Topics in matrix analysis
Efficient encoding of low-density parity-check codes
IEEE Transactions on Information Theory
Design methods for irregular repeat-accumulate codes
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
Generalized Low-Density Parity-Check Codes Based on Hadamard Constraints
IEEE Transactions on Information Theory
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A low-complexity algorithm for the design of efficiently-encodable rate-compatible (RC) low-density parity-check (LDPC) codes by deterministically extending an irregular repeat-accumulate (IRA) is introduced. The extending structure is based on circulants shifted according a truncated Vandermonde matrix (VM) and therefore termed as "extended VM" (eVM). The novel extending algorithm is significantly less computationally complex than other known similar methods since it does not require any optimization of the extending profile or any post-construction girth conditioning. To improve the codes' properties and correcting capabilities in low code rate applications, the optimal proportions of degree-1 and degree-2 parity bits for the extended nodes are investigated and, in contrast to existing deterministic extending approaches for RC-IRA codes, an extending increment step equal to half the information block length is chosen. Various bit error rate (BER) and frame error rate (FER) have been obtained for different code rates, R, and information block length k 0 = 512 and 1024 bits considering an additive white Gaussian noise (AWGN) channel. The results have demonstrated that the proposed eVM RC-LDPC codes, despite their very simple structure and very low computational complexity, exhibit excellent performance only slightly inferior to both dedicated IRA and previously known RC-IRA codes for different data block sizes.