Design and Performance Analysis of Protograph LDPC Codes

1963年，R.Gallager首次提出了一种性能优秀的纠错码—低密度奇偶校验(Low-Density-Parity-Check,LDPC)码。这种码型在信度传播(BeliefPropagation,BP)译码算法下的纠错性能非常接近香农限，并已被广泛应用在各种通信标准之中。然而，传统LDPC码存在一些固有的缺陷，如编译码复杂度高、存在错误地板及码率不可扩展等。最近，美国空气动力实验室(JetPropulsionLaboratory,JPL)提出了一类新型LDPC码—原模图LDPC码。原模图LDPC码克服了传统LDPC码的诸多缺点，不仅具有优秀的纠错性能，而且能够实现线性编译码。基于以上优点，...As a superior error-correction code, low-density-parity-check (LDPC) code was first proposed by R. Gallager in 1963. Exploiting the belief propagation (BP) decoding algorithm, LDPC codes can perform very close to the Shannon limit and hence have been widely used in many communication standards. However, the conventional LDPC codes possess some drawbacks, e.g., relatively high encoding/decoding com...学位：工学博士院系专业：信息科学与技术学院_通信与信息系统学号：2332010015404

새로운 소실 채널을 위한 자기동형 군 복호기 및 부분 접속 복구 부호 및 일반화된 근 프로토그래프 LDPC 부호의 설계

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 전기·컴퓨터공학부, 2019. 2. 노종선.In this dissertation, three main contributions are given asi) new two-stage automorphism group decoders (AGD) for cyclic codes in the erasure channel, ii) new constructions of binary and ternary locally repairable codes (LRCs) using cyclic codes and existing LRCs, and iii) new constructions of high-rate generalized root protograph (GRP) low-density parity-check (LDPC) codes for a nonergodic block interference and partially regular (PR) LDPC codes for follower noise jamming (FNJ), are considered. First, I propose a new two-stage AGD (TS-AGD) for cyclic codes in the erasure channel. Recently, error correcting codes in the erasure channel have drawn great attention for various applications such as distributed storage systems and wireless sensor networks, but many of their decoding algorithms are not practical because they have higher decoding complexity and longer delay. Thus, the AGD for cyclic codes in the erasure channel was introduced, which has good erasure decoding performance with low decoding complexity. In this research, I propose new TS-AGDs for cyclic codes in the erasure channel by modifying the parity check matrix and introducing the preprocessing stage to the AGD scheme. The proposed TS-AGD is analyzed for the perfect codes, BCH codes, and maximum distance separable (MDS) codes. Through numerical analysis, it is shown that the proposed decoding algorithm has good erasure decoding performance with lower decoding complexity than the conventional AGD. For some cyclic codes, it is shown that the proposed TS-AGD achieves the perfect decoding in the erasure channel, that is, the same decoding performance as the maximum likelihood (ML) decoder. For MDS codes, TS-AGDs with the expanded parity check matrix and the submatrix inversion are also proposed and analyzed. Second, I propose new constructions of binary and ternary LRCs using cyclic codes and existing two LRCs for distributed storage system. For a primitive work, new constructions of binary and ternary LRCs using cyclic