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International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS)

Stochastic resonance in iterative decoding: Message passing and gradient descent bit flipping

Predrag Ivaniš, Srdan S. Brkic, Bane V. Vasic

Published Oct 1, 2017• 1 citation
Publisher

Abstract

This paper contains a survey on iterative decoders of low-density parity-check (LDPC) codes made of unreliable logic gates that are capable to provide lower probability of error, when compared to their perfectly reliable counterparts. We have recently shown that the error-floor performance of message-passing decoders can be improved, if randomness that exists in unreliable logic gates is incorporated into decoding deliberately, without any complexity cost. Furthermore, we have shown that controlling the level of unreliability enable us to exploit the stochastic resonance phenomenon, previously observed in theoretical physics, electronic and magnetic systems. In contrary to common belief, we have shown that for a narrow range of gate failure probability the overall decoding performance is dramatically increased. In this paper, we show that the effect of stochastic resonance is even more noticeable for the case of the gradient descent bit-flipping (GDBF) algorithm. This decoder combines the simplest iterative decoding algorithm with gradient descent optimization, making it an attractive solution for a variety of low complexity storage systems, or code-based cryptosystems. In addition, we show that getting the most of the stochastic resonance is essentially a deep learning problem, since setting the levels of unreliability for individual parts of the decoder by a training process is a step toward incorporating the machine learning techniques into design and analysis of iterative decoders of LDPC codes.

DOI
10.1109/telsks.2017.8246285

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This paper contains a survey on iterative decoders of low-density parity-check (LDPC) codes made of unreliable logic gates that are capable to provide lower probability of error, when compared to their perfectly reliable counterparts. We have recently shown that the error-floor performance of message-passing decoders can be improved, if randomness that exists in unreliable logic gates is incorporated into decoding deliberately, without any complexity cost. Furthermore, we have shown that controlling the level of unreliability enable us to exploit the stochastic resonance phenomenon, previously observed in theoretical physics, electronic and magnetic systems. In contrary to common belief, we have shown that for a narrow range of gate failure probability the overall decoding performance is dramatically increased. In this paper, we show that the effect of stochastic resonance is even more noticeable for the case of the gradient descent bit-flipping (GDBF) algorithm. This decoder combines the simplest iterative decoding algorithm with gradient descent optimization, making it an attractive solution for a variety of low complexity storage systems, or code-based cryptosystems. In addition, we show that getting the most of the stochastic resonance is essentially a deep learning problem, since setting the levels of unreliability for individual parts of the decoder by a training process is a step toward incorporating the machine learning techniques into design and analysis of iterative decoders of LDPC codes.
Gradient descent bit-flipping (GDBF) decoding for low-density parity-check (LDPC) codes has gained great attentions because of low complexity and relatively good performance. However, the performance of the GDBF decoding is still much poorer than that of the MS algorithm. To further improve the performance, the iterative decoding process is introduced to GDBF decoding in this paper. At the end of each iteration, the latest information is used to update the reliability of the flipped bit, by which its reliability is greatly improved. Simulation results indicate that the proposed algorithm has about 0.4 dB performance gains compared to GDBF. Meanwhile, there is small computational complexity increased.
It is known that the Gradient descent bit flipping (GDBF) algorithm is an effective hard-decision decoding algorithm for low-density parity-check (LDPC) codes. However, trapping in a local maximum limits its error-rate performance. This paper presents a modified GDBF scheme that can mitigate the trapping problem and hence can improve the error-rate performance. Compared to the conventional GDBF algorithm, the proposed method is able to improve the decoding performance of 0.3dB for an (18582, 16626) code. The (18582, 16626) LDPC decoder integrates 636k logic gates and achieves a throughput of 12.4 Gbps at a clock frequency of 200 MHz in a 90nm process.
The Gradient descent bit flipping (GDBF) algorithm is a representative approach for decoding low-density parity-check (LDPC) codes, which offers a good tradeoff between decoding performance and complexity. Unfortunately, the decoding performance of GDBF algorithm degenerates dramatically for structured LDPC codes due to their large column weight. To address the above issue, we propose to improve GDBF algorithm by introducing a weighted parameter in the energy function of each bit. Specifically, this parameter compensates for the computational error of the energy function due to the large column weight of the parity-check matrices of structured LDPC codes. Moreover, the flipping number of each bit in the iterative process is included in the energy function to avoid consecutive bit flips in the decoding. Simulation results on typical structured LDPC codes indicate that the performance of the proposed algorithm is better than the standard GDBF algorithm at the cost of slight increment in the algorithmic complexity. The increase operations can be easily implemented, which indicates the proposed algorithm is suitable for practical purposes.
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.
Gradient descent bit-flipping (GDBF) algorithm achieves good error performance for decoding low density parity check codes. In the GDBF algorithm, a search point is apt to be trapped in a local optimum, which causes performance degradation of the GDBF algorithm. To overcome this issue, the noisy GDBF algorithm introduces random perturbation into the inversion function of each symbol, which decreases the probability of being trapped in a local optimum. In this paper, we develop the noisy GDBF algorithm by enhancing the threshold adaptation in multi-bit flipping procedure to improve the BER performance without increasing the time complexity.
Low-complexity and high-performance low-density parity-check (LDPC) decoders are highly demanded in various modern communication and storage systems. In this paper, a novel hard-decision decoding algorithm, called tabu-list random-penalty gradient descent bit-flipping (TRGDBF) algorithm, is proposed. Compared to the state-of-the-art hard-decision algorithms, the TRGDBF algorithm has much better error-correction performance due to several algorithmic improvements. First, a random-penalty term is introduced to the inversion function to help the decoder escape from trapping sets, which are the main causes of the error-floor phenomenon. Second, a tabu-list is employed to improve the decoding efficiency. Numerical results show that the TRGDBF algorithm can achieve up to two orders of magnitude better error-correction performance than the probabilistic gradient descent bit-flipping (PGDBF) algorithm and reduce the average iteration count by about 15%. In addition, a well-optimized hardware architecture is developed to implement the TRGDBF algorithm. Algorithmic transformation and architecture optimization are well explored to reduce the hardware complexity and latency. Synthesis results show that the TRGDBF decoder can work at a higher frequency and offer a larger throughput than the PGDBF decoder.