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International Conference on Advanced Communication Technology

Random-permutation-matrix-based cyclically-coupled LDPC codes

Francis C. M. Lau, Fanlu Mo, Wai M. Tarn, Chiu‐Wing Sham

Published Jan 1, 2017• 3 citations
Publisher

Abstract

Cyclically-coupled quasi-cyclic low-density parity-check (CC-QC-LDPC) codes are a new class of QC-LDPC codes which can achieve excellent error performance and relatively low hardware requirement. In this paper, we modify the CC-QC-LDPC code construction by using random permutation matrices instead of circulant permutation matrices, forming the “random-permutation-matrix-based CC-LDPC (RP-CC-LDPC) code”. The objective is to achieve a better error performance under the same code length. We simulate the bit error rate using FPGA simulations. We also compare the BER results and decoder complexity of the above codes with those of regular and irregular QC-LDPC codes under the same code length and code rate.

DOI
10.23919/icact.2017.7890139

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•Jan 1, 2009•1 citation
Cyclically-coupled quasi-cyclic low-density parity-check (CC-QC-LDPC) codes are a new class of QC-LDPC codes which can achieve excellent error performance and relatively low hardware requirement. In this paper, we modify the CC-QC-LDPC code construction by using random permutation matrices instead of circulant permutation matrices, forming the “random-permutation-matrix-based CC-LDPC (RP-CC-LDPC) code”. The objective is to achieve a better error performance under the same code length. We simulate the bit error rate using FPGA simulations. We also compare the BER results and decoder complexity of the above codes with those of regular and irregular QC-LDPC codes under the same code length and code rate.
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.
In this paper, we proposed a new method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on circulant permutation matrices via the one-coincidence sequences. 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.
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.
In this paper, we propose a new class of quasi-cyclic low-density parity-check (QC-LDPC) codes, namely cyclically-coupled QC-LDPC (CC-QC-LDPC) codes, and their RAM-based decoder architecture. CC-QC-LDPC codes have a simple structure and are constructed by cyclically-coupling a number of QC-LDPC subcodes. They can achieve throughput and error performance as excellent as LDPC convolutional codes, but with much lower hardware requirements. They are therefore promising candidates for future generations of communication systems such as long-haul optical communication systems. In particular, a rate-5/6 CC-QC-LDPC decoder has been implemented onto a field-programmable gate array (FPGA) and it achieves a throughput of 3.0 Gb/s at 100 MHz clock rate with 10-iteration decoding. No error floor is observed up to anEb/N0E_{b}/N_{0}Eb​/N0​of 3.50 dB, where all1.14×10161.14\times 10^{16}1.14×1016transmitted bits have been decoded correctly.
The existing design of quasi-cyclic(QC) low-density parity-check(LDPC) codes has not considered the problems of short length girths and the rows' dependency.The first problem leads to the BER performance of QC LDPC codes to be much poorer than that of randomly constructed LDPC codes,while the second problem leads to the difficulty of construction of generator matrices from parity-check matrices.To solve the first problem,the constraint conditions for designing the QC LDPC codes are proposed,and the dimension and shift factors of the circulant matrices of the given sparse parity-check matrix are adjusted according to the test results of both girth 4 and girth 6.To solve the second problem,an approach of irregular QC LDPC codes is proposed.The proposed approach is to replace some sub-matrices by zero matrices and identity matrices at special positions in the given sparse parity-check matrix so as to get a nonsingular square matrix for the construction of the generator matrix.Though adopting bidiagonal submatrices in parity-check matrix can solve the rows' dependency problem,many code words with low weights will occur,which leads to the BER performance can not be better by increasing code lengths.Examples are provided for the proposed design of QC LDPC codes,and computer simulation results show that the proposed QC LDPC codes achieve good BER performance.
In this paper, we propose a novel method with low complexity for constructing quasi-cyclic LDPC codes. The algorithm chooses every circulant permutation matrix sequentially, and makes sure that the current circulant permutation matrix forms no cycles of length 4 and 6 with the existent matrices, finally a family of (3,L)(3,L)(3,L) QC-LDPC codes with girth at least 8 is obtained. The main complexity of the algorithm is checking cycles of length 6, the number of which is no more than L2L^2L2. Simulation results show that, when block length is 1008 and using the iterative belief propagation decoding, the LDPC code constructed by the proposed algorithm out performs the random code about 0.1dB at the bit-error-rate of $ 10^{ - 5}$.