LDPC Decoding Mappings That Maximize Mutual Information

• Published in: IEEE journal on selected areas in communications Vol. 34; no. 9; pp. 2391 - 2401
• Main Authors: Romero, Francisco Javier Cuadros, Kurkoski, Brian M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-09-2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Binary system; Codes; Decoding; Decoding mapping functions; Iterative decoding; lDPC codes; Memory; Memoryless systems; Mutual information; quantization; Quantization (signal)
• ISSN: 0733-8716; 1558-0008
• DOI: 10.1109/JSAC.2016.2603708

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.