March 2011
Intermediate
680 pages
25h 12m
English
Chapter 3
Soft Decoding and Performance of BCH Codes
3.1 Introduction
In Chapter 3 of [144] the basic concepts of Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) codes as well as their hard-decision-based algebraic decoding is detailed. However, no deep knowledge concerning the algebraic decoding of these RS and BCH codes is required for following the discussions of this chapter but, again, the basic code construction principles will not be repeated here from the previous chapter. It is also an advantage if one is familiar with the underlying concepts of convolutional coding and the rudiments of Viterbi decoding, since in this chapter the Viterbi algorithm (VA) will be invoked again, although this time for the decoding of binary BCH codes.
As mentioned in the previous chapter, BCH codes were discovered by Hocquenghem [14] and independently by Bose and Chaudhuri [15] in 1959 and 1960, respectively. These codes constitute a prominent class of cyclic block codes that have multiple-error detection and correction capabilities.
In this chapter, we will commence with an introduction to BCH codes in Section 3.2. Their state and trellis diagrams are constructed in Section 3.2.2. The trellis decoding of BCH codes using the VA [8] is detailed in Section 3.3.2. Simulation results of various BCH codes employing the Berlekamp-Massey Algorithm (BMA) [31–34] and the VA are given in Section 3.3.5. Finally, in Section 3.4 we investigate the low-complexity Chase algorithm [28] in the context ...
