Low complexity LDPC codes for partial response channels

This paper constructs and analyzes a class of regular LDPC codes with column weight of j=2, in contrast to the often-used j≥3 setting. These codes possess several significant features. First, they are free of 6-cycle, and can be easily constructed for a large range of code rates. Secondly, the parity check matrix of the code can be represented by a simple set, thus lending itself to a low complexity implementation. Thirdly, the proposed codes concatenated with proper precoder outperform j≥3 LDPC codes for partial response (PR) channels. Finally, they exhibit block error statistics significantly different from LDPC codes with j≥3, making them more compatible with Reed-Solomon error correction codes. The LDPC coded partial response (PR) channel is formulated as a dynamical model and analyzed using density evolution technique, which is used to explain the behavior of the concatenated system. A high rate (8/9) code with block size 4608 is constructed as an example, and its bit error rate (BER), block error statistics, and decoding convergence over ideal PR channel are investigated using simulation. The simulation results are consistent with the density evolution analysis, both indicating that LDPC codes with j=2 are attractive for partial response channels. PR targets for magnetic recording channel are used as examples to illustrate the performance of the proposed codes.