Generalized Mutual Information-Maximizing Quantized Decoding of LDPC Codes with Layered Scheduling

In this paper, we propose a framework of the mutual information-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes by using simple mappings and fixed-point additions. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and can be implemented based on either the belief propagation (BP) algorithm or the min-sum (MS) algorithm. In particular, we propose the MIM density evolution (MIM-DE) to construct the lookup tables (LUTs) for the node updates. The computational complexity and implementation complexity are discussed and compared to the LUT decoder variants. To accelerate the convergence speed of decoding quasi-cyclic LDPC codes, we consider the layered schedule, and develop the layered MIM-DE to design the LUTs based on MS algorithm, leading to the MIM layered quantized MS (MIM-LQMS) decoder. An optimization method is further introduced to reduce the memory requirement for storing the LUTs. Simulation results show that the MIM quantized decoders outperform the state-of-the-art LUT decoders in the waterfall region with both 3-bit and 4-bit precision. Moreover, the 4-bit MIM-LQMS decoder can approach the error performance of the floating-point layered BP decoder within 0:1 dB.