Reliability Ratio Based Weighted Bit-Flipping Decoding for LDPC Codes

In this contribution, a novel reliability-ratio based weighted bit-flipping(RRWBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes. The RRWBF algorithm proposed is benchmarked against the conventional weighted bit-flipping (WBF) algorithm [1] and the improved weighted bit-flipping (IWBF) algorithm [2]. More than 1 and 2 dB coding gain was achieved at an BER of 10-5 while invoking the RRWBF algorithm in comparison to the two benchmarking schemes, when communicating over an AWGN and an uncorrelated Rayleigh channel, respectively. Furthermore, the decoding complexity of the proposed RRWBF algorithm is maintained at the same level as that of the conventional WBF algorithm

Efficient Hardware Implementation of Probabilistic Gradient Descent Bit Flipping

This paper presents a new Bit Flipping (BF) decoder, called Probabilistic Parallel Bit Flipping (PPBF) for Low-Density Parity-Check (LDPC) codes on the Binary Symmetric Channel. In PPBF, the flipping operation is preceded with a probabilistic behavior which is shown to improve significantly the error correction performance. The advantage of PPBF comes from the fact that, no global computation is required during the decoding process and from that, all the computations can be executed in the local computing units and in-parallel. PPBF provides a considerable improvement of the decoding frequency and complexity, compared to other known BF decoders, while obtaining a significant gain in error correction. One improved version of PPBF, called non-syndrome PPBF (NS-PPBF) is also introduced, in which the global syndrome check is moved out of the critical path and a new terminating mechanism is proposed. In order to show the superiority of the new decoders in terms of hardware efficiency and decoding throughput, the corresponding hardware architectures are presented in the second part of the paper. The ASIC synthesis results confirm that, the decoding frequency of the proposed decoders is significantly improved, much higher than the BF decoders of literature while requiring lower complexity to be efficiently implemented

Compound codes based on irregular graphs and their iterative decoding.

Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2004.Low-density parity-check (LDPC) codes form a Shannon limit approaching class of linear block codes. With iterative decoding based on their Tanner graphs, they can achieve outstanding performance. Since their rediscovery in late 1990's, the design, construction, and decoding of LDPC codes as well as their generalization have become one of the focal research points. This thesis takes a few more steps in these directions. The first significant contribution of this thesis is the introduction of a new class of codes called Generalized Irregular Low-Density (GILD) parity-check codes, which are adapted from the previously known class of Generalized Low-Density (GLD) codes. GILD codes are generalization of irregular LDPC codes, and are shown to outperform GLD codes. In addition, GILD codes have a significant advantage over GLD codes in terms of encoding and decoding complexity. They are also able to match and even beat LDPC codes for small block lengths. The second significant contribution of this thesis is the proposition of several decoding algorithms. Two new decoding algolithms for LDPC codes are introduced. In principle and complexity these algorithms can be grouped with bit flipping algorithms. Two soft-input soft-output (SISO) decoding algorithms for linear block codes are also proposed. The first algorithm is based on Maximum a Posteriori Probability (MAP) decoding of low-weight subtrellis centered around a generated candidate codeword. The second algorithm modifies and utilizes the improved Kaneko's decoding algorithm for soft-input hard-output decoding. These hard outputs are converted to soft-decisions using reliability calculations. Simulation results indicate that the proposed algorithms provide a significant improvement in error performance over Chase-based algorithm and achieve practically optimal performance with a significant reduction in decoding complexity. An analytical expression for the union bound on the bit error probability of linear codes on the Gilbert-Elliott (GE) channel model is also derived. This analytical result is shown to be accurate in establishing the decoder performance in the range where obtaining sufficient data from simulation is impractical

Optimizing the Bit-flipping Method for Decoding Low-density Parity-check Codes in Wireless Networks by Using the Artificial Spider Algorithm

In this paper, the performance of Low-Density Parity-Check (LDPC) codes is improved, which leads to reduce the complexity of hard-decision Bit-Flipping (BF) decoding by utilizing the Artificial Spider Algorithm (ASA). The ASA is used to solve the optimization problem of decoding thresholds. Two decoding thresholds are used to flip multiple bits in each round of iteration to reduce the probability of errors and accelerate decoding convergence speed while improving decoding performance. These errors occur every time the bits are flipped. Then, the BF algorithm with a low-complexity optimizer only requires real number operations before iteration and logical operations in each iteration. The ASA is better than the optimized decoding scheme that uses the Particle Swarm Optimization (PSO) algorithm. The proposed scheme can improve the performance of wireless network applications with good proficiency and results. Simulation results show that the ASA-based algorithm for solving highly nonlinear unconstrained problems exhibits fast decoding convergence speed and excellent decoding performance. Thus, it is suitable for applications in broadband wireless networks

Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes

A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported GDBF variant, and comes within 0.5 dB of the belief propagation algorithm for several tested codes. Unlike other previous GDBF algorithms that provide an escape from local maxima, the proposed algorithm uses only local, fully parallelizable operations and does not require computing a global objective function or a sort over symbol metrics, making it highly efficient in comparison. The proposed NGDBF algorithm requires channel state information which must be obtained from a signal to noise ratio (SNR) estimator. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.Comment: 16 pages, 22 figures, 2 table