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Bit Flipping Decoders for LDPC Codes: A Short Survey

Kurakula Madhukar

Published Nov 23, 2020• 1 citation
Publisher

Abstract

In the domain of wireless communication systems, Error Control Coding schemes are one of the widely relied upon or responsible methodology for securing the integrity and authenticity of the data transmission process. In the last decade, due to the advent of modern communication standards and their wide range of services, there has been a resurgence of interest and support in the research community towards the conception of efficient and versatile error control coding techniques. Recent developments in the wireless communication-based technologies have witnessed the pliable nature of low-density parity-check (LDPC) codes and their contributions which cannot be overstated. As of now, the decoding schemes based on LDPC codes have emerged as one of the most promising and efective coding scheme for addressing several key problems of reliable data communication. In this article, comprehensive overview on the on some well-known LDPC hard decision decoding algorithms is provided. In addition, simulations carried out on various LDPC decoding algorithms based on their performance is also presented. Finally, at the end of this review, the scope for future prospects are forecasted through discussions.

DOI
10.5281/zenodo.18656091

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In the domain of wireless communication systems, Error Control Coding schemes are one of the widely relied upon or responsible methodology for securing the integrity and authenticity of the data transmission process. In the last decade, due to the advent of modern communication standards and their wide range of services, there has been a resurgence of interest and support in the research community towards the conception of efficient and versatile error control coding techniques. Recent developments in the wireless communication-based technologies have witnessed the pliable nature of low-density parity-check (LDPC) codes and their contributions which cannot be overstated. As of now, the decoding schemes based on LDPC codes have emerged as one of the most promising and efective coding scheme for addressing several key problems of reliable data communication. In this article, comprehensive overview on the on some well-known LDPC hard decision decoding algorithms is provided. In addition, simulations carried out on various LDPC decoding algorithms based on their performance is also presented. Finally, at the end of this review, the scope for future prospects are forecasted through discussions.
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.
Differently from bounded-distance decoders used for algebraic codes, iterative decoders used for low-density parity-check (LDPC) codes are not characterized by a deterministic decoding radius. Therefore, the error rates of LDPC-coded transmissions are usually estimated heuristically through simulations. This is adequate for many applications like wireless communications, where a frame error rate (FER) in the order of 10-6or higher is usually targeted. However, lower values of FER can barely be assessed through simulations, and this limits the use of LDPC codes in applications requiring a lower FER, like optical communications and code-based cryptography. In this paper we introduce and study a version of the classic bit flipping (BF) decoder for which we are able to devise and develop a theoretical characterization of the FER. In addition, we consider a two-iteration hard-decision decoder for LDPC codes derived from BF, and discuss its error rate performance. Our results are validated through numerical simulations.
Introduction. In all types of digital communication, error control coding techniques are used. Many digital communication standards, such as Wi-Fi and 5G, use low density parity check (LDPC) codes. These codes are popular because they provide building encoders and decoders with low computational complexity. This work objective is to increase the error correcting capability of the well-known bit-flipping decoder (BF) of LDPC-codes. For this purpose, a modification of the decoder is built, which enables to dynamically control one of its main parameters whose choice affects significantly the quality of decoding. Materials and Methods. The well-known bit-flipping decoder of binary LDPC-codes is considered. This decoder has several parameters that are not rigidly bound with the code parameters. The dependence of the decoding quality on the selection of the output parameters of the bit-flipping decoder was investigated through simulation modeling. It is shown that the decoding results in this case are significantly affected by the input parameter of the decoder — threshold T. A modification of the BF-decoder of binary LDPC-codes has been developed, in which it is proposed to set the threshold dynamically during the execution of the algorithm depending on the error rate. A comparative analysis of the error- correcting capability of decoders is carried out by the simulation modeling method. Results. A lemma on the maximum value of the decoder threshold T is formulated and proved. Upper bounds for the number of operations are found for the original and modified decoders. A simulation model that implements a digital noise-immune communication channel has been built. In the model, the initial data is encoded with a given LDPC-code, then it is made noisy by additive uniformly distributed errors, and thereafter, it is decoded in turn by the bit-flipping algorithm with different threshold T parameters, as well as by a modified decoder. Based on the input and output data, the correction capacity of the decoders used is estimated. Experiments have shown that the error-correcting capability of the modified decoder in the range of the real error rate is higher than that of the original decoder, regardless of the selection of its parameters. Discussion and Conclusions. The lemma, proved in the paper, sets the upper bound on the threshold value in the original decoder, which simplifies its adjustment. The developed modification of the decoder has a better error- correcting capability compared to the original decoder. Nevertheless, the complexity of the modification is slightly increased compared to the original algorithm. It has been pointed out that the decoding quality of a modified decoder develops with a decrease in the number of cycles in the Tanner graph and an increase in the length of the code.
Forward error correction code with Low Density Parity Check (LDPC) gives substantial results very close to Shannon limit. This can be achieved when complexity and delay time is unlimited. Thus, it is significant to recognize the limitation of those parameters in the decoding of LDPC. In this research, a study of LDPC performance with three decoding algorithms namely; bit-flipping, log domain, and prob domain are presented. The first one is related to hard decision family while the last two types are the soft decision that follows the sum-product algorithm. A simulation model of a wireless communication system included LDPC are evaluated with the motioned three types of decoding using Matlab Package, version 2018a. The results show that the log domain and prob domain are outperforming the bit-flipping algorithm by a significant amount of Signal to Noise Ratio (SNR). Finally, optimum values of LDPC parameters are chosen according to the achieved results that will give better results are presented.
Low density parity checking codes (LDPC) are one of the most important issues in coding theory at present. LDPC-code are a type of linear-block LDPC-codes. Channel coding might be considered as the finest conversant and most potent components of cellular communications systems, that was employed for transmitting errors corrections imposed by noise, fading and interfering. LDPC-codes are advanced coding gain, i.e., new area in coding. the performances of LDPC-code are similar to the Shannon-limiting, this led to the usage of decoding in several applications in digital communications systems, like DVB-S2 and WLAN802.1..This paper aims to know what is LDPC,what its application and introduce encoding algorithms that gives rise to a linear encoding time and also show that the regular and irregular LDPC performance and also introduce different methods for decoding LDPC. I discuss in detail LDPC decoding algorithm: bit flipping algorithm, as a type from hard decision .belief propagation algorithm, sum product algorithm and minimum sum algorithm as examples from soft decision .I expect that at least some students or researchers involved in researching LDPC codes would find this paper helpful.