
Commun. Lett., vol. 9, pp. 16-18,Jan. 2005.
[8] C. D’Amours and J.-Y. Chouinard, “Parity
Bit Selected and Permutation Spreading for
CDMA/MIMO Systems,” in Proc. IEEE
Veh. Tech. Conf., pp. 1475-1479, Apr.
2007.
[9] Z. Ding and M. Rice, “Hybrid-ARQ Code
Combining for MIMO Using
Multidimensional Space-Time Trellis
Codes,” Proc. IEEE ISIT ’07, Glasgow,
Scotland, June 2007.
[10] Jung-Fu (Thomas) Cheng,” Coding
Performance of Hybrid ARQ Schemes”,
IEEE Transactions on Communications,
Vol. 54, No. 6, June 2006.

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  • 1. T. Yasodha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282 278 | P a g e Decoding For 8x8 MIMO System Using Convolution Coding Implemented In VLSI T. Yasodha Associate Professor, Department of ECE Christian College of Engineering and Technology Oddanchatram, Tamil Nadu, India-624619 Abstract The joint detection and decoding for spatial multiplexing multiple- Input multiple- output (MIMO) system which utilize convolution Code is been proposed . The bit error rate (BER) performance of the proposed approach is significantly better than that of systems which utilize separate detection and decoding blocks. Formal algorithms with two possible system setups are presented and their performance. In particular, for a reference 8x8, 64-QAM System using a rate 1/2 convolution code with generator polynomial [247, 371] and a constraint length of 8, improves the Signal to noise ratio (SNR) of 2.5 db and 3 db are achieved over Conventional soft decoding at a bit error ratio (BER) of 10 . The proof of concept VLSI architecture for one algorithm is provided and a novel way to reduce memory usage is demonstrated. Results indicate that better Performance over conventional systems is achievable with comparable hardware complexity. The proposed Design was synthesized and layout with 65-nm at 334- MHZ clock frequency. An average throughput of 267.2 mbps at a SNR of 13 db with area equivalent to 632 k gates was achieved. 1. INTRODUCTION In Transmitter and receiver, the data rate is increased by many techniques. One among them is MIMO that uses multiple antennas to increase the data rate. MIMO has the benefit of random fading and BER Performance of MIMO-CDMA Systems in Multi user Environment reduces the multipath delay spread. MIMO systems must work reliably in the noisy environment to be successful [1]. CDMA systems are designed to operate in an interference free environment and for this reason it is used in modern cellular systems. The combination of MIMO and CDMA can further improve the system transmission rate over the traditional CDMA system. Multiuser MIMO CDMA systems are considered where each user has multiple transmit antennas, different transmit antennas of the same user use the same spreading code. The developing wireless services require higher data rates for future cellular wireless communication systems [3]. However, new radio frequency bands are very scarce if available at all. CDMA is a promising technique for beyond 3G wireless systems [2]. For the efficient bandwidth utilization in both the network and physical layers, some new solutions are necessary. The MIMO systems provide efficient coding, modulation methods, transmission adaptation schemes, and antenna systems. Multiple-input multiple-output (MIMO) communications based on multiple transmit and receive antennae is a very promising technique to increase bandwidth efficiency, and is seen as a potential key solution for fading channels with rich enough scattering. The frequency selectivity challenge means that the multipath delay spread of the channel is very large due to the large bandwidth, causing very severe inter symbol interference (ISI). Multiple-input and multiple- output (MIMO) is a technique to increase data rate significantly with multiple antennas at both the transmitter and receiver [6]. In MIMO systems, there are many spatial coding schemes including space time codes with spatial code rate less than or equal to 1 and spatial multiplexing with spatial code rate > 1 [5]. Combining both CDMA and MIMO will improve the system transmission efficiency when compared to the traditional CDMA system. Different modulation schemes are been followed in MIMO-CDMA architecture. The existing MIMO system using QPSK modulation is studied in [4]. The proposed Convolutional coded MIMO-CDMA system is compared with the existing modulation scheme in this paper. 2. RELATED WORK D’Amours [2005] suggested the idea of using parity bit to be selected for spreading code technique, based on systematic linear block codes [7]. D’Amours et al., [2007] investigated the T- designs to design the different spreading permutations. In their work, they designed the spreading code permutations based on Space-Time Block Codes (STBC).They also showed that the STBC-based design can improve the error rate of the receiver over the flat fading channel without increasing the system complexity [8]. Z. Ding and M. Rice [2007] suggested the HARQ techniques in the emerging wireless systems that use bit-interleaved coded modulation (BICM). The design of BICM-based wireless systems involving HARQ is explained by a special
