224 research outputs found
New Protograph-Based Construction of GLDPC Codes for Binary Erasure Channel and LDPC Codes for Block Fading Channel
ํ์๋
ผ๋ฌธ(๋ฐ์ฌ) -- ์์ธ๋ํ๊ต๋ํ์ : ๊ณต๊ณผ๋ํ ์ ๊ธฐยท์ ๋ณด๊ณตํ๋ถ, 2022.2. ๋
ธ์ข
์ ๊ต์๋.์ด ํ์ ๋
ผ๋ฌธ์์๋ ๋ค์ ๋ ๊ฐ์ง์ ์ฐ๊ตฌ๊ฐ ์ด๋ฃจ์ด์ก๋ค: i) ์ด์ง ์์ค ์ฑ๋์์ ์๋ก์ด ๊ตฌ์กฐ์ ํ๋กํ ๊ทธ๋ํ ๊ธฐ๋ฐ generalized low-density parity-check (GLDPC) ๋ถํธ์ ์ค๊ณ ๋ฐฉ๋ฒ ii) ๋ธ๋ก ํ์ด๋ฉ ์ฑ๋์ ์ํ ํ๋กํ ๊ทธ๋ํ ๊ธฐ๋ฐ์ LDPC ๋ถํธ ์ค๊ณ.
์ฒซ ๋ฒ์งธ๋ก, ์ด์ง ์์ค ์ฑ๋์์ ์๋กญ๊ฒ ์ ์๋ ๋ถ๋ถ์ ๋ํ ๊ธฐ๋ฒ์ ์ด์ฉํ ํ๋กํ ๊ทธ๋ํ ๊ธฐ๋ฐ์ GLDPC ๋ถํธ๊ฐ ์ ์๋์๋ค. ๊ธฐ์กด์ ํ๋กํ ๊ทธ๋ํ ๊ธฐ๋ฐ์ GLDPC ๋ถํธ์ ๊ฒฝ์ฐ ํ๋กํ ๊ทธ๋ํ ์์ญ์์ single parity-check (SPC) ๋
ธ๋๋ฅผ generalized constraint (GC) ๋
ธ๋๋ก ์นํ(๋ํ)ํ๋ ํํ๋ก ๋ถํธ๊ฐ ์ค๊ณ๋์ด ์ฌ๋ฌ ๋ณ์ ๋
ธ๋ ๊ฑธ์ณ GC ๋
ธ๋๊ฐ ์ฐ๊ฒฐ๋๋ ํํ๋ฅผ ๊ฐ์ง๋ค. ๋ฐ๋ฉด, ์ ์๋ ๋ถ๋ถ์ ๋ํ ๊ธฐ๋ฒ์ ํ ๊ฐ์ ๋ณ์ ๋
ธ๋์ GC ๋
ธ๋๋ฅผ ์ฐ๊ฒฐํ๋๋ก ๋ง๋ค ์ ์๋ค. ๋ฐ๊ฟ ๋งํ๋ฉด, ์ ์๋ ๋ถ๋ถ์ ๋ํ ๊ธฐ๋ฒ์ ๋ ์ธ๋ฐํ ๋ํ์ด ๊ฐ๋ฅํด์ ๊ฒฐ๊ณผ์ ์ผ๋ก ๋ถํธ ์ค๊ณ์ ์์ด ๋์ ์์ ๋๋ฅผ ๊ฐ์ง๊ณ ๋ ์ธ๋ จ๋ ๋ถํธ ์ต์ ํ๊ฐ ๊ฐ๋ฅํ๋ค. ๋ณธ ํ์ ๋
ผ๋ฌธ์์๋ ๋ถ๋ถ์ ๋ํ๊ณผ PEXIT ๋ถ์์ ์ด์ฉํ์ฌ partially doped GLDPC (PD-GLDPC) ๋ถํธ๋ฅผ ์ค๊ณํ๊ณ ์ต์ ํ ํ์๋ค. ๋๋ถ์ด, PD-GLDPC ๋ถํธ์ ์ผ๋ฐ์ ์ต์ ๊ฑฐ๋ฆฌ๋ฅผ ๊ฐ์ง๋ ์กฐ๊ฑด์ ์ ์ํ์๊ณ ์ด๋ฅผ ์ด
๋ก ์ ์ผ๋ก ์ฆ๋ช
ํ์๋ค. ๊ฒฐ๊ณผ์ ์ผ๋ก, ์ ์๋ PD-GLDPC ๋ถํธ๋ ํ์กดํ๋ GLDPC ๋ถํธ์ ์ฑ๋ฅ๋ณด๋ค ์ ์๋ฏธํ๊ฒ ์ํฐํ ์ฑ๋ฅ์ด ์ข์๊ณ ๋์์ ์ค๋ฅ ๋ง๋ฃจ๊ฐ ์์๋ค. ๋ง์ง๋ง์ผ๋ก, ์ต์ ํ๋ PD-GLDPC ๋ถํธ๋ ํ์กดํ๋ ์ต์ ๋ธ๋ก LDPC ๋ถํธ๋ค์ ๊ทผ์ ํ ์ฑ๋ฅ์ ๊ฐ์ง์ ๋ณด์ฌ์ฃผ์๋ค.
