A Combined Matrix Ensemble of Low-Density Parity-Check Codes for Correcting a Solid Burst Erasure

A new ensemble of low-density parity-check (LDPC) codes for correcting a solid burst erasure is proposed. This ensemble is an instance of a combined matrix ensemble obtained by concatenating some LDPC matrices. We derive a new bound on the critical minimum span ratio of stopping sets for the proposed code ensemble by modifying the bound for ordinary code ensemble. By calculating this bound, we show that the critical minimum span ratio of stopping sets for the proposed code ensemble is better than that of the conventional one with keeping the same critical exponent of stopping ratio for both ensemble. Furthermore from experimental results, we show that the average minimum span of stopping sets for a solid burst erasure of the proposed codes is larger than that of the conventional ones. key words: low-density parity-check code, solid burst erasure, stopping set, minimum span, belief-propagation decoding