codes and their concatenation are proposed. Some of proposed binary LRCs with Hamming weights 4, 5, and 6 are optimal in terms of the upper bounds. In addition, the similar method of the binary case is applied to construct the ternary LRCs with good parameters. Also, new constructions of binary LRCs with large Hamming distance and disjoint repair groups are proposed. The proposed binary linear LRCs constructed by using existing binary LRCs are optimal or near-optimal in terms of the bound with disjoint repair group. Last, I propose new constructions of high-rate GRP LDPC codes for a nonergodic block interference and anti-jamming PR LDPC codes for follower jamming. The proposed high-rate GRP LDPC codes are based on nonergodic two-state binary symmetric channel with block interference and Nakagami-$m$ block fading. In these channel environments, GRP LDPC codes have good performance approaching to the theoretical limit in the channel with one block interference, where their performance is shown by the channel threshold or the channel outage probability. In the proposed design, I find base matrices using the protograph extrinsic information transfer (PEXIT) algorithm. Also, the proposed new constructions of anti-jamming partially regular LDPC codes is based on follower jamming on the frequency-hopped spread spectrum (FHSS). For a channel environment, I suppose follower jamming with random dwell time and Rayleigh block fading environment with M-ary frequnecy shift keying (MFSK) modulation. For a coding perspective, an anti-jamming LDPC codes against follower jamming are introduced. In order to optimize the jamming environment, the partially regular structure and corresponding density evolution schemes are used. A series of simulations show that the proposed codes outperforms the 802.16e standard in the presence of follower noise jamming.이 논문에서는, i) 소실 채널에서 순환 부호의 새로운 이단 자기동형 군 복호기 , ii) 분산 저장 시스템을 위한 순환 부호 및 기존의 부분 접속 복구 부호(LRC)를 이용한 이진 혹은 삼진 부분 접속 복구 부호 설계법, 및 iii) 블록 간섭 환경을 위한 고부효율의 일반화된 근 프로토그래프(generalized root protograph, GRP) LDPC 부호 및 추적 재밍 환경을 위한 항재밍 부분 균일 (anti-jamming paritally regular, AJ-PR) LDPC 부호가 연구되었다. 첫번째로, 소실 채널에서 순환 부호의 새로운 이단 자기동형 군 복호기를 제안하였다. 최근 분산 저장 시스템 혹은 무선 센서 네트워크 등의 응용으로 인해 소실 채널에서의 오류 정정 부호 기법이 주목받고 있다. 그러나 많은 복호기 알고리즘은 높은 복호 복잡도 및 긴 지연으로 인해 실용적이지 못하다. 따라서 낮은 복호 복잡도 및 높은 성능을 보일 수 있는 순환 부호에서 이단 자기 동형 군 복호기가 제안되었다. 본 연구에서는 패리티 검사 행렬을 변형하고, 전처리 과정을 도입한 새로운 이단 자기동형 군 복호기를 제안한다. 제안한 복호기는 perfect 부호, BCH 부호 및 최대 거리 분리 (maximum distance separable, MDS) 부호에 대해서 분석되었다. 수치 분석을 통해, 제안된 복호 알고리즘은 기존의 자기 동형 군 복호기보다 낮은 복잡도를 보이며, 몇몇의 순환 부호 및 소실 채널에서 최대 우도 (maximal likelihood, ML)과 같은 수준의 성능임을 보인다. MDS 부호의 경우, 확장된 패리티검사 행렬 및 작은 크기의 행렬의 역연산을 활용하였을 경우의 성능을 분석한다. 두 번째로, 분산 저장 시스템을 위한 순환 부호 및 기존의 부분 접속 복구 부호 (LRC)를 이용한 이진 혹은 삼진 부분 접속 복구 부호 설계법을 제안하였다. 초기 연구로서, 순환 부호 및 연접을 활용한 이진 및 삼진 LRC 설계 기법이 연구되었다. 최소 해밍 거리가 4,5, 혹은 6인 제안된 이진 LRC 중 일부는 상한과 비교해 보았을 때 최적 설계임을 증명하였다. 또한, 비슷한 방법을 적용하여 좋은 파라미터의 삼진 LRC를 설계할 수 있었다. 