๋ ๋ฒ์งธ๋ก, ๋ธ๋ก ํ์ด๋ฉ (BF) ์ฑ๋์์ resolvable block design (RBD)๋ฅผ ์ด์ฉํ ํ๋กํ ๊ทธ๋ํ LDPC ๋ถํธ ์ค๊ณ๊ฐ ์ด๋ฃจ์ด์ก๋ค. ์ ์๋ ๋ถํธ์ ์ฑ๋ฅ์ ํ์ธํ๊ธฐ ์ํ ๋นํธ ์ค๋ฅ์จ์ ์ํ์ ๊ฐ๋ง ์งํ๋ผ๋ ์ ์๋ ๊ธฐ๋ฒ์ ์ด์ฉํด ์ ๋ํ์๋ค. ๋ํ, ์๋ฎฌ๋ ์ด์
์ ํตํด ์ ๋๋ ์ค๋ฅ์จ ์ํ๊ณผ ๋ถํธ์ ํ๋ ์ ์ค๋ฅ์จ์ด ๋์ SNR ์์ญ์์ ์ฑ๋ outage ํ๋ฅ ์ ๊ทผ์ ํจ์ ์ ์ ์๋ค.In this dissertation, two main contributions are given as: i) new construction methods for protograph-based generalized low-density parity-check (GLDPC) codes for the binary erasure channel using partial doping technique and ii) new design of protograph-based low-density parity-check (LDPC) codes for the block fading channel using resolvable block design.
First, a new code design technique, called partial doping, for protograph-based GLDPC codes is proposed. While the conventional construction method of protograph-based GLDPC codes is to replace some single parity-check (SPC) nodes with generalized constraint (GC) nodes applying to multiple connected variable nodes (VNs) in the protograph, the proposed technique of partial doping can select any number of partial VNs in the protograph to be protected by GC nodes.
In other words, the partial doping technique enables finer tuning of doping, which gives higher degrees of freedom in the code design and enables a sophisticated code optimization. The proposed partially doped GLDPC (PD-GLDPC) codes are constructed using the partial doping technique and optimized by the protograph extrinsic information transfer (PEXIT) analysis.
In addition, the condition guaranteeing the linear minimum distance growth of the PD-GLDPC codes is proposed and analytically proven so that the PD-GLDPC code ensembles satisfying this condition have the typical minimum distance.
Consequently, the proposed PD-GLDPC codes outperform the conventional GLDPC codes with a notable improvement in the waterfall performance and without the error floor phenomenon.
Finally, the PD-GLDPC codes are shown to achieve a competitive performance compared to the existing state-of-the-art block LDPC codes.
Second, the protograph-based LDPC codes constructed from resolvable balanced incomplete block design (RBIBD) are designed and proposed for block fading (BF) channel.
In order to analyze the performance of the proposed LDPC codes, the upper bounds on bit error rate (BER) using the novel method called gamma evolution are derived.
In addition, the numerical analysis shows that the upper bound and the frame error rate (FER) of the proposed LDPC codes approach the channel outage probability in a finite signal-to-noise ratio (SNR) region.1 INTRODUCTION 1
1.1 Background 1
1.2 Overview of Dissertation 3
2 Overview of LDPC Codes 5
2.1 LDPC Codes 5
2.2 Decoding of LDPC Codes in the BEC 7
2.3 Analysis tool for LDPC Codes 8
2.3.1 Density Evolution 8
2.4 Protograph-Based LDPC Codes 9
3 Construction of Protograph-Based Partially Doped Generalized LDPC Codes 11
3.1 Code Structure of Protograph-Based GLDPC Ensembles 14
3.1.1 Construction of Protograph Doped GLDPC Codes 14
3.1.2 PEXIT Analysis and Decoding Process of Protograph Doped GLDPC Codes 15
3.2 The Proposed PD-GLDPC Codes 18
3.2.1 Construction Method of PD-GLDPC Codes 18
3.2.2 PEXIT Analysis of PD-GLDPC Codes 22
3.2.3 Condition for the Existence of the Typical Minimum Distance of the PD-GLDPC Code Ensemble 23
3.2.4 Comparison between Proposed PD-GLDPC Codes and Protograph Doped GLDPC Codes 25
3.3 Optimization of PD-GLDPC Codes 26
3.3.1 Construction of PD-GLDPC Codes from Regular Protographs 26
3.3.2 Differential Evolution-Based Code Construction from the Degree Distribution of Random LDPC Code Ensembles 28
3.3.3 Optimization of PD-GLDPC Codes Using Protograph Differential Evolution 32
3.4 Numerical Results and Analysis 36
3.4.1 Simulation Result for Optimized PD-GLDPC Code from Regular and Irregular Random LDPC Code Ensembles 36
3.4.2 Simulation Result for PD-GLDPC Code from Optimized Protograph 43
3.5 Proof of Theorem 1: The Constraint for the Existence of the Typical Minimum Distance of the Proposed Protograph-Based PD-GLDPC Codes 45
4 Design of Protograph-Based LDPC Code Using Resolvable Block Design for Block Fading Channel 52
4.1 Problem Formulation 53
4.1.1 BF Channel Model 53
4.1.2 Performance Metrics of BF Channel 54
4.1.3 Protograph-Based LDPC Codes and QC LDPC Codes 57
4.2 New Construction of Protograph-Based LDPC Codes from Resolvable Block Designs 57
4.2.1 Resolvable Block Designs 57
4.2.2 Construction of the Proposed Protograph-Based LDPC Codes 59
4.2.3 Theoretical Analysis of the Proposed Protograph-Based LDPC Code from RBD 61
4.2.4 Numerical Analysis of the Proposed Protograph-Based LDPC Code Codes for BF Channel 65
4.2.5 BER Comparison with Analytical Results from Gamma Evolution 65
4.2.6 FER Comparison with Channel Outage Probability 67
5 Conclusions 69
Abstract (In Korean) 78๋ฐ
Spatially Coupled LDPC Codes Constructed from Protographs
