Protograph-based LDPC codes for partial response channels

This paper addresses the design of a protograph-based LDPC code which can approach the independent and uniformly distributed (i.u.d.) capacity of partial response channels. We propose a method to calculate the iterative decoding threshold of a joint graph between a protograph and the state structure of a partial response channel using the extrinsic information transfer (EXIT) chart. We then describe a simple method to search for a protograph code whose threshold is close to the i.u.d. capacity limit. This new class of codes is needed because experiments show a protograph that is capacity approaching in the AWGN channel may not perform well in partial response channels. In particular, protographs with punctured nodes are often used to produce good AWGN codes, but they perform poorly with the BCJR equalizer. Numerical results support our analysis.