Analyzing low-density parity-check codes on partial response channels with erasures using density evolution

We have developed a numerical technique based on density evolution to analyze low-density parity-check (LDPC) codes on partial response channels with erasures. We computed the average bit-error rates and signal-to-noise ratio thresholds and used them as criteria to evaluate the asymptotic performance of an ensemble of LDPC codes. We defined and estimated two important erasure parameters, namely, the fading depth threshold for erasure insertion and the erasure recovery capability of LDPC codes. We found that, at least asymptotically, LDPC codes are well suited for handling erasures in magnetic recording. Index Terms--Bit-error rate (BER), density evolution, erasure, low-density parity-check (LDPC) codes, magnetic recording, partial-response (PR) channels, SNR threshold.