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Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes

Communication system links that do not have the ability to retransmit generally rely on forward error correction (FEC) techniques that make use of error correcting codes (ECC) to detect and correct errors caused by the noise in the channel. There are several ECC’s in the literature that are used...

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Main Author: Anggraeni, Silvia
Format: Thesis
Language:English
Published: 2009
Online Access:http://utpedia.utp.edu.my/2920/1/Full_Thesis_Silvia.pdf
http://utpedia.utp.edu.my/2920/
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spelling my-utp-utpedia.29202017-01-25T09:44:18Z http://utpedia.utp.edu.my/2920/ Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes Anggraeni, Silvia Communication system links that do not have the ability to retransmit generally rely on forward error correction (FEC) techniques that make use of error correcting codes (ECC) to detect and correct errors caused by the noise in the channel. There are several ECC’s in the literature that are used for the purpose. Among them, the low density parity check (LDPC) codes have become quite popular owing to the fact that they exhibit performance that is closest to the Shannon’s limit. This thesis proposes a novel code-construction method for constructing not only (3, k) regular but also irregular LDPC codes. The choice of designing (3, k) regular LDPC codes is made because it has low decoding complexity and has a Hamming distance, at least, 4. In this work, the proposed code-construction consists of information submatrix (Hinf) and an almost lower triangular parity sub-matrix (Hpar). The core design of the proposed code-construction utilizes expanded deterministic base matrices in three stages. Deterministic base matrix of parity part starts with triple diagonal matrix while deterministic base matrix of information part utilizes matrix having all elements of ones. The proposed matrix H is designed to generate various code rates (R) by maintaining the number of rows in matrix H while only changing the number of columns in matrix Hinf. All the codes designed and presented in this thesis are having no rank-deficiency, no pre-processing step of encoding, no singular nature in parity part (Hpar), no girth of 4-cycles and low encoding complexity of the order of (N + g2) where g2«N. The proposed (3, k) regular codes are shown to achieve code performance below 1.44 dB from Shannon limit at bit error rate (BER) of 10 −6 when the code rate greater than R = 0.875. They have comparable BER and block error rate (BLER) performance with other techniques such as (3, k) regular quasi-cyclic (QC) and (3, k) regular random LDPC codes when code rates are at least R = 0.7. In addition, it is also shown that the proposed (3, 42) regular LDPC code performs as close as 0.97 dB from Shannon limit at BER 10 −6 with encoding complexity (1.0225 N), for R = 0.928 and N = 14364 – a result that no other published techniques can reach. 2009 Thesis NonPeerReviewed application/pdf en http://utpedia.utp.edu.my/2920/1/Full_Thesis_Silvia.pdf Anggraeni, Silvia (2009) Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes. Masters thesis, UNIVERSITI TEKNOLOGI PETRONAS.
institution Universiti Teknologi Petronas
building UTP Resource Centre
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Petronas
content_source UTP Electronic and Digitized Intellectual Asset
url_provider http://utpedia.utp.edu.my/
language English
description Communication system links that do not have the ability to retransmit generally rely on forward error correction (FEC) techniques that make use of error correcting codes (ECC) to detect and correct errors caused by the noise in the channel. There are several ECC’s in the literature that are used for the purpose. Among them, the low density parity check (LDPC) codes have become quite popular owing to the fact that they exhibit performance that is closest to the Shannon’s limit. This thesis proposes a novel code-construction method for constructing not only (3, k) regular but also irregular LDPC codes. The choice of designing (3, k) regular LDPC codes is made because it has low decoding complexity and has a Hamming distance, at least, 4. In this work, the proposed code-construction consists of information submatrix (Hinf) and an almost lower triangular parity sub-matrix (Hpar). The core design of the proposed code-construction utilizes expanded deterministic base matrices in three stages. Deterministic base matrix of parity part starts with triple diagonal matrix while deterministic base matrix of information part utilizes matrix having all elements of ones. The proposed matrix H is designed to generate various code rates (R) by maintaining the number of rows in matrix H while only changing the number of columns in matrix Hinf. All the codes designed and presented in this thesis are having no rank-deficiency, no pre-processing step of encoding, no singular nature in parity part (Hpar), no girth of 4-cycles and low encoding complexity of the order of (N + g2) where g2«N. The proposed (3, k) regular codes are shown to achieve code performance below 1.44 dB from Shannon limit at bit error rate (BER) of 10 −6 when the code rate greater than R = 0.875. They have comparable BER and block error rate (BLER) performance with other techniques such as (3, k) regular quasi-cyclic (QC) and (3, k) regular random LDPC codes when code rates are at least R = 0.7. In addition, it is also shown that the proposed (3, 42) regular LDPC code performs as close as 0.97 dB from Shannon limit at BER 10 −6 with encoding complexity (1.0225 N), for R = 0.928 and N = 14364 – a result that no other published techniques can reach.
format Thesis
author Anggraeni, Silvia
spellingShingle Anggraeni, Silvia
Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes
author_facet Anggraeni, Silvia
author_sort Anggraeni, Silvia
title Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes
title_short Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes
title_full Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes
title_fullStr Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes
title_full_unstemmed Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes
title_sort novel code-construction for (3, k) regular low density parity check codes
publishDate 2009
url http://utpedia.utp.edu.my/2920/1/Full_Thesis_Silvia.pdf
http://utpedia.utp.edu.my/2920/
_version_ 1739830976364675072
score 13.211869

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