Digital Communications 1

5Concatenated Codes and Iterative Decoding

5.1. Introduction

Since the works of Shannon in 1948 [SHA 48], researchers have proposed different error correcting codes with a reasonable complexity and if possible a high minimum distance. The idea of combining a few simple codes to obtain a stronger code was proposed in 1954 by Elias [ELI 54]. In his thesis in 1963, Gallager introduced the low density parity check codes (LDPCs) which were then forgotten for a few decades. In fact, this idea enables us to obtain codes with characteristics close to random coding but with a much simpler coding and decoding structure. In 1966, Forney [FOR 66] introduced the serial concatenation of a convolutional code and a linear block code. This structure has been a standard for decades in communication systems. However, all these structures were based on decoding algorithms performing only hard decisions.

Battail [BAT 87, BAT 89] showed the importance of soft input soft output decoding and the use of random coding as a criterion to build good codes. In 1993, Berrou, Glavieux and Thitimajshima [BER 93] proposed a new class of error correcting codes called turbo codes or parallel concatenated convolutional codes. While concatenation of codes, soft output decoding and iterative decoding had been previously proposed, this discovery permitted significant progress in the research of codes with performance close to the Shannon capacity (a few tenths of dB for frames of several thousand bits). This work on ...