Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding

TLDR

A serially concatenated code with interleaver cascades an outer encoder, an interleaver, and an inner encoder, and this construction can be extended to h cascaded encoders separated by h − 1 interleavers. The study aims to derive design guidelines for outer and inner encoders that maximize interleaver gain and the asymptotic error‑slope, and to propose a low‑complexity iterative decoding algorithm. The authors analyze serially concatenated block and convolutional codes, derive upper bounds on average maximum‑likelihood bit‑error probability, and design encoder guidelines that maximize interleaver gain and error‑slope, leading to the proposed iterative decoding algorithm. The study provides upper bounds on average maximum‑likelihood bit‑error probability for serially concatenated block and convolutional codes and demonstrates, via extensive comparisons with turbo codes, that the proposed scheme achieves superior performance.

Abstract

A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codewords bits, and an inner encoder whose input words are the permuted outer codewords. The construction can be generalized to h cascaded encoders separated by h-1 interleavers. We obtain upper bounds to the average maximum-likelihood bit error probability of serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer and inner encoders that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a new, low-complexity iterative decoding algorithm. Throughout the paper, extensive comparisons with parallel concatenated convolutional codes known as "turbo codes" are performed, showing that the new scheme can offer superior performance.