In this paper, a transmission scheme based on Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes with an invertible quasi-cyclic Matrix Q is proposed over Additive White Gaussian Noise (AWGN) channel in order to obtain faster convergence of hard-decision decoding. Combined with the soft information from channel, another improved Reliability-based Q (RQ) decoding algorithm is proposed. The new design can also be applied to QC-LDPC codes in IEEE 802.16e Standards. The simulation results show that the proposed scheme with Q or RQ decoding algorithm has better error correction performance and lower average number of iterations than Bit-Flipping (BF) or weighted Bit-Flipping (WBF) decoding algorith
In this paper, a transmission scheme based on Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes with an invertible quasi-cyclic Matrix Q is proposed over Additive White Gaussian Noise (AWGN) channel in order to obtain faster convergence of hard-decision decoding. Combined with the soft information from channel, another improved Reliability-based Q (RQ) decoding algorithm is proposed. The new design can also be applied to QC-LDPC codes in IEEE 802.16e Standards. The simulation results show that the proposed scheme with Q or RQ decoding algorithm has better error correction performance and lower average number of iterations than Bit-Flipping (BF) or weighted Bit-Flipping (WBF) decoding algorith
In the multi-paths environment,since the performance of orthogonal frequency division multiplexing(OFDM) system may be severely degraded by the sub-carriers in deep fading,powerful error-correcting codes have to be applied to OFDM.This paper presents a novel quasi-cyclic low density parity check(QC-LDPC) coded OFDM system.In this system,the redundant bits of codeword are mapped to higher-order constellation,and a group shuffled message passing scheduling is used in the iterative decoding.According to the mapping scheme,the QC-LDPC code is optimized by density evolution based on group shuffled message passing with Gaussian approximation.Simulation results show that the proposed system can achieve better error rate performance and faster decoding convergence than conventional approaches on both additive white Gaussian noise(AWGN) and Rayleigh fading channels.
Next generation wireless systems, such as IEEE802.11n and 802.16e, need high error-correction capacity to achieve high data rate transmission. Therefore, a low-density parity-check code(LDPC code) is adopted as a FEC code. Quasi-cyclic LDPC code(QC-LDPC) code is an important branch of LDPC code research. IEEE 802.16e proposes a parity-check matrix with quasi-cyclic character which makes the encoding very simply. This paper introduces the encoding process and several decoding algorithms for LDPC including Log-BP algorithm, Min-Sum(MS) algorithm and modified MS algorithm. Simulations results under a next generation wireless LAN system show that MS comparing with the Log-BP performance has approximately 0.5dB loss for high-speed rates codes over AWGN channel, however the performance of normalized MS and row weight matched MS with relatively low complexity is nearly the same as that of Log-BP algorithm.
For the issue of determining cyclic shift coefficients of the quasi-cyclic sub-matrix in the quasi-cyclic low-density parity-check, a method was presented based on Yang Hui triangle to compute the cyclic shift coefficients. By this method, cyclic shift coefficients could be expressed in simple analytic expressions, and cycles of length four in parity matrix were eliminated. The parity matrix is quasi-cyclic to save required memory and is prone to coding and decoding, and has high flexibility with respect to the design of code length and rate. Over an additive white Gauss noise channel and under the BP decoding algorithm, simulations show that the SNR of the QC-LDPC codes with the proposed algorithm is better than random codes close to 0.3 dB at the BER performance of 10-4 and better than the LDPC codes in DVB-S2 0.2 dB at the BER performance of 10-6. Moreover, the BER performance of the new codes is no less than the LDPC codes in IEEE 802.16e under the same conditions. Furthermore, the simulation result also indicates that by making a reasonable choice of the size of the cyclic shift matrix, the BER performance of the codeword can be improved.
In this paper, we propose a simple mathematical structure to improve the BER (bit error rate) performance of quasi-cyclic low-density parity-check (QC-LDPC) codes. Since the proposed structure can be defined in-between those of random codes and structured codes, these proposed QC-LDPC codes not only perform as well as random-LDPC codes, but also preserve the advantage of structured LDPC codes which is easier to implement over coding hardware. Moreover, the proposed structure, constructed from balanced incomplete block design (BIBD), can reduce the density of parity-check matrix and hence reduce the number of short cycles, which generally lead to better performance. At the end, we show that the error floor performance of QC-LDPC codes can be improved by proposed hybrid structures and perform well over binary-input additive white Gaussian noise (BI-AWGN) channel.
In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes. This paper shows that finite fields can also be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding. Methods of construction are presented. LDPC codes constructed by these methods are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN), binary random, and burst erasure channels with iterative decoding in terms of bit-error probability, block-error probability, error-floor, and rate of decoding convergence, collectively. Particularly, they have low error floors. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.
We present a novel construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with arbitrary column weight and girth at least eight. By carefully designing the parity-check matrix, our approach ensures both structural flexibility and improved error-correction capabilities. We evaluate the performance of these codes under the additive white Gaussian noise (AWGN) channel. Simulation results demonstrate that the proposed QC-LDPC codes outperform the protograph LDPC codes included in the Consultative Committee for Space Data Systems (CCSDS) telecommand standards. Additionally, we benchmark our proposed codes against existing short-length codes with girth 8, observing improvements in the decoding performance while ensuring suitability for hardware implementation. The findings of this work contribute to the ongoing development of efficient LDPC codes suitable for ultra-reliable low-latency communications and area-efficient architecture designs for the Internet of Things (IoT), machine-to-machine (M2M), and satellite communications.