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52 3 Communication
codes, they were independently rediscovered by MacKay et al. [17]. Because of the
simple structure, they have been the focus of many theoretical analyses. They have
been proven to be capable of approaching the Shannon limit more closely than any
other class of codes.
Similar to Hamming codes, LDPC codes are linear block codes. They can be rep-
resented as (n,k) codes, where n is the code length and k is the information dimen-
sion. Here we consider binary LDPC codes only. For a LDPC code (n, k), the source
is a k ×1 vector and a codeword is a n ×1 vector. The generator matrix G is n×k and
the parity check matrix H is m×n, where m = n−k. The LDPC code can be specified
by the parity check matrix H. Before we discuss how to