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IEEE Access

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

Huaan Li, Baoming Bai, Xijin Mu, Ji Zhang, Hengzhou Xu

Published Jan 1, 2018• 79 citations
Publisher

Abstract

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 analgebra-assistedmethod for constructing QC-LDPC codes with such properties. We will first review the encoding mechanism and requirements of 5G LDPC codes, and presentcycle analysisfor such emerging codes. We then propose a metric, referred to asweighted average number of cycles(WANC), from the perspective of cycle structure for constructing the QC-LDPC codes that can supportmultiple lifting sizes. 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.

DOI
10.1109/access.2018.2868963

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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 analgebra-assistedmethod for constructing QC-LDPC codes with such properties. We will first review the encoding mechanism and requirements of 5G LDPC codes, and presentcycle analysisfor such emerging codes. We then propose a metric, referred to asweighted average number of cycles(WANC), from the perspective of cycle structure for constructing the QC-LDPC codes that can supportmultiple lifting sizes. 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.
In this letter, we present an efficient method for constructing a family of quasi-cyclic low-density parity-check (QC-LDPC) codes specified only by one single exponent matrix that can support multiple lifting sizes. Our method adopts the small-lifting-size-first design strategy and the resulting exponent matrix of larger lifting size has non-decreasing girth. Numerical results show that all constituent codes can perform as well as (outperform) the CCSDS (5G) LDPC codes over the AWGN channel with the iterative decoding algorithms. This fact demonstrates the feasibility and validity of our proposed method and makes it competitive in some applications, e.g., enhancing short and medium-length LDPC codes to support longer length.
Quasi‐cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5Genhanced 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.
We introduce quasi-cyclic extension method for performance improving of the length adaptive Multi-Edge Type (MET) Quasi-cyclic LDPC (QC-LDPC) codes below the Block Error Rate (BLER) 10-5. Proposed method allows to construct MET QC-LDPC Codes for variable code length with the modular lifting of 5G eMBB Base Graph 2. Simulation results under 50 iterations of sum-product decoding over an AWGN channel with QPSK modulation are provided. It shows near same performance for information length k600 compared with 5G eMBB codes.
In wireless communication, transmission error can be caused by multi-path fading, shadowing, scattering, interference and noise. As a result, errors generated in digital communication can be classified as burst errors, random bit errors, crosstalk and echo. For reliable communication, channel coding is used which adds redundancy to the information bits. Reliable and low latency communication are crucial for future communication systems involving satellite constellations and 5G communication systems, which underscores the importance of channel coding. Various codes exist for channel coding, among which low-density parity-check (LDPC) codes, polar codes and tail biting convolution codes are mentioned for 5G ultra-reliable low latency communication and enhanced mobile broadband systems. In the literature, the performance of large block-length codes has been well-studied. But these codes lead to high latency. The design of short block-length codes remains an open problem due to the trade-off between latency and performance. In this paper, we develop a systematic procedure for construction of hybrid quasi-cyclic LDPC (QC-LDPC) codes and compare the performance of the proposed approach with random LDPC and existing QC-LDPC codes for short block-lengths and phase shift keying (PSK) signal characteristics. The proposed method exploits Euclidean geometry and circulant decomposition resulting in a QC-LDPC matrix that avoids shorter girths for iterative decoding cycles. We emphasize that the proposed approach is different from the protographic construction method, masking method, identity matrix replacement method, algebraic based construction method, and base graph method used for the construction of QC-LDPC codes.
We introduce a quasi-cyclic construction method for improving performance of length and rate adaptive Multi-Edge Type LDPC (MET-LDPC)codes below Block Error Rate (BLER)10-5Proposed method allows to construct nested code families with a code length variability based on 5G eMBB modular lifting of Base Graph 2. Constructed codes are optimized by code distance and graph properties. Simulation results under 50 iterations of sum-product decoding over an AWGN channel with QPSK modulation are provided for comparing to 5G eMBB codes. It shows near the same performance for information length , 0.1 - 0.3 dB coding gain on under rate 1/3, and coding gain around 0.3 dB under rate 1/5.
An algorithm for constructing nonbinary Quasi-cyclic LDPC (QC-LDPC) codes on the basis of masking and puncturing techniques in consideration of the shortage of algebraic construction algorithm and time-varying performance of wireless channels is proposed . This scheme can reduce the complexity of the hardware implementation, enhance the error correction performance of the LDPC codes constructed by structure algorithm based on masking technology, and improve the average effectiveness of the communication system by realizing a rate-compatible encoding based on puncturing technology. The simulation results show that the nonbinary LDPC codes constructed with masking and puncturing techniques can provide significantly stronger error correction capabilities as compared with those constructed with algebraic method which are used directly.