그 외에 기존의 LRC를 활용하여 큰 해밍 거리의 새로운 LRC를 설계하는 방법을 제안하였다. 제안된 LRC는 분리된 복구 군 조건에서 최적이거나 최적에 가까운 값을 보였다. 마지막으로, GRP LDPC 부호는 Nakagami-$m$ 블록 페이딩 및 블록 간섭이 있는 두 상태의 이진 대칭 채널을 기반으로 한다. 이러한 채널 환경에서 GRP LDPC 부호는 하나의 블록 간섭이 발생했을 경우, 이론적 성능에 가까운 좋은 성능을 보여준다. 이러한 이론 값은 채널 문턱값이나 채널 outage 확률을 통해 검증할 수 있다. 제안된 설계에서는, 변형된 PEXIT 알고리즘을 활용하여 기초 행렬을 설계한다. 또한 AJ-PR LDPC 부호는 주파수 도약 환경에서 발생하는 추적 재밍이 있는 환경을 기반으로 한다. 채널 환경으로 MFSK 변복조 방식의 레일리 블록 페이딩 및 무작위한 지속 시간이 있는 재밍 환경을 가정한다. 이러한 재밍 환경으로 최적화하기 위해, 부분 균일 구조 및 해당되는 밀도 진화 (density evolution, DE) 기법이 활용된다. 여러 시뮬레이션 결과는 추적 재밍이 존재하는 환경에서 제안된 부호가 802.16e에 사용되었던 LDPC 부호보다 성능이 우수함을 보여준다.Contents Abstract Contents List of Tables List of Figures 1 INTRODUCTION 1.1 Background 1.2 Overview of Dissertation 1.3 Notations 2 Preliminaries 2.1 IED and AGD for Erasure Channel 2.1.1 Iterative Erasure Decoder 2.1.1 Automorphism Group Decoder 2.2. Binary Locally Repairable Codes for Distributed Storage System 2.2.1 Bounds and Optimalities of Binary LRCs 2.2.2 Existing Optimal Constructions of Binary LRCs 2.3 Channels with Block Interference and Jamming 2.3.1 Channels with Block Interference 2.3.2 Channels with Jamming with MFSK and FHSS Environment. 3 New Two-Stage Automorphism Group Decoders for Cyclic Codes in the Erasure Channel 3.1 Some Definitions 3.2 Modification of Parity Check Matrix and Two-Stage AGD 3.2.1 Modification of the Parity Check Matrix 3.2.2 A New Two-Stage AGD 3.2.3 Analysis of Modification Criteria for the Parity Check Matrix 3.2.4 Analysis of Decoding Complexity of TS-AGD 3.2.5 Numerical Analysis for Some Cyclic Codes 3.3 Construction of Parity Check Matrix and TS-AGD for Cyclic MDS Codes 3.3.1 Modification of Parity Check Matrix for Cyclic MDS Codes . 3.3.2 Proposed TS-AGD for Cyclic MDS Codes 3.3.3 Perfect Decoding by TS-AGD with Expanded Parity Check Matrix for Cyclic MDS Codes 3.3.4 TS-AGD with Submatrix Inversion for Cyclic MDS Codes . . 4 New Constructions of Binary and Ternary LRCs Using Cyclic Codes and Existing LRCs 4.1 Constructions of Binary LRCs Using Cyclic Codes 4.2 Constructions of Linear Ternary LRCs Using Cyclic Codes 4.3 Constructions of Binary LRCs with Disjoint Repair Groups Using Existing LRCs 4.4 New Constructions of Binary Linear LRCs with d ≥ 8 Using Existing LRCs 5 New Constructions of Generalized RP LDPC Codes for Block Interference and Partially Regular LDPC Codes for Follower Jamming 5.1 Generalized RP LDPC Codes for a Nonergodic BI 5.1.1 Minimum Blockwise Hamming Weight 5.1.2 Construction of GRP LDPC Codes 5.2 Asymptotic and Numerical Analyses of GRP LDPC Codes 5.2.1 Asymptotic Analysis of LDPC Codes 5.2.2 Numerical Analysis of Finite-Length LDPC Codes 5.3 Follower Noise Jamming with Fixed Scan Speed 5.4 Anti-Jamming Partially Regular LDPC Codes for Follower Noise Jamming 5.4.1 Simplified Channel Model and Corresponding Density Evolution 5.4.2 Construction of AJ-PR-LDPC Codes Based on DE 5.5 Numerical Analysis of AJ-PR LDPC Codes 6 Conclusion Abstract (In Korean)Docto

