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IEEE Transactions on Communications

Variable-Weight Block Dual-Diagonal Structure for Low-Rate QC LDPC Codes With Low Error Floors

Hosung Park, Hee-Youl Kwak, Seokbeom Hong, Jong‐Seon No, Dong‐Joon Shin

Published Dec 4, 2019• 3 citations
Publisher

Abstract

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.

DOI
10.1109/tcomm.2019.2957474

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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.
The block dual-diagonal (BDD) parity structure is widely adopted in many practical irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes. These QC LDPC codes have good error-correcting performance in waterfall region but usually show relatively high error floors in low error rate region. In this paper, by using multi-weight circulants, a new BDD structure is proposed for the parity part of irregular QC LDPC codes to lower error floors and support efficient encoding. Since the parity part of parity-check matrices has flexible degree distribution with the aid of multi-weight circulants, QC LDPC codes with the proposed BDD structure can have large minimum Hamming distance compared to those with the conventional BDD structure, especially, in the low-rate case. Simulation results show that QC LDPC codes with the proposed BDD structure have lower error floor than those with the conventional BDD structure.
High-speed, high-reliability requirements and strict power limitation of near-earth communications yield that the channel coding must have high coding gain and lower error floor. In this paper, an irregular quasi-cyclic low-density parity- check (QC-LDPC) code for specific use in near-earth communications is proposed. In order to eliminate the impact of short-cycles and further improve the performance of codes, a base matrix with girth at least 8 is employed. Then dual- diagonal structure is adopted in parity check matrix to reduce encoding complexity. Besides, circulant permutation matrices and zero matrices with different sizes are used to fill the nonzero positions and zero positions of the base matrix so as to remove the complexity of the selection of cyclic shift coefficients. The adoption of circulant permutation matrices with different sizes ensures that the parity check matrix is full rank, which makes the code rate controllable. Finally, simulation results are given to demonstrate the performance of the constructed codes by comparing with several existing codes. Index Terms—Low-density parity-check codes, parity check matrix, circulant permutation matrix, near-earth communications
In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.
A novel block triple-diagonal (BTD) parity structure with all nodes of degree three is proposed for quasi-cyclic (QC) low-density parity-check (LDPC) codes. The BTD structure without low node degree can effectively improve the error floor performance and, meanwhile, enable low complexity encoding. With this structure, we use a modulo-lifting technology to construct a family of QC-LDPC codes, which supports scalable code lengths with a simple and flexible encoding solution. The simulation results show that our coding schemes for short and moderate lengths achieve better performance in the error floor region.
In this paper, we propose a construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes with multi-weight circulants (MQC-LDPC codes) which is suitable for high-rate LDPC codes with moderate length. MQC-LDPC codes can achieve better degree distributions, Hamming weight distributions, and stopping set weight distributions than conventional QC-LDPC codes with single-weight circulants (SQC-LDPC codes). Within the same framework, we generalize and simplify the error minimization progressive edge growth (EMPEG) algorithm for supporting the structure with multi-weight circulants. Simulation results show that the constructed MQC-LDPC codes offer better performance at both high and low signal to noise ratio (SNR) regions in additive white Gaussian noise (AWGN) channels than the conventional SQC-LDPC codes defined in 802.11ad and 802.16e.