Download or read book Flexible Low Density Parity Check Codes Rate Length and Complexity written by Moritz Beermann and published by . This book was released on 2015-11-20 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Code Rate Low density Parity check Codes with Guaranteed Minimum Distance and Stopping Weight written by John A. Miller and published by . This book was released on 2003 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algebraic and Combinatorial Constructions of Low density Parity check Codes written by Ivana Djurdjevic and published by . This book was released on 2003 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Enhancements to Low Density Parity Check Codes written by Khaled ElMahgoub and published by LAP Lambert Academic Publishing. This book was released on 2010-02 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: LDPC Codes are considered to be serious competitors to turbo codes in terms of performance and complexity. They are specified by a sparse parity check matrix containing mostly 0s and relatively few 1s. In this book, LDPC codes used in the IEEE 802.16 standard physical layer were studied. Two novel techniques to enhance the performance of such codes are introduced. In the first technique, a novel parity check matrix for LDPC codes over GF(4) is proposed based on the binary parity check matrix used in the IEEE 802.16 standard . The proposed code has proven to outperform the binary code used in the IEEE 802.16 standard over both AWGN and SUI-3 channel model. In the second technique, high rate LDPC code is used, in a concatenated coding structure, as an outer code, with a convolutional code as an inner code. The performance of such a concatenated codes is compared with the commonly used one utilizing Reed-Solomon codes over the standard SUI-3 channel model, and show better performance.

Download or read book Design of Rate compatible Structured Low density Parity check Codes written by Jaehong Kim and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of our research is to design practical low-density parity-check (LDPC) codes which provide a wide range of code rates in a rate-compatible fashion. To this end, we first propose a rate-compatible puncturing algorithm for LDPC codes at short block lengths (up to several thousand symbols). The proposed algorithm is based on the claim that a punctured LDPC code with a smaller level of recoverability has better performance. The proposed algorithm is verified by comparing performance of intentionally punctured LDPC codes (using the proposed algorithm) with randomly punctured LDPC codes. The intentionally punctured LDPC codes show better bit error rate (BER) performances at practically short block lengths. Even though the proposed puncturing algorithm shows excellent performance, several problems are still remained for our research objective. First, how to design an LDPC code of which structure is well suited for the puncturing algorithm. Second, how to provide a wide range of rates since there is a puncturing limitation with the proposed puncturing algorithm. To attack these problems, we propose a new class of LDPC codes, called efficiently-encodable rate-compatible (E2RC) codes, in which the proposed puncturing algorithm concept is imbedded. The E2RC codes have several strong points. First, the codes can be efficiently encoded. We present low-complexity encoder implementation with shift-register circuits. In addition, we show that a simple erasure decoder can also be used for the linear-time encoding of these codes. Thus, we can share a message-passing decoder for both encoding and decoding in transceiver systems that require an encoder/decoder pair. Second, we show that the non-systematic parts of the parity-check matrix are cycle-free, which ensures good code characteristics. Finally, the E2RC codes having a systematic rate-compatible puncturing structure show better puncturing performance than any other LDPC codes in all ranges of code rates.

Download or read book Low density Parity check Codes with Reduced Decoding Complexity written by Benjamin Smith and published by . This book was released on 2007 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents new methods to design low-density parity-check (LDPC) codes with reduced decoding complexity. An accurate measure of iterative decoding complexity is introduced. In conjunction with extrinsic information transfer (EXIT) chart analysis, an efficient optimization program is developed, for which the complexity measure is the objective function, and its utility is demonstrated by designing LDPC codes with reduced decoding complexity. For long block lengths, codes designed by these methods match the performance of threshold-optimized codes, but reduce the decoding complexity by approximately one-third. The performance of LDPC codes is investigated when the decoder is constrained to perform a sub-optimal decoding algorithm. Due to their practical relevance, the focus is on the design of LDPC codes for quantized min-sum decoders. For such a decoder, codes designed for the sum-product algorithm are sub-optimal, and an alternative design strategy is proposed, resulting in gains of more than 0.5 dB.

