Hybrid Concatenated Codes and Iterative Decoding

A hybrid concatenated code with two interleavers is the parallel concatenation of an encoder, which accepts the permuted version of the information sequence as its input, with a serially concatenated code, which accepts the unpermuted information sequence. The serially concatenated code consists of an outer encoder, an interleaver, and an inner encoder. An upper bound to the average maximum-likelihood bit-error probability of the hybrid concatenated convolutional coding schemes is obtained. Design rules for the parallel, outer, and inner codes that maximize the interleaver’s gain and the asymptotic slope of the error-probability curves are presented. Finally, a low-complexity iterative decoding algorithm that yields performance close to maximum-likelihood decoding is proposed. A special case of hybrid concatenated code where the outer code is a repetition code is analyzed, and another special case called self-concatenated code is introduced. Comparisons with parallel concatenated convolutional codes, known as “turbo codes,” and with recent serially concatenated convolutional codes are discussed, showing that the new scheme offers better performance at very low bit-error rates when low-complexity codes are used. An example of the proposed scheme for deep-space communications is presented.