Performance Evaluation of Concatenated Channel Codes and Space Time Codes under Fading Channels

Abstract

The use of multiple antennas at the transmitter and/or the receiver provides high data rate and diversity in many different forms. This can be useful to meet the ever growing demand of high data rate wireless services, provided we concatenate the multiple antenna systems with channels codes to efficiently exploit the advantages of the these system. Low density parity check (LDPC) codes are linear block codes constructed by sparse parity check matrices. These codes are powerful in terms of error performance and, especially, have low decoding complexity. LDPC codes when employed with multiple antenna system yields astonishing performance close to the Shannon theoretical limits. In the first part of the thesis, LDPC coded systems that employ single transmit and multiple receive antennas, i.e., single-input multiple-output (SIMO) systems are studied. In particular Low Density parity check codes are combined with optimum diversity combining (LDPC-OC) scheme that works efficiently in the presence of interferer for both additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. The analytical bounds on the bit error rate (BER) performance are derived for the under loaded case (when the number of interferers are less than or equal to number of antenna array elements) and over loaded case (when the number of interferers are greater than antenna array elements. In particular, the analytical bounds are derived for the special case of single interferer (under loaded case) and for large number of interferers (overloaded case). For the proposed systems, the results obtained with analytical bounds are verified with the help of simulation results. It is demonstrated that these bounds can be efficiently used to evaluate the error performance.

The second part of the thesis studies LDPC coded systems that employ multiple transmit and multiple receive antennas, i.e., multiple-input multiple-output (MIMO) systems. Particularly the proposed system is based on the concatenation of LDPC codes with space time block codes (LDPC-STBC). Two scenarios for the proposed LDPC-STBC system have been considered (i) Concatenated LDPC-STBC system without antenna selection (ii) Concatenated LDPC-STBC system with antenna selection. The concatenation is done such that all code words in one subset/sub-code are associated with an identical pair wise error probability. For both scenarios, first we obtained the results using Monte Carlo simulation for various modulation schemes in various fading environment. We also derived the analytical tight bound for both scenarios using Chernoff bounds. It is shown that on the quasi-static fading channel full diversity can be achieved and an increase in coding gain results from the concatenation. For the concatenated LDPC-STBC system with antenna selection, it is analytically shown that the diversity gain does not change. We can exploit the full diversity advantage promised by the MIMO system that uses all available antenna elements, provided that the space-time code employed has full spatial diversity. It is also shown that the coding gain with antenna selection deteriorates significantly compared to the full-complexity one. When the simulation results are compared with the analytical results, an SNR gap of less than 2 dB between the waterfall positions of the tight bounds and the simulation results is evident.