Download or read book Flexible Encoder and Decoder Designs for Low density Parity check Codes written by Sunitha Kopparthi and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Future technologies such as cognitive radio require flexible and reliable hardware architectures that can be easily configured and adapted to varying coding parameters. The objective of this work is to develop a flexible hardware encoder and decoder for low-density parity-check (LDPC) codes. The design methodologies used for the implementation of a LDPC encoder and decoder are flexible in terms of parity-check matrix, code rate and code length. All these designs are implemented on a programmable chip and tested. Encoder implementations of LDPC codes are optimized for area due to their high complexity. Such designs usually have relatively low data rate. Two new encoder designs are developed that achieve much higher data rates of up to 844 Mbps while requiring more area for implementation. Using structured LDPC codes decreases the encoding complexity and provides design flexibility. The architecture for an encoder is presented that adheres to the structured LDPC codes defined in the IEEE 802.16e standard. A single encoder design is also developed that accommodates different code lengths and code rates and does not require re-synthesis of the design in order to change the encoding parameters. The flexible encoder design for structured LDPC codes is also implemented on a custom chip. The maximum coded data rate of the structured encoder is up to 844 Mbps and for a given code rate its value is independent of the code length. An LDPC decoder is designed and its design methodology is generic. It is applicable to both structured and any randomly generated LDPC codes. The coded data rate of the decoder increases with the increase in the code length. The number of decoding iterations used for the decoding process plays an important role in determining the decoder performance and latency. This design validates the estimated codeword after every iteration and stops the decoding process when the correct codeword is estimated which saves power consumption. For a given parity-check matrix and signal-to-noise ratio, a procedure to find an optimum value of the maximum number of decoding iterations is presented that considers the affects of power, delay, and error performance.

Download or read book Low Density Parity Check Codes Based on Finite Geometries written by National Aeronautics and Space Adm Nasa and published by . This book was released on 2018-09-15 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.Kou, Yu and Lin, Shu and Fossorier, MarcGoddard Space Flight CenterEUCLIDEAN GEOMETRY; ALGORITHMS; DECODING; PARITY; ALGEBRA; INFORMATION THEORY; PROJECTIVE GEOMETRY; TWO DIMENSIONAL MODELS; COMPUTERIZED SIMULATION; ERRORS; BLOCK DIAGRAMS...

Download or read book Low Density Parity Check Code for Next Generation Communication System written by Mayank Ardeshana and published by LAP Lambert Academic Publishing. This book was released on 2011-12 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: Channel coding provides the means of patterning signals so as to reduce their energy or bandwidth consumption for a given error performance. LDPC codes have been shown to have good error correcting performance which enables efficient and reliable communication. LDPC codes have linear decoding complexity but performance approaching close to shannon capacity with iterative probabilistic decoding algorithm. In this dissertation, the performance of different error correcting code such as convolution, Reed Solomon(RS), hamming, block code are evaluated based on different parameters like code rate, bit error rate (BER), Eb/No, complexity, coding gain and compare with LDPC code. In general, message passing algorithm and the sum-product algorithm are used to decode the message. We showed that logarithmic sum-product algorithm with long block length code reduces multiplication to addition by introducing logarithmic likelihood ratio so that it achieves the highest BER performance among all the decoding algorithms. The astonishing performance combined with proposed modified MS decoding algorithm make these codes very attractive for the next generations digital broadcasting system (ABS - S).

Download or read book Low density Parity check Codes with Erasures and Puncturing written by Jeongseok Ha Ha and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we extend applications of Low-Density Parity-Check (LDPC) codes to a combination of constituent sub-channels, which is a mixture of Gaussian channels with erasures. This model, for example, represents a common channel in magnetic recordings where thermal asperities in the system are detected and represented at the decoder as erasures. Although this channel is practically useful, we cannot find any previous work that evaluates performance of LDPC codes over this channel. We are also interested in practical issues such as designing robust LDPC codes for the mixture channel and predicting performance variations due to erasure patterns (random and burst), and finite block lengths. On time varying channels, a common error control strategy is to adapt the coding rate according to available channel state information (CSI). An effective way to realize this coding strategy is to use a single code and puncture it in a rate-compatible fashion, a so-called rate-compatible punctured code (RCPC). We are interested in the existence of good puncturing patterns for rate-changes that minimize performance loss. We show the existence of good puncturing patterns with analysis and verify the results with simulations. Universality of a channel code across a broad range of coding rates is a theoretically interesting topic. We are interested in the possibility of using the puncturing technique proposed in this thesis for designing universal LDPC codes. We also consider how to design high rate LDPC codes by puncturing low rate LDPC codes. The new design method can take advantage of longer effect block lengths, sparser parity-check matrices, and larger minimum distances of low rate LDPC codes.

