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International Conference on Telecommunications and Signal Processing (TSP)

Construction of High Performance Block and Convolutional Multi-Edge Type QC-LDPC codes

Vasiliy S. Usatyuk, Ilya Vorobyev

Published Jul 1, 2019• 4 citations
Publisher

Abstract

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.

DOI
10.1109/tsp.2019.8769083

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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 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.
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.
To obtain efficient and pragmatic channel codes high signal-to-noise ratios (SNRs), an optimized construction of short and high rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is presented. Based on an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base quasi-cyclic (QC) matrix is generated with required code rate and length. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive edge growth (PEG) algorithm is employed to find the optimized positions of the QC submatrices, which brings larger girth for better code performance. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC improved approximated cycle extrinsic message degree (QCI-ACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph and thus it improves the error floor. Simulation results show that the codes produced by the proposed method demonstrate quite good bit error rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency by the high code rate, as well as the low complexity by the short code length. Therefore, the proposed code construction can be efficiently applied in the design of short and high rate protograph QC-LDPC codes with high rate and rational complexity.
There is an important breakthrough in the field of forward error correction techniques, low-density parity-check (LDPC) codes. These codes have potential to approach the Shannon limit with reliable performance on a given channel, known as the channel capacity. Recently, researchers pay much more attention towards LDPC codes because its performance is better than Turbo codes. However, the LDPC code is the best when it is an irregular code and uses with a very large block-length. Although, the short block-length LDPC codes perform not so well, they are easy to implement in various practical applications. Therefore, there is still a demand of new development on the encoding side of LDPC codes for various ranges of code rate and code length so as to capable of using in many applications.This thesis proposes the development of quasi-cyclic (QC) LDPC codes for column weight 3. In the first part of this thesis, we propose a new construction algorithm of QC-LDPC codes for medium to large block-length by combining QC-LDPC codes of small block-length as their component codes, via Chinese remainder theorem (CRT). Such component codes were constructed by permuting each column block sequentially to attain the desire local girth. After combining all component codes to generate an expanded parity-check matrix, the resulting girth is greater than or at least equal to the maximum girth of the component codes. Simulation results show that our proposed construction method of the parity-check matrix significantly outperforms the other well-known existing methods in terms of low error-floor, simple structure, high performance, and can reduce encoding complexity.In addition, this thesis also proposes two new construction methods for QC-LDPC codes, namely a base matrix method and a subtraction based method. A base matrix based method is a simple, less computational complexity method for constructing the exponent matrix (3, K) of girth 8, 10 and 12 of QC-LDPC codes. Another method is a subtraction method, which has a similar exponent matrix as a base matrix method and has a girth at least 8. Results indicate that the LDPC codes constructed from these two methods have flexibility for arbitrary block-column length K and have a similar BER performance if compared to existing methods.
To obtain efficient channel codes with high power efficiency at moderate signal-to-noise ratios (SNRs), an efficient high-rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is optimally constructed. By an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base QC matrix template is generated with required code rate and length by the extrinsic information transfer (EXIT) chart for better decoding threshold. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive-edge-growth (PEG) algorithm is employed to find the optimized positions of the QC sub-matrices to obtain larger girth for better error floor performance. Moreover, an asymptotic weight distribution (AWD) is employed to keep a low-code-error floor for the code. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC oriented nested loop approximated cycle extrinsic message degree (QC-NLACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph to cut the error floor. Simulation results show that the codes produced by the proposed method show quite good bit-error-rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency brought by the high code rate, and the low complexity by the short code length. Moreover, a series of different rate-compatible LDPC codes can be generated from the same protograph framework with some variable node extensions, which significantly eases the code design. Therefore, the proposed code construction can be efficiently applied in the optimal construction of high-rate and short-length rate-compatible QC-LDPC codes with a high data rate and rational complexity, which makes the codes extremely suited for use in new-generation power-constrained wireless communications.