MULTI-PARITY TENSOR-PRODUCT CODE FOR DATA CHANNEL

Encoder and decoder apparatus and methods derive a plurality of parity bits from a single codeword. Encoder apparatus may include a receive module receiving a data stream, a parity generation module generating a plurality of parity bits based on the data stream and a word of a tensor-product code, and a parity insertion module combining the plurality of parity bits and the data stream to generate encoded bits. Decoder apparatus may include a detector receiving and outputting encoded data, a first decoder generating first log-likelihood ratios (LLRs) from the encoded data, an error recovery module generating second LLRs from the encoded data, a second decoder that derives syndrome data from the first and second LLRs, a post-processor that combines data from the first decoder with error events from the error recovery module to generate corrected data, the post-processor further identifying a plurality of parity bits in the corrected data.