Noise-aided gradient descent bit-flipping decoders approaching maximum likelihood decoding

International audienceIn the recent literature, the study of iterative LDPC decoders implemented on faulty-hardware has led to the counter-intuitive conclusion that noisy decoders could perform better than their noiseless version. This peculiar behavior has been observed in the finite codeword length regime, where the noise perturbating the decoder dynamics help to escape the attraction of fixed points such as trapping sets. In this paper, we will study two recently introduced LDPC decoders derived from noisy versions of the gradient descent bit-flipping decoder (GDBF). Although the GDBF is known to be a simple decoder with limited error correction capability compared to more powerful soft-decision decoders, it has been shown that the introduction of a random perturbation in the decoder could greatly improve the performance results, approaching and even surpassing belief propagation or min-sum based decoders. For both decoders, we evaluate the probability of escaping from a Trapping set, and relate this probability to the parameters of the injected noise distribution, using a Markovian model of the decoder transitions in the state space of errors localized on isolated trapping sets. In a second part of the paper, we present a modified scheduling of our algorithms for the binary symmetric channel, which allows to approach maximum likelihood decoding (MLD) at the cost of a very large number of iterations

Interior Point Decoding for Linear Vector Channels

In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector channels include many practically important channels such as inter symbol interference channels and partial response channels. It is shown that the maximum likelihood decoding (MLD) rule for a linear vector channel can be relaxed to a convex optimization problem, which is called a relaxed MLD problem. The proposed decoding algorithm is based on a numerical optimization technique so called interior point method with barrier function. Approximate variations of the gradient descent and the Newton methods are used to solve the convex optimization problem. In a decoding process of the proposed algorithm, a search point always lies in the fundamental polytope defined based on a low-density parity-check matrix. Compared with a convectional joint message passing decoder, the proposed decoding algorithm achieves better BER performance with less complexity in the case of partial response channels in many cases.Comment: 18 pages, 17 figures, The paper has been submitted to IEEE Transaction on Information Theor

Linear-time encoding and decoding of low-density parity-check codes

Low-density parity-check (LDPC) codes had a renaissance when they were rediscovered in the 1990’s. Since then LDPC codes have been an important part of the field of error-correcting codes, and have been shown to be able to approach the Shannon capacity, the limit at which we can reliably transmit information over noisy channels. Following this, many modern communications standards have adopted LDPC codes. Error-correction is equally important in protecting data from corruption on a hard-drive as it is in deep-space communications. It is most commonly used for example for reliable wireless transmission of data to mobile devices. For practical purposes, both encoding and decoding need to be of low complexity to achieve high throughput and low power consumption. This thesis provides a literature review of the current state-of-the-art in encoding and decoding of LDPC codes. Message- passing decoders are still capable of achieving the best error-correcting performance, while more recently considered bit-flipping decoders are providing a low-complexity alternative, albeit with some loss in error-correcting performance. An implementation of a low-complexity stochastic bit-flipping decoder is also presented. It is implemented for Graphics Processing Units (GPUs) in a parallel fashion, providing a peak throughput of 1.2 Gb/s, which is significantly higher than previous decoder implementations on GPUs. The error-correcting performance of a range of decoders has also been tested, showing that the stochastic bit-flipping decoder provides relatively good error-correcting performance with low complexity. Finally, a brief comparison of encoding complexities for two code ensembles is also presented

Descodificação através de Machine Learning

In recent years, machine learning has become one of the most rapidly expanding technologies in a variety of technological fields. In general, it allows a computer to learn from data without being expressly designed for a particular purpose. This thesis investigates the application of decoding methods inspired by machine learning to linear block codes, such as Reed-Muller (RM) codes.Recentemente, o Machine Learning tornou-se uma das tecnologias em mais rápida expansão numa variedade de campos tecnológicos. Em geral, permite que um computador aprenda com os dados sem ser expressamente concebido para um fim específico. Esta dissertação investiga a aplicação de métodos de descodificação inspirados no Machine Learning a códigos de blocos lineares, tais como os códigos de Reed-Muller