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IEEE East-West Design & Test Symposium (EWDTS)

Construction of Length and Rate Adaptive MET QC-LDPC Codes by Cyclic Group Decomposition

Vasiliy S. Usatyuk, Егоров Сергей Иванович, German Svistunov

Published Sep 1, 2019• 2 citations
Publisher

Abstract

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.

DOI
10.1109/ewdts.2019.8884427

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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.
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.
We introduce the protograph sieving method as a tool for optimization of moderate length Multi-Edge Type Quasi-Cyclic Low-Density Parity-Check (MET QC-LDPC)codes. The proposed method allows to improve code distance property with defined graph balanced cycles and construct MET-LDPC protograph for the code length in gap between Scattering PEXIT-chart and Covariance Evolution methods. We show that this approach improves code distance properties and achieves 0.2 dB gain in terms of block error rate (BLER)over the additive white Gaussian noise (AWGN)channel for information length of 600 bits and rate 1/3, at a target BLER of 10-6when compared to BG2 MET-LDPC code proposed at 5G standard.
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.
This paper proposes a systematic permutation-based construction method for multi-rate quasi-cyclic low-density parity-check (QC-LDPC) codes. We first present a graph-theoretic framework in which any regular QC-LDPC code can be normalized to a canonical base matrix that is uniquely determined by a permutation π. This normalization reduces the complex code design to a single combinatorial optimization problem over the symmetric group. Based on this normalization, we analyze the cycle structure of the lifted Tanner graph and derive necessary and sufficient conditions for 4-cycle elimination in terms of the permutation difference function. We develop two complementary algorithms: a simulated annealing algorithm that searches for permutations that minimize a weighted sum of 4-cycles and 6-cycles, and a progressive column-ordering algorithm that ensures every prefix subgraph maintains high girth. This approach yields a nested family of rate-compatible codes. Simulation results show that the constructed codes outperform the 5G-LDPC codes. The nested base matrix structure facilitates seamless rate switching, which makes the proposed code family well suited for adaptive transmission systems in future wireless networks.
We present code sieving method for construction of long-length high performance Block and Convolutional Multi-Edge Type QC-LDPC codes (MET QC-LDPCC) under the fixed point (Quantized) reduced complexity box-plus (QRCBP) decoder. Proposed method use iterative decoding threshold protograph sieving and simulated annealing method for QC lifting with cycles EMD maximization. Using proposed method we construct base matrix of MET-LDPC code with size 92 20, maximal column weight 17, with weight one circulants, code rate 0.8, 2 variable nodes punctured which have iterative decoding threshold Eb/No = 2.333 dB under 200 iterations of QRCBP over an AWGN channel with QPSK modulation on Bit Error Rate below 10-, 0.289 dB from Shannon limit. Simulation results of Block with code length N = 261924 and MET QC-LDPCC codes, equivalent block length N = 785772 constructed using simulated annealing lifting of base matrix under 32 iterations of QRCBP show Eb/No = 2.56dB, Eb/No = 2.478dB below BER10-15, respectively. Cole's importance sampling under QRCBP show that proposed codes error-floor BER ≈ 10-16.
We propose an approach for optimizing nonbinary (NB) quasi-cyclic (QC) LDPC codes. This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the so-called generalized girth of the NB LDPC code Tanner graph. Tightened random coding bounds based on the average binary spectra for ensembles of "almost regular" NB LDPC codes of finite lengths over extensions of the binary Galois field are derived. The simulated FER performance of the sum-product BP decoding of "almost regular" NB QC-LDPC block codes are presented and compared with the derived finite-length random coding bounds as well as with the same performance of the optimized binary QC-LDPC block code in the 5G standard. In the waterfall region our finite-length bounds on the error probability of ML decoding are about 0.1--0.2 dB away from the simulated FER performance of BP decoding.