Optimized low-density parity-check codes for partial response channels

We optimize irregular low-density parity-check (LDPC) codes to closely approach the independent and uniformly distributed (i.u.d.) capacities of partial response channels. In our approach, we use the degree sequences optimization method for memoryless channels proposed by Richardson, Shokrollahi, and Urbanke and appropriately modify it for channels with memory. With this optimization algorithm we construct codes whose noise tolerance thresholds are within 0.15 dB of the i.u.d. channel capacities. Our simulation results show that irregular LDPC codes with block lengths 10/sup 6/ bits yield bit error rates 10/sup -6/ at signal-to-noise ratios 0.22 dB away from the channel capacities.