Serially Concatenated Codes and Iterative Algorithms

Abstract

Abstract A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer code word bits, and an inner encoder whose input words are the permuted outer code words. Decoding is performed by an iterative technique based on two soft‐input soft‐output algorithms tailored to the trellis of the outer and inner encoders. The iterative algorithm can be easily extended to other forms of concatenation, where one or both encoders are replaced with system modules with some form of memory performing different functions, like a modulator, a channel with intersymbol interference, a multiuser combiner. In this paper, we give upper bounds to the average maximum‐likelihood error probability of serially concatenated block and convolutional coding schemes. Then, we present design guidelines for the outer and inner encoders that maximize the interleaver gain and the asymptotic slope of the error probability curves, describe the iterative decoding algorithm, and, finally, propose extensions to different schemes.