Decoding Techniques of Error Control Codes called LDPC (original) (raw)
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Low-density parity check ( LDPC ) codes : A new era in coding
2015
Low Density comes from the characteristic of their parity-check matrix that contains small number of 1s in comparison to the amount of 0s in them. This sparseness of parity check matrix guarantees two features: First, a decoding complexity which increases only linearly with the code length and second, a minimum distance which also increases linearly with the code length. These codes are practical implementation of Shannon noisy coding theorem[1]. LDPC codes are similar to other linear block codes. Actually, every existing code can be successfully implemented with the LDPC iterative decodSukhleen Bindra Narang, Kunal Pubby*, Hashneet Kaur Department of Electronics Technology, Guru Nanak Dev University, Amritsar, (INDIA) E-mail: kunalpubby02@gmail.com
New Decoding Methods for LDPC Codes on Error and Error-Erasure Channels
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.
A decoding algorithm for LDPC codes over erasure channels with sporadic errors
2010
An efficient decoding algorithm for low-density parity-check (LDPC) codes on erasure channels with sporadic errors (i.e., binary error-and-erasure channels with error probability much smaller than the erasure probability) is proposed and its performance analyzed. A general single-error multipleerasure (SEME) decoding algorithm is first described, which may be in principle used with any binary linear block code. The algorithm is optimum whenever the non-erased part of the received word is affected by at most one error, and is capable of performing error detection of multiple errors. An upper bound on the average block error probability under SEME decoding is derived for the linear random code ensemble. The bound is tight and easy to implement. The algorithm is then adapted to LDPC codes, resulting in a simple modification to a previously proposed efficient maximum likelihood LDPC erasure decoder which exploits the parity-check matrix sparseness. Numerical results reveal that LDPC codes under efficient SEME decoding can closely approach the average performance of random codes.
Low-Density Parity-Check Codes: Construction and Implementation
2007
Low-Density Parity-Check Codes: Construction and Implementation by Gabofetswe A. Malema Low-density parity-check (LDPC) codes have been shown to have good error correcting performance approaching Shannon's limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost, time, power and bandwidth requirements of target applications. The constructed codes should also meet error rate performance requirements of those applications. Since their rediscovery, there has been much research work on LDPC code construction and implementation. LDPC codes can be designed over a wide space with parameters such as girth, rate and length. There is no unique method of constructing LDPC codes. Existing construction methods are limited in some way in producing good error correcting performing and easily implementable codes for a given rate and length. There is a need to develop methods of constructing codes over a wide range of rates and lengths with good performance and ease of hardware implementability. LDPC code hardware design and implementation depend on the structure of target LDPC code and is also as varied as LDPC matrix designs and constructions. There are several factors to be considered including decoding algorithm computations,processing nodes interconnection network, number of processing nodes, amount of memory, number of quantization bits and decoding delay. All of these issues can be handled in several different ways. This thesis is about construction of LDPC codes and their hardware implementation. LDPC code construction and implementation issues mentioned above are too many to be addressed in one thesis. The main contribution of this thesis is the development of LDPC code construction methods for some classes of structured LDPC codes and techniques for reducing decoding time. We introduce two main methods for constructing structured codes. In the first method, column-weight two LDPC codes are derived from distance graphs. A wide range of girths, rates and lengths are obtained compared to existing
On the error-correcting capability of LDPC codes
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.
Generalized Low-Density Parity-Check Codes: Construction and Decoding Algorithms
Error Detection and Correction [Working Title]
Scientists have competed to find codes that can be decoded with optimal decoding algorithms. Generalized LDPC codes were found to compare well with such codes. LDPC codes are well treated with both types of decoding; HDD and SDD. On the other hand GLDPC codes iterative decoding, on both AWGN and BSC channels, was not sufficiently investigated in the literature. This chapter first describes its construction then discusses its iterative decoding algorithms on both channels so far. The SISO decoders, of GLDPC component codes, show excellent error performance with moderate and high code rate. However, the complexities of such decoding algorithms are very high. When the HDD BF algorithm presented to LDPC for its simplicity and speed, it was far from the BSC capacity. Therefore involving LDPC codes in optical systems using such algorithms is a wrong choice. GLDPC codes can be introduced as a good alternative of LDPC codes as their performance under BF algorithm can be improved and they would then be a competitive choice for optical communications. This chapter will discuss the iterative HDD algorithms that improve decoding error performance of GLDPC codes. SDD algorithms that maintain the performance but lowering decoding simplicity are also described.