  • 2. T. Yasodha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282 279 | P a g e case of IR-HARQ, where a different combination of bits of a mother code is sent in each transmission period. In optimal receiver implementations, IR- HARQ out performs CC-HARQ because of its coding gain. But in multiple-input multiple-output (MIMO) systems, the performance of IR-HARQ gets affected due to its sub optimal implementations [9]. Jung-Fu and Cheng [2006] analyzed and identified the performance of hybrid automatic repeat request (HARQ) schemes over incremental redundancy (IR) and Chase combining (CC). The above cases are induced by fast time-variant fading or long retransmission delays. The robust solution for the above case is provided by the self-decodable IR and the CC schemes. They evaluated and offered solutions for the enhanced performance of the conventional IR systems [10]. 3. PROPOSED WORK This design is targeted to process a system using Algorithm I with 512 bits (i.e., 64 channel realizations). The BER performance of such a system was presented. The channel entries are represented using 7 bits for the integral part and 7 bits for fractional part and the path metrics are represented using 10 bits for the integral part and 5 bits for fractional part. The proposed joint MIMO decoder was designed and upgraded up to 8x8 for high data transmission. FIG 3.1 Block Diagram of 8x8 MIMO system The above figure shows the proposed MIMO-CDMA architecture. The 8x8 MIMO systems have different blocks like QPSK modulator, ideal channel, channel estimation block and QPSK demodulation. QPSK modulator takes the binary bits as input. Here the inputs bits are taken as symbols. For example 00, 01, 10, 11 are 8 inputs symbols for QPSK. The symbols are converted into complex values. The complex output of the modulator is appended with the training sequence at 2 transmitters. Here the diversity technique is used to send the same data with different training sequences. The channel coefficients are multiplied with the modulated data. Here 8 paths are considered for 8x8 channels. The channel is an ideal channel i.e. the noise is not considered. The reliability is increased by employing the diversity technique i.e. transmitting the same information across multiple channels. The redundant data is transmitted so that the fading can be reduced. If one of the channel is not used or if the data is lost in space then the information/data can still be recovered from redundant transmission over the channels and hence the reliability of the communication system is improved. The data transmitted from transmitter tx1 across the channels h11 and h12 and received by both the receiver’s rx1 and rx2. Here the use of the available channels is done to increase the capacity and reliability. Then the received sequence is taken into the channel estimation block to find the estimated channel coefficients. The received data from LS channel estimator block are the given to the decision block in the QPSK demodulator block to get back the sent binary sequence. The transmitted sequence is then checked with the received sequence at the QPSK modulator and the Demodulator block respectively. 4. IMPLEMENTATION 8x8 MIMO system is designed using VHDL and simulated in Modelsim. Each block separately verified for its functionality. Each block is synthesized and the integrated output is also verified by implementing Xilinx FPGA.
  • 3. T. Yasodha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282 280 | P a g e The top block of 8x8 MIMO system block diagram from Xilinx is shown in Fig.3.1 All the blocks in 8x8 MIMO system like QPSK modulator/demodulator, ideal channel and the LS channel estimation blocks are integrated and the connections are shown in Fig.4.1, with inputs and the outputs. The output of integrated 8x8 MIMO system design is as shown in Fig.4.2 The fig.4.3 shows the 8x8 MIMO system output waveform. FIG 4.1 MIMO System with QPSK Design FIG 4.2 The 8X8 MIMO System output The 8x8 MIMO system code is simulated in Modelsim and synthesized using Xilinx before giving to Design Compiler for timing analysis. Design compiler is tools which synthesize the design using the user given constraints, libraries and the RTL code. The clock is to be specified as a constraint for which approximately the design work is determined using Xilinx. A clock of 50-60% from Xilinx is created for timing verification. Clock network delay or min latency of 25% of the clock, uncertainty for setup is given as 10% of the clock, for hold 5% of the VLSI Implementation of Least Square Channel Estimation and QPSK Modulation Technique for 8x8 MIMO System.
