A Study of Low Density Parity-Check Codes Using Systematic Repeat-Accumulate Codes
A Study of Low Density Parity-Check Codes Using Systematic Repeat-Accumulate Codes

Author:

Publisher:

Published: 2015

Total Pages: 82

ISBN-13:

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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.

Iterative Error Correction
Iterative Error Correction

Author: Sarah J. Johnson

Publisher:

Published: 2014-05-14

Total Pages: 356

ISBN-13: 9780511691294

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Presents all of the key ideas needed to understand, design, implement and analyse iterative-based error correction schemes.

Design of Rate-compatible Structured Low-density Parity-check Codes
Design of Rate-compatible Structured Low-density Parity-check Codes

Author: Jaehong Kim

Publisher:

Published: 2006

Total Pages:

ISBN-13:

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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.

Enhancements to Low Density Parity Check Codes
Enhancements to Low Density Parity Check Codes

Author: Khaled ElMahgoub

Publisher: LAP Lambert Academic Publishing

Published: 2010-02

Total Pages: 88

ISBN-13: 9783838340906

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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.

Incremental Redundancy Low-density Parity-check Codes for Hybrid FEC/ARQ Schemes
Incremental Redundancy Low-density Parity-check Codes for Hybrid FEC/ARQ Schemes

Author: Woonhaing Hur

Publisher:

Published: 2007

Total Pages: 125

ISBN-13:

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This dissertation also examines how to improve throughput performance in HybridARQ schemes with low-complexity by exploiting irregular repeat accumulate (IRA) codes. The proposed adaptive transmission method with adaptive puncturing patterns of IRA codes shows higher throughput performance in all of operating code ranges than does any other single mode in IR-HybridARQ schemes.

Low-density Parity-check Codes with Erasures and Puncturing
Low-density Parity-check Codes with Erasures and Puncturing

Author: Jeongseok Ha Ha

Publisher:

Published: 2003

Total Pages:

ISBN-13:

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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.