Thresholds and scheduling for LDPC-coded partial response channels

Low-density parity check (LDPC) codes exhibit a threshold phenomenon over a wide variety of channels. The threshold serves as a good parameter for system and code design, and is usually very close to channel capacity. There has been a great deal of recent work surrounding the use of LDPC and turbo codes with iterative decoding for partial response (PR) channels. In this paper, we calculate thresholds for LDPC codes over binary-input PR channels using a Gaussian approximation. We show that the threshold varies according to decoder schedule, and we identify schedules that result in good thresholds. Conversely, we use our results to guide the design of decoder schedules that minimize the number of computationally expensive Bahl-Cocke-Jelinek-Raviv algorithm steps.