Graph-Matched LDPC Codes for Partial-Response Channels

In this paper, we propose an LDPC coding scheme based on repeat-accumulate (RA) codes for partial-response (PR) channels. We modify the original RA encoder in such a way that there exists a one-to-one relationship between a sequence called the D-codeword (which is not the transmitted codeword but contains the information bits) and the noiseless received sequence at the output of the PR channel. A consequence of this is that the graph used for decoding the D-codeword, which is different from the encoder graph, is of low complexity. Moreover, with the appropriate modification of the RA encoder, the graph used for decoding is the same of any PR channel, which makes sense calling these codes graph-matched. The simplicity of the decoder, resulting from the "binary" interference removal (precoding) and the linear, as opposed to quadratic, complexity of the encoder make the proposed scheme attractive. For a code rate R = 3641/4096 = 0.89 and for the PR4 channel, an LDPC code has been designed and a simulated coding gain of about 5 dB for a bit error rate less than 10^-5 was obtained.