Nonuniform error correction using low-density parity-check codes

This correspondence introduces a framework to design and analyze low-density parity-check (LDPC) codes over nonuniform channels. We study LDPC codes for channels with nonuniform noise distributions, rate-adaptive coding, and unequal error protection. First, we propose a technique to design LDPC codes for volume holographic memory (VHM) systems for which the noise distribution is nonuniform. We show that the proposed coding scheme has an easy design procedure and results in efficient codes for holographic memories. An important property of the proposed technique is the design of the codes that have a low error floor and low variable node degrees, while maintaining performance close to the Shannon limit. We then show that punctured LDPC codes can be studied as a special case of our design methodology for nonuniform channels. Finally, we propose a method to generate LDPC codes that can provide unequal error protection in addition to having a good overall performance. Moreover, the highly protected bits can be decoded without requiring the entire word to be decoded.