Quasi-Cyclic Asymptotically Regular LDPC Codes

Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles with varying code rates, minimum distance that grows linearly with block length, and capacity approaching iterative decoding thresholds, despite the fact that the terminated ensembles are almost regular. In this paper, we investigate the properties of the quasi-cyclic (QC) members of such an ensemble. We show that an upper bound on the minimum Hamming distance of members of the QC sub-ensemble can be improved by careful choice of the component protographs used in the code construction. Further, we show that the upper bound on the minimum distance can be improved by using arrays of circulants in a graph cover of the protograph.Comment: To be presented at the 2010 IEEE Information Theory Workshop, Dublin, Irelan

Array Convolutional Low-Density Parity-Check Codes

This paper presents a design technique for obtaining regular time-invariant low-density parity-check convolutional (RTI-LDPCC) codes with low complexity and good performance. We start from previous approaches which unwrap a low-density parity-check (LDPC) block code into an RTI-LDPCC code, and we obtain a new method to design RTI-LDPCC codes with better performance and shorter constraint length. Differently from previous techniques, we start the design from an array LDPC block code. We show that, for codes with high rate, a performance gain and a reduction in the constraint length are achieved with respect to previous proposals. Additionally, an increase in the minimum distance is observed.Comment: 4 pages, 2 figures, accepted for publication in IEEE Communications Letter