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

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.