Iterative Decoding of Turbo Product Codes (TPCs) Using the Chase-Pyndiah Turbo Decoder

The ground breaking error correction codes that could achieve low bit error rates (near Shannon’s limit) were Turbo Codes (TCs) introduced by Berrou, Glavieux in 1993. The encoders for these outstanding codes were created by parallel concatenation of two recursive systematic convolutional codes separated by an interleaver. For decoding TCs Log-MAP algorithm could be used due to its gain in computational speed and improvement in precision. The only problem with turbo coding and decoding is that, the choice of interleaver for the encoder may cause an error floor due to their inherent poor distance properties. Turbo product codes (TPCs) are powerful linear block codes formed by combining more than one simple linear block codes. They classify under serially concatenated codes however unlike TCs they do not rely on an interleaver and hence they have no error floor problem. TPCs which date as early as 1954, are multi-dimensional codes that are constructed by two or more linear block codes also known as component codes. The product code is obtained by placing (k1k2) information bits in an array with k1 rows and k2 columns. Important parameters of a product code are the length of the codeword (n), the length of the information (k) and the minimum distance (d). Turbo product decoding is possible using either hard or soft decoding. In hard decision decoding, the input must be a binary sequence, whereas in soft decision decoding the values are immediately processed by the decoder to gauge a code sequence. A SISO decoder can be utilized to generate the soft decision decoder outputs. Some of the soft decoding algorithms include: the maximum a posteriori probability (MAP) algorithm, Chase-Pyndiah iterative decoder, symbol based MAP algorithm, the Soft Output Viterbi Algorithm, sliding‐window based MAP decoder, and the forward recursion based MAP decoder. The work presented in this thesis presents the bit-error-rate (BER) versus signal-to-noise-ratio (SNRdB) for soft decision (SD) decoding. The modulation type is BPSK and encoded symbols are transmitted over AWGN and Rayleigh fading channels. For SD the Chase-Pyndiah decoding algorithm was simulated to lower the bit error rate from iteration to iteration. We assumed an information array of (4×4) and the coded array had dimensions (7×7) for the first code, and an information array of (11×11) and the coded array had dimensions (15×15) for the second one. BER results were obtained as ensemble average of many runs (repetitions). Simulation results indicate that the SD with Chase-Pyndiah algorithm provides nearly 1.1dB lower BER in comparison to the uncoded BPSK over AWGN channel for (7,4)2 and 2.6dB when using the (15,11)2 at target BER of 10-3. For flat fading Rayleigh channel, the simulation achieved at around 18dB SNR value for the (7,4)2 TPC and at 15dB for the (15,11)2 at target BER of 10-3, whereas the uncoded BPSK could achieve the same target BER beyond 20dB. Keywords: Turbo product codes, Iterative decoding, Chase-Pyndiah algorithm.