On the error-correcting capabilities of low-complexity decoded irregular LDPC codes
2014
Low-density parity-check (LDPC) codes can be constructed using constituent block codes other than single parity-check (SPC) codes. This paper considers random LDPC codes with constituent Hamming codes and investigates their asymptotic performance over the binary erasure channel. It is shown that there exist Hamming code-based LDPC codes which, when decoded with a low-complexity iterative algorithm, are capable of correcting any erasure pattern with a number of erasures that grows linearly with the code length. The number of decoding iterations, required to correct the erasures, is a logarithmic function of the code length. The fraction of correctable erasures is computed numerically for various choices of code parameters.
Deterministic Design of Low-Density Parity-Check Codes for Binary Erasure Channels
IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference, 2007
We propose a deterministic method to design irregular Low-Density Parity-Check (LDPC) codes for binary erasure channels (BEC). Compared to the existing methods, which are based on the application of asymptomatic analysis tools such as density evolution or Extrinsic Information Transfer (EXIT) charts in an optimization process, the proposed method is much simpler and faster. Through a number of examples, we demonstrate that the codes designed by the proposed method perform very closely to the best codes designed by optimization. An important property of the proposed designs is the flexibility to select the number of constituent variable node degrees P. The proposed designs include existing deterministic designs as a special case with P = N-1, where N is the maximum variable node degree. Compared to the existing deterministic designs, for a given rate and a given δ > 0, the designed ensembles can have a threshold in δ-neighborhood of the capacity upper bound with smaller values of P and N. They can also achieve the capacity of the BEC as N, and correspondingly P and the maximum check node degree tend to infinity. Index Terms-channel coding, low-density parity-check (LDPC) codes, binary erasure channel (BEC), deterministic design. I. INTRDOUCTION Low-Density Parity-Check (LDPC) codes have received much attention in the past decade due to their attractive performance/complexity tradeoff on a variety of communication channels. In particular, on the Binary Erasure Channel (BEC), they achieve the channel capacity asymptotically [1-4]. In [1],[5],[6] a complete mathematical analysis for the performance of LDPC codes over the BEC, both asymptotically and for finite block lengths, has been developed. For other types of channels such as the Binary Symmetric Channel (BSC) and the Binary Input Additive White Gaussian Noise (BIAWGN) channel, only asymptotic analysis is available [7]. For irregular LDPC codes, the problem of finding ensemble
2013
The decoding of Low-Density Parity-Check (LDPC) codes is operated over a redundant structure known as the bipartite graph, meaning that the full set of bit nodes is not absolutely necessary for decoder convergence. In 2008, Soyjaudah and Catherine designed a recovery algorithm for LDPC codes based on this assumption and showed that the error-correcting performance of their codes outperformed conventional LDPC Codes. In this work, the use of the recovery algorithm is further explored to test the performance of LDPC codes while the number of iterations is progressively increased. For experiments conducted with small blocklengths of up to 800 bits and number of iterations of up to 2000, the results interestingly demonstrate that contrary to conventional wisdom, the errorcorrecting performance keeps increasing with increasing number of iterations.
Low-complexity LDPC codes with near-optimum performance over the BEC
2008
Recent works showed how low-density parity-check (LDPC) erasure correcting codes, under maximum likelihood (ML) decoding, are capable of tightly approaching the performance of an ideal maximum-distance-separable code on the binary erasure channel. Such result is achievable down to low error rates, even for small and moderate block sizes, while keeping the decoding complexity low, thanks to a class of decoding algorithms which exploits the sparseness of the paritycheck matrix to reduce the complexity of Gaussian elimination (GE). In this paper the main concepts underlying ML decoding of LDPC codes are recalled. A performance analysis among various LDPC code classes is then carried out, including a comparison with fixed-rate Raptor codes. The results show that LDPC and Raptor codes provide almost identical performance in terms of decoding failure probability vs. overhead. Index Terms-LDPC codes, Raptor codes, binary erasure channel, maximum likelihood decoding, ideal codes, MBMS, packet-level coding. • Wireless video/audio streaming. Link-layer coding is currently applied to the video streams in the framework of the DVB-H/SH standards. In such a context, erasure correcting codes take care of the fading mitigation, which is