LDPC Decoding Mappings That Maximize Mutual Information

Abstract

For low-density parity-check (LDPC) codes widely used in NAND flash memories, the bit-error rate performance is closely tied to the number of bits per message used by the message-passing decoder. This paper describes a technique to generate message-passing decoding mapping functions for LDPC codes using 3 and 4 bits per message. These maps are not derived from belief-propagation decoding or one of its approximations, instead, the maps are based on a channel quantizer that maximizes mutual information. More precisely, the construction technique is a systematic method, which uses an optimal quantizer at each step of density evolution to generate message-passing decoding mappings. Numerical results show, for high-rate codes suitable for flash memories, that 4 bits per message and a few iterations (10–20 iterations) are sufficient to approach full belief-propagation decoding, less than 5–7 bits per message typically needed. The construction technique is flexible, since it can generate maps for arbitrary number of bits per message, and can be applied to arbitrary memoryless channels.