VLSI Implementation of LDPC Codes

International Journal of Scientific Research in Science, Engineering and Technology

The integrity of received data is a critical consideration in the design of digital communications and storage systems. The technique involved in attaining data reliability while transmission over a wireless channel is to use Channel Coding. These coding methods involve the use of Error Control Codes and there are two basic ways of controlling errors. They are Automatic Repeat Request and Forward Error Correction. This thesis concentrates on Forward error correction that deals with error detection and error correction. There are two types of error control codes: Block Codes and Convolutional Codes. The extent to which the errors are detected is a measure of the success of the code. The main trade-off in the error correction/detection technique lies in the key parameters involved in evaluating a coding system. Various block codes are analyzed using the performance metrics, namely, Improvement ratio and Error Resilience. It is observed that Cyclic Redundancy Check (CRC) codes showed b...

2013 Australasian Telecommunication Networks and Applications Conference (ATNAC), 2013

This thesis investigates four FEC (forward error correction) coding schemes for their suitability for a broadcast system where there is one energy-rich transmitter and many energy-constrained receivers with a variety of channel conditions. The four coding schemes are: repetition codes (the baseline scheme); Reed-Solomon (RS) codes; Luby-Transform (LT) codes; and a type of RS and LT concatenated codes. The schemes were tested in terms of their ability to achieve both high average data reception success probability and short data reception time at the receivers (due to limited energy). The code rate (R c) is fixed to either 1/2 or 1/3. Two statistical channel models were employed: the memoryless channel and the Gilbert-Elliott channel. The investigation considered only the data-link layer behaviour of the schemes. During the course of the investigation, an improvement to the original LT encoding process was made, the name LTAM (LT codes with Added Memory) was given to this improved coding method. LTAM codes reduce the overhead needed for decoding short-length messages. The improvement can be seen for decoding up to 10000 number of user packets. The maximum overhead reduction is as much as 10% over the original LT codes. The LT-type codes were found to have the property that can both achieve high success data reception performance and flexible switch off time for the receivers. They are also adaptable to different channel characteristics. Therefore it is a prototype of the ideal coding scheme that this project is looking for. This scheme was then further developed by applying an RS code as an inner code to further improve the success probability of packet reception. The results show that LT&RS code has a significant improvement in the channel error tolerance over that of the LT codes without an RS code applied. The trade-off is slightly more reception time needed and more decoding complexity. This LT&RS code is then determined to be the best scheme that fulfils the aim in the context of this project which is to find a coding scheme that both has a high overall data reception probability and short overall data reception time.

2016 Symposium on Communications and Vehicular Technologies (SCVT), 2016

We compare the performance of short-length linear binary codes on the binary erasure channel and the binaryinput Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based Maximum-Likelihood decoder on the erasure channel and probabilistic Ordered Statistics Decoder on the Gaussian channel. As such we compare codes and not decoders. The word error rate versus the channel parameter is found for LDPC, Reed-Muller, Polar, and BCH codes at length 256 bits. BCH codes outperform other codes in absence of cyclic redundancy check. Under joint decoding, the concatenation of a cyclic redundancy check makes all codes perform very close to optimal lower bounds.

Problems of Information Transmission, 2008

We consider the ensemble of low-density parity-check (LDPC) codes introduced by Gallager [1]. The Zyablov-Pinsker majority-logic iterative algorithm [2] for decoding LDPC codes is analyzed on the binary symmetric channel. An analytical lower bound on the errorcorrecting capability τ max that grows linearly in the code block length is obtained.

Journal of Electrical Engineering, 2015

Error control codes (ECC) as well as translation codes (TC) are used today in many different systems such as computer storages, communications systems and consumer electronic devices. ECC introduce redundancy into the encoded digital sequence in order to decrease the number of errors at output of its decoder [1]. TC introduce redundancy, in order to translate any digital sequence at the input of TC encoder to such output sequence, which fulfills constrains deduced from practical requirements. It is possible to construct codes, which have both of these properties, so called Transcontrol codes or their subclass error control run length limited (ECRLL) codes. In this manuscript a new approach to construction of EC-RLL codes is presented. The new construction is based on some parity check matrix properties of a linear binary block code from which the new EC-RLL code is obtained.

Computing Research Repository, 2008

We investigate the relation between the girth and the guaranteed error correction capability of gamma-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms. A lower bound on the number of variable nodes which expand by a factor of at least 3gamma/4 is found based on the Moore bound. An upper bound on the guaranteed correction capability is established by studying the sizes of smallest possible trapping sets.

IEEE Transactions on Information Theory, 1963

A low-density parity-check code is a code specified by a parity-check matrix with the following properties : each column contains a small fixed numberj > 3 of I's and each row contains a small fixed number k > j of 1's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j. When used with maximum likelihood decoding on a snfhciently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixedj.

2018

Low Density Parity Check (LDPC) code meets the desired Shannon limit performance for extended code lengths and binary fields. LDPC codes offer noteworthy error correction performance and they also increase the design space for communication systems. LDPC codes can offer a close proximity to Shannon Limit performance, when execution complexity and latency are not system boundaries, by using large code lengths and ever-increasing the number of iterations in the decoding process. In this paper, using 16-Quadrature Amplitude Modulation (QAM) modulation technique an LDPC decoder is simulated. It further provides the error performance of LDPC decoder over AWGN channel with Min-Sum algorithm (MSA) and their effects on Bit Error Rate (BER) versus Signal to Noise Ratio graph (SNR).

2010

For low-end devices with limited battery or computational power, low complexity decoders are beneficial. In this research we have searched for low complexity decoder alternatives for error and error-erasure channels. We have especially focused on low complexity error erasure decoders, which is a topic that has not been studied by many researchers.

2018

We present a comparative study of the performance of various polar code constructions in an additive white Gaussian noise (AWGN) channel. A polar code construction is any algorithm that selects K best among N possible polar bit-channels at the design signal-to-noise-ratio (design-SNR) in terms of bit error rate (BER). Optimal polar code construction is hard and therefore many suboptimal polar code constructions have been proposed at different computational complexities. Polar codes are also non-universal meaning the code changes significantly with the design-SNR. However, it is not known which construction algorithm at what design-SNR constructs the best polar codes. We first present a comprehensive survey of all the well-known polar code constructions along with their full implementations. We then propose a heuristic algorithm to find the best design-SNR for constructing best possible polar codes from a given construction algorithm. The proposed algorithm involves a search among se...