Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes

Abstract

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

Error Errore Eicitur: A Stochastic Resonance Paradigm for Reliable Storage of Information on Unreliable Media

“…A closely related technique of adding noise to messages in a BP decoder on the AWGN channel is by Leduc-Primeau et al [14] for reducing error floor in the context of noiseless decoders. Recently it was shown by Sundararajan et al [15] that random perturbations can be used to increase the performance of a gradient descent bit flipping decoder (GDBF), introduced by Wadayama et al [16]. At the same time, we observed that the randomness coming from computational noise even more improves the GDBF decoding performance.…”

Dynamic Weighted Bit-Flipping Decoding Algorithms for LDPC Codes

“…A multi-bit GDBF algorithm with a probabilistic FBS rule was also suggested in [16] for hard-decision decoding. With the FF (9) and FBS rule of [15], the multibit NGDBF (M-NGDBF) algorithm [17] achieves the same BER performance as that of the HGDBF decoder with much less decoding iterations. However, [18] found that new trapping set conditions may exist in the M-NGDBF decoder but can be eliminated by re-decoding with a different perturbation sequence.…”

“…It was shown that the GDBF algorithm outperforms most known WBF algorithms when the VN degree is small. Sundararajan et al [17] modified this FF by introducing a weighting on syndrome and a zero-mean Gaussian perturbation term. The resulting noisy GDBF (NGDBF) algorithm improves the performance of the GDBF algorithm which is further enhanced by adding a re-decoding process [18].…”

Frequency memory based gradient descent bit flipping algorithm

“…This algorithm is called the “GDBFwithEscape” algorithm. Sundararajan et al proposed the noisy GDBF (NGDBF) algorithm . The NGDBF algorithm uses a random perturbation to the threshold value in the escape process similar to the GDBFwithEscape algorithm.…”