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Mathematical Problems in Engineering

Weighted-Bit-Flipping-Based Sequential Scheduling Decoding Algorithms for LDPC Codes

Zhu Qing, Lenan Wu

Published Jan 1, 2013• 6 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes can be applied in a lot of different scenarios such as video broadcasting and satellite communications. LDPC codes are commonly decoded by an iterative algorithm called belief propagation (BP) over the corresponding Tanner graph. The original BP updates all the variable-nodes simultaneously, followed by all the check-nodes simultaneously as well. We propose a sequential scheduling algorithm based on weighted bit-flipping (WBF) algorithm for the sake of improving the convergence speed. Notoriously, WBF is a low-complexity and simple algorithm. We combine it with BP to obtain advantages of these two algorithms. Flipping function used in WBF is borrowed to determine the priority of scheduling. Simulation results show that it can provide a good tradeoff between FER performance and computation complexity for short-length LDPC codes.

DOI
10.1155/2013/371206

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Low-density parity-check (LDPC) codes can be applied in a lot of different scenarios such as video broadcasting and satellite communications. LDPC codes are commonly decoded by an iterative algorithm called belief propagation (BP) over the corresponding Tanner graph. The original BP updates all the variable-nodes simultaneously, followed by all the check-nodes simultaneously as well. We propose a sequential scheduling algorithm based on weighted bit-flipping (WBF) algorithm for the sake of improving the convergence speed. Notoriously, WBF is a low-complexity and simple algorithm. We combine it with BP to obtain advantages of these two algorithms. Flipping function used in WBF is borrowed to determine the priority of scheduling. Simulation results show that it can provide a good tradeoff between FER performance and computation complexity for short-length LDPC codes.
Abstract We propose a method to substantially reduce the computational complexity of iterative decoders of low-density parity-check (LDPC) codes which are based on the weighted bit-flipping (WBF) algorithm. In this method, the WBF-based decoders are modified so that the flipping function is calculated only over a reduced set of variable nodes. An explicit expression for the achieved complexity gain is provided and it is shown that for a code of block length N, the decoding complexity is reduced from O(N2) to O(N). Moreover, we derive an upper bound for the difference in the frame error rate of the reduced-set decoders and the original WBF-based decoders, and it is shown that the error performances of the two decoders are essentially the same.
To improve the decoding speed and performance of Weighted Bit Flipping (WBF) decoding algorithm for Low Density Parity Check (LDPC) codes, a two-stage WBF algorithm with a multi-/single-bit switching mechanism is proposed. It first performs multi-bit flipping decoding in the first-stage decoder. When cyclic flipping is detected or the maximum flipping function value is less than zero, it switches to the second-stage decoder. Simulation results show that the proposed algorithm obtains gains both in average decoding iteration number and in decoding performance compared with the Sum of the Magnitude based WBF (SMWBF) and the Variable node updating based SMWBF (VSMWBF).
Abstract- Low Density Parity Check (LDPC) codes can be decoded in various ways, namely the Bit-Flipping (BF) algorithm, the Weighted BF algorithm (WBF) ， the Belief Propagation (BP) algorithm and so on. These algorithms provide a wide range of tradeoffs among decoding complexity, decoding speed, and error rate performance. In this paper, a novel self-reliability-based weighted bit-flipping decoding scheme for low-density parity-check codes is proposed. Improvement in performance is observed in comparison with the modified weighted bit-flipping decoding scheme, and the decoding complexity can be significantly reduced as well. Key-Words:- Low-density parity-check (LDPC) codes, decoding algorithm, bit flipping, self reliability
Bit-flipping (BF) decoding of low-density parity-check codes is of low complexity but gives inferior performance in general. To improve performance and provide new BF decoder options for complexity-performance tradeoffs, we propose new designs for the flipping function (FF), the flipped bit selection (FBS) rule and the checksum weight updating schedule. The new FF adjusts the checksum weights in every iteration while our FBS rules take more information into account. These two modifications represent efforts to track more closely the evolutions of both check and variable nodes' reliabilities. Two selective update schedules are proposed to offer more performance and complexity tradeoffs. The combinations of the new FBS rule and known FFs result in new BF decoders with improved performance and a modest complexity increase. On the other hand, combining the new FF and FBS rule gives a new decoder with performance comparable to that of the normalized min-sum algorithm while if we use a much simpler FBS rule instead, the decoder suffers little performance loss with reduced complexity. We also present a simple decision-theoretical argument to justify the new checksum weight formula and a time-expanded factor graph model to explain the proposed selective weight-updating schedules.
In order to improve the bit-flipping (BF) decoding algorithms, a weighted hard-decision based BF decoding algorithm for low-density parity-check (LDPC) codes is presented, in which the weights of variable-nodes are employed. A new metric is defined for the weight of candidate bits not only in unsatisfied parity check equations but also in satisfied ones. The connection between min-sum decoding algorithm and the proposed algorithm is presented. Simulation results show that the new decoding algorithm can provide better FER performance and faster convergence speed than the original candidate bit based bit-flipping (CBBF) algorithm.