High-performance low-complexity error-correcting codes

Abstract

A method of encoding data is described herein. According to the method, source data elements are coded using one or more product codes having a common component code. The resulting one or more primary product codewords consist of a plurality of first codewords of the common component code. One or more first sets of codewords of the common component code are assembled such that each of the first sets comprises two or more distinct first codewords forming part of a same primary product codeword. Each of the codewords of each of the first sets is codeword-mapped to a second codeword of the common component code using a one-to-one codeword-mapping. One or more second sets of second codewords are provided, where each second set corresponds to a first set of codewords. The codeword-mapping includes re-ordering, according to a known interleaving pattern, the symbols within a codeword. The codeword-mappings are such that if all of the codewords of a first set are from a same primary product codeword, then some codeword-mappings applied to the codewords of the first set are different, and if two or more repetitions of a same codeword are included in a single first set, then the codeword-mappings applied to those repetitions are different. Each set of second codewords is coded using a systematic code so as to generate a secondary product codeword for a product code having as component codes the common component code and the systematic code. Then, the primary product codewords and the non-systematic portion of the secondary product codewords are provided as encoded output data.