Construction Of Quasi-cyclic LDPC Codes Research Articles

Efficient Construction of Quasi-Cyclic LDPC Codes With Multiple Lifting Sizes

Efficient Construction of Quasi-Cyclic LDPC Codes With Multiple Lifting Sizes

Layered Construction of Quasi-Cyclic LDPC Codes

A layered construction of LDPC codes on 3-dimensional rectangular lattices is explored in this letter. By analyzing the governing conditions of in-layer polygons and inter-layer polygons, and elaborately selecting the slopes of in-layer and inter-layer lines, we remove all the 6-cycles as well as inter-layer 8-cycles which results in a class of LDPC codes without small trapping sets. We further remove the in-layer 8-cycles to design a class of LDPC codes with girth 10.

Construction of Quasi-Cyclic LDPC Codes Using a Class of Balanced Incomplete Block Designs with Irregular Block Sizes

Construction of Quasi-Cyclic LDPC Codes Using a Class of Balanced Incomplete Block Designs with Irregular Block Sizes

Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

Quasi-cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5G enhanced mobile broadband (eMBB) data channel. In this paper, we study the construction of QC LDPC codes based on an arbitrary given expansion factor (or lifting degree). First, we analyze the cycle structure of QC LDPC codes and give the necessary and sufficient condition for the existence of short cycles. Based on the fundamental theorem of arithmetic in number theory, we divide the integer factorization into three cases and present three classes of QC LDPC codes accordingly. Furthermore, a general construction method of QC LDPC codes with girth of at least 6 is proposed. Numerical results show that the constructed QC LDPC codes perform well over the AWGN channel when decoded with the iterative algorithms.

Algebra-Assisted Construction of Quasi-Cyclic LDPC Codes for 5G New Radio

Quasi-cyclic LDPC (QC-LDPC) codes have been accepted as the standard codes of 5G enhanced mobile broadband data channel. These standard codes are designed to support multiple lifting sizes and possess rate-compatible property, which can help adapt various information lengths and code rates well. In this paper, we propose an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">algebra-assisted</i> method for constructing QC-LDPC codes with such properties. We will first review the encoding mechanism and requirements of 5G LDPC codes, and present <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cycle analysis</i> for such emerging codes. We then propose a metric, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">weighted average number of cycles</i> (WANC), from the perspective of cycle structure for constructing the QC-LDPC codes that can support <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple lifting sizes</i> . Based on the WANC metric and algebraic methods, we develop a simple and practical algorithm to construct this kind of QC-LDPC codes. We finally apply the proposed algorithm to construct the exponent matrices for cases of 5G LDPC codes and the standard LDPC codes of consultative committee for space data systems, respectively. Simulation results show that the proposed WANC metric and designed algorithm are feasible and effective, and thus can be utilized to design other similar QC-LDPC codes.

Construction of quasi-cyclic LDPC codes based on a two-dimensional MDS code

In this letter, we first propose a general framework for constructing quasi-cyclic low-density parity-check (QCLDPC) codes based on a two-dimensional (2-D) maximum distance separable (MDS) code. Two classes of QC-LDPC codes are defined, whose parity-check matrices are transposes of each other. We then use a 2-D generalized Reed-Solomon (GRS) code to give a concrete construction. The decoding parity-check matrices have a large number of redundant parity-check equations while their Tanner graphs have a girth of at least 6. The minimum distances of the codes are very respectable. Experimental studies show that the constructed QC-LDPC codes perform well with the sum-product algorithm (SPA).

Construction of Quasi-Cyclic LDPC Codes From Prime Fields

Construction of Quasi-Cyclic LDPC Codes From Prime Fields

Construction of Quasi-Cyclic LDPC Codes and the Performance on the PR4-Equalized MRC Channel

In this paper, we constructed a type of parity-check matrices of QC-LDPC codes based on the progressive edge-growth (PEG) algorithm with suggested unreliable factors incorporated. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. With this method, we can avoid the unreliable information transferred in decoding as far as possible. The proposed QC-LDPC codes are hardware-friendly due to the benefit from the quasi-cyclic structure of such codes. Simulation results demonstrate that the codes constructed with the proposed algorithm have better performance than those constructed with the PEG algorithm over the additive white Gaussian noise (AWGN) channel and the PR4-equalized magnetic recording channel (MRC).

Construction of quasi-cyclic LDPC codes from quadratic congruences

In this paper, we proposed a novel method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on circulant permutation matrices via a simple quadratic congruential equation. The main advantage is that QC-LDPC codes with a variety of block lengths and rates can be easily constructed with no cycles of length four or less. Simulation results show that the proposed QC-LDPC codes perform slight better than the random regular LDPC codes for short to moderate block lengths and have almost the same performance as Sridara-Fuja-Tanner codes.

New Constructions of Quasi-Cyclic LDPC Codes Based on Special Classes of BIBDs for the AWGN and Binary Erasure Channels

New Constructions of Quasi-Cyclic LDPC Codes Based on Special Classes of BIBDs for the AWGN and Binary Erasure Channels