Construction of Multiple-Burst-Correction Codes in Transform Domain and Its Relation to LDPC Codes

This paper analyzes and explicitly constructs quasi-cyclic (QC) codes for correcting multiple bursts via matrix transformations. Our analysis demonstrates that the multiple-burst-correction capability of QC codes is determined by sub-matrices in the diagonal of their transformed parity-check matrices. By well designing these sub-matrices, the proposed QC codes are able to achieve optimal or asymptotically optimal multiple-burst-correction capability. Moreover, it proves that these codes can be QC low-density parity-check (QC-LDPC) codes, if the diagonal sub-matrices of their transformed parity-check matrices are Hadamard powers of base matrices. Analysis and simulation results show that our QC-LDPC codes perform well over not only random symbol error/erasure channels, but also burst channels.