Download or read book A Study of Low Density Parity Check Codes Using Systematic Repeat Accumulate Codes written by and published by . This book was released on 2015 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low Density Parity-Check, or LDPC, codes have been a popular error correction choice in the recent years. Its use of soft-decision decoding through a message-passing algorithm and its channel-capacity approaching performance has made LDPC codes a strong alternative to that of Turbo codes. However, its disadvantages, such as encoding complexity, discourages designers from implementing these codes. This thesis will present a type of error correction code which can be considered as a subset of LDPC codes. These codes are called Repeat-Accumulate codes and are named such because of their encoder structure. These codes is seen as a type of LDPC codes that has a simple encoding method similar to Turbo codes. What makes these codes special is that they can have a simple encoding process and work well with a soft-decision decoder. At the same time, RA codes have been proven to be codes that will work well at short to medium lengths if they are systematic. Therefore, this thesis will argue that LDPC codes can avoid some of its encoding disadvantage by becoming LDPC codes with systematic RA codes. This thesis will also show in detail how RA codes are good LDPC codes by comparing its bit error performance against other LDPC simulation results tested at short to medium code lengths and with different LDPC parity-check matrix constructions. With an RA parity-check matrix describing our LDPC code, we will see how changing the interleaver structure from a random construction to that of a structured can lead to improved performance. Therefore, this thesis will experiment using three different types of interleavers which still maintain the simplicity of encoding complexity of the encoder but at the same time show potential improvement of bit error performance compared to what has been previously seen with regular LDPC codes.

Download or read book Finite Geometry Low Density Parity Check Codes written by Yu Kou and published by . This book was released on 2001 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Low density Parity check Codes written by Gabofetswe Alafang Malema and published by . This book was released on 2007 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Two main methods for constructing structured codes are introduced. 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 methods. The performance and implementation complexity of obtained codes depends on the structure of their corresponding distance graphs. In the second method, a search algorithm based on bit-filing and progressive-edge growth algorithms is introduced for constructing quasi-cyclic LDPC codes. The algorithm can be used to form a distance or Tanner graph of a code. This method could also obtain codes over a wide range of parameters. The outcome of this study is a simple, programmable and high throughput decoder architecture based on matrix permutation and space restriction techniques.

Download or read book Linear time Encodable Low density Parity check Codes written by Amir Meidan and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, a class of Low-Density Parity-Check codes with the property that encoding can be performed in time linearly proportional to block length, is presented. These codes were named Linear-Time Encodable Low-Density Parity-Check codes (LE-LDPC). The necessary background theory is examined, concentrating on factor graphs and APP iterative decoding algorithms. Furthermore, the various details of the construction of LE-LDPC codes are also examined. A number of algorithmic modifications which yielded significant improvement in decoding performance are proposed. Simulation results are presented wherein code performance is examined as a function of a variety of construction parameters such as block size and graph structure. Lastly, LE-LDPC codes are shown to perform well compared with similar codes; even at the relatively short block lengths necessary for application in personal communication systems.

Download or read book Low Density Parity Check Codes written by Gordon McDonald and published by . This book was released on 2006 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Weight Distributions and Constructions of Low density Parity check Codes written by Chung-Li Wang and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-density parity-check (LDPC) codes are currently the most promising coding technique to achieve the Shannon capacities for a wide range of channels. These codes were first discovered by Gallager in 1962 and then rediscovered in late 1990's. Ever since their rediscovery, a great deal of research effort has been expended in design, construction, encoding, decoding, performance analysis, generalizations, and applications of LDPC codes. This research is set up to investigate two major aspects of LDPC codes: weight distributions and code constructions. The research focus of the first part is to analyze the asymptotic weight distributions of various ensembles. Analysis shows that for generalized LDPC (G-LDPC) and doubly generalized LDPC (DG-LDPC) code ensembles with some conditions, the average minimum distance grows linearly with the code length. This implies that both ensembles contain good codes. The effect of changing the component codes of the ensemble on the minimum distance is clarified. The computation of asymptotic weight and stopping set enumerators is improved. Furthermore, the average weight distribution of a multi-edge type code ensemble is investigated to obtain its upper and lower bounds. Based on them, the growth rate of the number of codewords is defined. For the growth rate of codewords with small linear, logarithmic, and constant weights, the approximations are given with two critical coefficients. It is shown that for infinite code length, the properties of the weight distribution are determined by its asymptotic growth rate. The second part of the research emphasizes specific designs and constructions of LDPC codes that not only perform well but can also be efficiently encoded. One such construction is the serial concatenation of an LDPC outer code and an accumulator with an interleaver. Such construction gives a code called an LDPCA code. The study shows that well designed LDPCA codes perform just as well as the regular LDPC codes. It also shows that the asymptotic minimum distance of regular LDPCA codes grows linearly with the code length.

Download or read book Low density Parity Check Codes written by Vijay Nagarajan and published by . This book was released on 2004 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: