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Encoding Algorithm of Binary and Non-binary Irregular LDPC Codes via Block Triangular Matrices with Low Weight Diagonal Submatrices

Iketoh Yuta, T. Nozaki

Published Aug 30, 2019• 1 citation
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Irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes with the block dual-diagonal (BDD) parity structure are widely adopted in many communication standards because the BDD structure supports an efficient encoding and many degree-2 variable nodes inside are adequate for the construction of mid- to high-rate codes. However, we observe that low-rate irregular QC LDPC codes with the BDD parity structure inherently contain too many degree-2 variable nodes and suffer from error floors in high signal-to-noise ratio (SNR) region. In this paper, a generalized BDD structure including double-weight circulants as well as circulant permutation matrices is proposed for low-rate irregular QC LDPC codes with low error floors which is achieved with a little bit giving up error performance in the waterfall region. When constructing the parity part of a code with the generalized BDD structure, the portion of double-weight circulants is variable so that the resulting LDPC code can achieve a desired degree distribution including degrees 2 and 3 while supporting the efficient encoding. We show that low-rate QC LDPC codes constructed with the proposed BDD structure have better theoretical properties and lower error floor than those with the conventional BDD structure.

IEEE Transactions on Communications•Dec 4, 2019•3 citations
We propose an efficient encoding algorithm for the binary and non-binary low-density parity-check codes. This algorithm transforms the parity part of the parity-check matrix into a block triangular matrix with low weight diagonal submatrices by row and column permutations in the preprocessing stage. This algorithm determines the parity part of a codeword by block back-substitution to reduce the encoding complexity in the encoding stage. Numerical experiments show that this algorithm has a lower encoding complexity than existing encoding algorithms. Moreover, we show that this algorithm encodes the non-binary cycle codes in linear time.
Irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes with the block dual-diagonal (BDD) parity structure are widely adopted in many communication standards because the BDD structure supports an efficient encoding and many degree-2 variable nodes inside are adequate for the construction of mid- to high-rate codes. However, we observe that low-rate irregular QC LDPC codes with the BDD parity structure inherently contain too many degree-2 variable nodes and suffer from error floors in high signal-to-noise ratio (SNR) region. In this paper, a generalized BDD structure including double-weight circulants as well as circulant permutation matrices is proposed for low-rate irregular QC LDPC codes with low error floors which is achieved with a little bit giving up error performance in the waterfall region. When constructing the parity part of a code with the generalized BDD structure, the portion of double-weight circulants is variable so that the resulting LDPC code can achieve a desired degree distribution including degrees 2 and 3 while supporting the efficient encoding. We show that low-rate QC LDPC codes constructed with the proposed BDD structure have better theoretical properties and lower error floor than those with the conventional BDD structure.