Construction of High-Rate Regular Quasi-Cyclic LDPC Codes Based on Cyclic Difference Families

摘要

For a high-rate case, it is difficult to randomly construct good low-densityparity-check (LDPC) codes of short and moderate lengths because their Tannergraphs are prone to making short cycles. Also, the existing high-ratequasi-cyclic (QC) LDPC codes can be constructed only for very restricted codeparameters. In this paper, a new construction method of high-rate regular QCLDPC codes with parity-check matrices consisting of a single row of circulantswith the column-weight 3 or 4 is proposed based on special classes of cyclicdifference families. The proposed QC LDPC codes can be constructed for variouscode rates and lengths including the minimum achievable length for a givendesign rate, which cannot be achieved by the existing high-rate QC LDPC codes.It is observed that the parity-check matrices of the proposed QC LDPC codeshave full rank. It is shown that the error correcting performance of theproposed QC LDPC codes of short and moderate lengths is almost the same as thatof the existing ones through numerical analysis.