Improving Decodability of Polar Codes by Adding Noise

Abstract

This paper presents an online perturbed and directed neural-evolutionary (Online-PDNE) decoding algorithm for polar codes, in which the perturbation noise and online directed neuro-evolutionary noise sequences are sequentially added to the received sequence for re-decoding if the standard polar decoding fails. The new decoding algorithm converts uncorrectable received sequences into error-correcting regions of their decoding space for correct decoding by adding specific noises. To reduce the decoding complexity and delay, the PDNE decoding algorithm and sole neural-evolutionary (SNE) decoding algorithm for polar codes are further proposed, which provide a considerable tradeoff between the decoding performance and complexity by acquiring the neural-evolutionary noise in an offline manner. Numerical results suggest that our proposed decoding algorithms outperform the other conventional decoding algorithms. At high signal-to-noise ratio (SNR) region, the Online-PDNE decoding algorithm improves bit error rate (BER) performance by more than four orders of magnitude compared with the conventional simplified successive cancellation (SSC) decoding algorithm. Furthermore, in the mid-high SNR region, the average normalized complexity of the proposed algorithm is almost the same as that of the SSC decoding algorithm, while preserving the decoding performance gain.

Bilayer LDPC Codes Combined with Perturbed Decoding for MLC NAND Flash Memory

“…Severe noise interference directly leads to the loss of stored information and affects the performance of the storage system. Based on the stochastic resonance phenomenon, artificially generating specific noise in the decoding space may compensate the effect caused by the channel noise and promote success in the decoding process [19].…”

“…In particular, the GA has been widely used in the field of channel coding, such as in LDPC code construction and decoding [28,29], polar code construction and decoding [30,31], etc. It has been demonstrated in [19] that, in an AWGN channel, a reasonable selection of noise variance, as well as the evolutionary criterion, can obtain the desired perturbation noise and thus improve the decoding performance. In the following section, a GA-based perturbed decoding algorithm is proposed for the application of bilayer LDPC codes in an MLC flash channel.…”

“…The authors of [18] proposed a cyclic redundancy check (CRC)-assisted perturbation algorithm for decoding polar codes, wherbey when the CRC of a simplified successive cancellation (SSC) decoder fails, a number of possible candidate vectors for re-decoding are obtained by adding perturbation noises. In our previous work [19], we proposed several decoding algorithms for polar codes in AWGN channels, which can convert uncorrectable received sequences into the error-correcting regions of the sequences' decoding space.…”

Editorial of Special Issue “Optimization and Applications of Modern Wireless Networks and Symmetry”

“…This book contains the successfully published submissions [1][2][3][4][5][6] to a Special Issue of Symmetry on the subject area of "Optimization and Applications of Modern Wireless Networks and Symmetry".…”

“…Moreover, PDNE decoding and sole neural-evolutionary (SNE) decoding for polar codes are further proposed to provide a considerable tradeoff between the decoding performance and complexity. Numerical results suggest that the proposed decoding outperforms other conventional decoding algorithms, such as simplified successive cancellation (SSC) [3]. In the next paper, entitled "A General Framework for Geometrically Uniform Codes and Signal Sets Matched to Groups", E. Gomes et al propose a general treatment of the metric, providing a necessary and sufficient condition for an isometry between a group G and a signal set S to be considered a matched labeling.…”