Parity concatenated turbo codes: study of their structure and performance bounds

Abstract

Turbo coding schemes involving block codes have been studied, with a significantly augmented overall performance. Usually, a turbo code uses different sets of parity information for the same set of information bits. We investigate the use of a turbo scheme using two different sets of information bits, each encoded by separate constituent block coders. Their encoded bits are then linked by a simple modulo-2 sum, originating an extra number of parity bits. The overall code can be seen as a turbo code, yielding enhanced performance at the expense of a small increase in complexity, since few decoding iterations are required to obtain good results. Using these turbo schemes, it is possible to obtain codes with low coding rate, which makes them especially suitable for spread spectrum systems where they can be used to achieve simultaneously error correction and bandwidth expansion. Both TCH (Tomlinson, Cercas, Hughes) codes and biorthogonal codes were considered for the constituent encoders of the turbo schemes, due to their properties which allow the decoder to have low complexity and, at the same time, to achieve good performance. Bound expressions were developed for quantifying the performance of the turbo schemes and they were compared with the original constituent codes. Simulations were also performed in order to determine effectively the performance of the sub-optimal iterative decoding algorithm versus the maximum likelihood (ML) decoding algorithm.