March 2011
Intermediate
680 pages
25h 12m
English
Chapter 5
Turbo BCH Coding
5.1 Introduction
Turbo coding [12] is a novel form of channel coding capable of achieving a performance near the Shannon limit [1]. As discussed in Chapter 4 typically so-called Recursive Systematic Convolutional (RSC) codes are used as their component codes. However, block codes can also be employed as their component codes and they have been shown, for example, by Hagenauer et al. [61,63] to perform impressively even at near-unity coding rates. Block codes are typically more appropriate for near-unity coding rates, since lower-rate block-based turbo codes exhibit a high decoding complexity. Hence usually convolutional constituent code-based turbo codes are used for coding rates lower than 2/3 [61]. In this chapter, we will concentrate entirely on the standard turbo code structure using binary BCH codes as the component codes.
Block-coding-based turbo codes can be decoded either using algebraic decoding principles [151,167,168] or by employing trellis-based decoding [61,63], which was the topic of Chapter 5. In this chapter we assume that the reader is familiar with the basic concepts discussed in Chapters 2–4 and hence only trellis-based turbo decoding will be discussed in this chapter.
In Chapter 4, we have provided a rudimentary introduction to the derivation of the log-likelihood ratio, soft channel outputs and the Maximum A Posteriori (MAP) algorithm [11] as well as the Max-Log-MAP and Log-MAP algorithms [50–52]. Here, we extend the derivation ...