In this paper, we construct protograph-based spatially coupled low-density
parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or
uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L,
we obtain a flexible family of code ensembles with varying rates and frame
lengths that can share the same encoding and decoding architecture for
arbitrary L. We demonstrate that the resulting codes combine the best features
of optimized irregular and regular codes in one design: capacity approaching
iterative belief propagation (BP) decoding thresholds and linear growth of
minimum distance with block length. In particular, we show that, for
sufficiently large L, the BP thresholds on both the binary erasure channel
(BEC) and the binary-input additive white Gaussian noise channel (AWGNC)
saturate to a particular value significantly better than the BP decoding
threshold and numerically indistinguishable from the optimal maximum
a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all
variable nodes in the coupled chain have degree greater than two,
asymptotically the error probability converges at least doubly exponentially
with decoding iterations and we obtain sequences of asymptotically good LDPC
codes with fast convergence rates and BP thresholds close to the Shannon limit.
Further, the gap to capacity decreases as the density of the graph increases,
opening up a new way to construct capacity achieving codes on memoryless
binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor
Quasi-Cyclic Asymptotically Regular LDPC Codes
Families of "asymptotically regular" LDPC block code ensembles can be formed
by terminating (J,K)-regular protograph-based LDPC convolutional codes. By
varying the termination length, we obtain a large selection of LDPC block code
ensembles with varying code rates, minimum distance that grows linearly with
block length, and capacity approaching iterative decoding thresholds, despite
the fact that the terminated ensembles are almost regular. In this paper, we
investigate the properties of the quasi-cyclic (QC) members of such an
ensemble. We show that an upper bound on the minimum Hamming distance of
members of the QC sub-ensemble can be improved by careful choice of the
component protographs used in the code construction. Further, we show that the
upper bound on the minimum distance can be improved by using arrays of
circulants in a graph cover of the protograph.Comment: To be presented at the 2010 IEEE Information Theory Workshop, Dublin,
Irelan
Low-Floor Tanner Codes via Hamming-Node or RSCC-Node Doping
We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the โdopingโ of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a codeโs protograph. We show that the doping of a โgoodโ graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult. Lastly, we perform a simple complexity analysis of our Tanner codes and examine the performance of lower-complexity, suboptimal Hamming-node decoders
On the Minimum Distance of Generalized Spatially Coupled LDPC Codes
Families of generalized spatially-coupled low-density parity-check (GSC-LDPC)
code ensembles can be formed by terminating protograph-based generalized LDPC
convolutional (GLDPCC) codes. It has previously been shown that ensembles of
GSC-LDPC codes constructed from a protograph have better iterative decoding
thresholds than their block code counterparts, and that, for large termination
lengths, their thresholds coincide with the maximum a-posteriori (MAP) decoding
threshold of the underlying generalized LDPC block code ensemble. Here we show
that, in addition to their excellent iterative decoding thresholds, ensembles
of GSC-LDPC codes are asymptotically good and have large minimum distance
growth rates.Comment: Submitted to the IEEE International Symposium on Information Theory
201
New Codes on Graphs Constructed by Connecting Spatially Coupled Chains
A novel code construction based on spatially coupled low-density parity-check
(SC-LDPC) codes is presented. The proposed code ensembles are described by
protographs, comprised of several protograph-based chains characterizing
individual SC-LDPC codes. We demonstrate that code ensembles obtained by
connecting appropriately chosen SC-LDPC code chains at specific points have
improved iterative decoding thresholds compared to those of single SC-LDPC
coupled chains. In addition, it is shown that the improved decoding properties
of the connected ensembles result in reduced decoding complexity required to
achieve a specific bit error probability. The constructed ensembles are also
asymptotically good, in the sense that the minimum distance grows linearly with
the block length. Finally, we show that the improved asymptotic properties of
the connected chain ensembles also translate into improved finite length
performance.Comment: Submitted to IEEE Transactions on Information Theor
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