  • 4. T. Yasodha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282 281 | P a g e Table 4.1 Synthesis and Timing Verification of 8x8 MIMO system Fig.4.3 Output wave form of 8x8 MIMO using convolutional code
  • 5. T. Yasodha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 4, Jul-Aug 2013, pp.278-282 282 | P a g e 5. CONCLUSION The simple working of a MIMO system is carried till backend of the VLSI flow. The designs simulated in to arrive at the specifications. The RTL code is successfully simulated in Modelsim . The design is synthesized and implemented on board. The synthesis and timing is verified and the timing is met for both setup and hold in DC and PT. DFT is also carried without timing violation. The top design takes about 3999 number of slices out of 4928 slices i.e. in Virtex2Pro the device selected is 2vp7ff896 at speed grade of 06 with operating frequency 7.27MHz and minimum period of 137.548ns. Timing verified is all met with positive slack with zero violations .In the design the channel is considered to be ideal. In the future work the noise is to be added and the estimation of channel using different channel models is to be carried. Different channel estimation is to be simulated in and then taken to the complete VLSI flow. The frequency of the design is to be optimized. The complete backend flow has to be completed till the tape-out of the design. Scope of the future work is to improve the design further for the noise to be included in the channel and use any improved matrix inversion technique for improving the design frequency of operation. This can be done using VHDL algorithm. Iterative algorithm is applied for the design so as to reduce the effect of noise on data. The iterative algorithms like Recursive LS, Least Mean Square,, etc. Channel estimation and compensation for different channel models for delays is to be implemented. Fixed point implementation of the design is to be carried out by obtaining the floating point values from because the fixed- point representation will be more efficient. MIMO performance can be improved by using by incorporating the performance of the overall system can be improved. REFERENCES [1] Joseph, W. Reynders, W. Debruyne, J. and Martens, L., “Influence of Channel Models and MIMO on the Performance of a System based on IEEE 802.16”,Wireless Communications and Networking Conference, ISBN 1-4244-0659-5, pp.1826-1830,11-15th March, 2007. [2] Simon S Haykin and Michael Moher,“Modern Wireless Communication, Second Edition,Prentice-Hall publication 2004, ISBN-13: 9780130224729. [3] George Tsoulos, “MIMO System Technology For Wireless Communications”,Revised Edition,CRC Publisher, 2006. [4] Chia-Liang Lui, “Impacts of I/Q Imbalance on QPSK –OFDM-QAM Detection”, IEEE Transactions on Consumer Electronics, vol. 44, no. 3, pp. (984-989), August, 1998. MIMO Systems, Theory and Applications. [5] Yantao Qiao, Songyu Yu, Pengcheng Su and Lijun Zhang, “Research on an Iterative Algorithm of LS Channel Estimation in MIMO OFDM Systems”, IEEE Transactions on Broadcasting, vol. 51, no. 1, pp. (149-153), March 2005. [6] S.Cui, A.J.Goldsmith and A.Bahai, “Energy Efficiency in MIMO and cooperative MIMO techniques in Sensor Networks”, IEEE Journal on Selective Areas in Communication,vol. 22, no. 6, pp. (1089-1098), August 2004. [7] C. D’Amours, “Parity Bit Selected Spreading Sequences: A Block Coding Approach To Spread Spectrum,” IEEE Commun. Lett., vol. 9, pp. 16-18,Jan. 2005. [8] C. D’Amours and J.-Y. Chouinard, “Parity Bit Selected and Permutation Spreading for CDMA/MIMO Systems,” in Proc. IEEE Veh. Tech. Conf., pp. 1475-1479, Apr. 2007. [9] Z. Ding and M. Rice, “Hybrid-ARQ Code Combining for MIMO Using Multidimensional Space-Time Trellis Codes,” Proc. IEEE ISIT ’07, Glasgow, Scotland, June 2007. [10] Jung-Fu (Thomas) Cheng,” Coding Performance of Hybrid ARQ Schemes”, IEEE Transactions on Communications, Vol. 54, No. 6, June 2006.