Network-coded MIMO-NOMA systems with FEC codes in two-way relay networks

This paper assumes two users and a two‐way relay network with the combination of 2×2 multi‐input multi‐output (MIMO) and nonorthogonal multiple access (NOMA). To achieve network reliability without sacrificing network throughput, network‐coded MIMO‐NOMA schemes with convolutional, Reed‐Solomon (RS), and turbo codes are applied. Messages from two users at the relay node are network‐coded and combined in NOMA scheme. Interleaved differential encoding with redundancy (R‐RIDE) scheme is proposed together with MIMO‐NOMA system. Quadrature phase‐shift keying (QPSK) modulation technique is used. Bit error rate (BER) versus signal‐to‐noise ratio (SNR) (dB) and average mutual information (AMI) (bps/Hz) versus SNR (dB) in NOMA and MIMO‐NOMA schemes are evaluated and presented. From the simulated results, the combination of MIMO‐NOMA system with the proposed R‐RIDE‐Turbo network‐coded scheme in two‐way relay networks has better BER and higher AMI performance than conventional coded NOMA system. Furthermore, R‐RIDE‐Turbo scheme in MIMO‐NOMA system outperforms the other coded schemes in both MIMO‐NOMA and NOMA systems

Optimized code design for constrained DNA data storage with asymmetric errors

With ultra-high density and preservation longevity, deoxyribonucleic acid (DNA)-based data storage is becoming an emerging storage technology. Limited by the current biochemical techniques, data might be corrupted during the processes of DNA data storage. A hybrid coding architecture consisting of modified variable-length run-length limited (VL-RLL) codes and optimized protograph low-density parity-check (LDPC) codes is proposed in order to suppress error occurrence and correct asymmetric substitution errors. Based on the analyses of the different asymmetric DNA sequencer channel models, a series of the protograph LDPC codes are optimized using a modified extrinsic information transfer algorithm (EXIT). The simulation results show the better error performance of the proposed protograph LDPC codes over the conventional good codes and the codes used in the existing DNA data storage system. In addition, the theoretical analysis shows that the proposed hybrid coding scheme stores ~1.98 bits per nucleotide (bits/nt) with only 1% gap from the upper boundary (2 bits/nt)

Analysis of low-density parity-check codes on impulsive noise channels

PhD ThesisCommunication channels can severely degrade a signal, not only due to fading effects but also interference in the form of impulsive noise. In conventional communication systems, the additive noise at the receiver is usually assumed to be Gaussian distributed. However, this assumption is not always valid and examples of non-Gaussian distributed noise include power line channels, underwater acoustic channels and manmade interference. When designing a communication system it is useful to know the theoretical performance in terms of bit-error probability (BEP) on these types of channels. However, the effect of impulses on the BEP performance has not been well studied, particularly when error correcting codes are employed. Today, advanced error-correcting codes with very long block lengths and iterative decoding algorithms, such as Low-Density Parity-Check (LDPC) codes and turbo codes, are popular due to their capacity-approaching performance. However, very long codes are not always desirable, particularly in communications systems where latency is a serious issue, such as in voice and video communication between multiple users. This thesis focuses on the analysis of short LDPC codes. Finite length analyses of LDPC codes have already been presented for the additive white Gaussian noise channel in the literature, but the analysis of short LDPC codes for channels that exhibit impulsive noise has not been investigated. The novel contributions in this thesis are presented in three sections. First, uncoded and LDPC-coded BEP performance on channels exhibiting impulsive noise modelled by symmetric -stable (S S) distributions are examined. Different sub-optimal receivers are compared and a new low-complexity receiver is proposed that achieves near-optimal performance. Density evolution is then used to derive the threshold signal-tonoise ratio (SNR) of LDPC codes that employ these receivers. In order to accurately predict the waterfall performance of short LDPC codes, a nite length analysis is proposed with the aid of the threshold SNRs of LDPC codes and the derived uncoded BEPs for impulsive noise channels. Second, to investigate the e ect of impulsive noise on wireless channels, the analytic BEP on generalized fading channels with S S noise is derived. However, it requires the evaluation of a double integral to obtain the analytic BEP, so to reduce the computational cost, the Cauchy- Gaussian mixture model and the asymptotic property of S S process are used to derive upper bounds of the exact BEP. Two closed-form expressions are derived to approximate the exact BEP on a Rayleigh fading channel with S S noise. Then density evolution of different receivers is derived for these channels to nd the asymptotic performance of LDPC codes. Finally, the waterfall performance of LDPC codes is again estimated for generalized fading channels with S S noise by utilizing the derived uncoded BEP and threshold SNRs. Finally, the addition of spatial diversity at the receiver is investigated. Spatial diversity is an effective method to mitigate the effects of fading and when used in conjunction with LDPC codes and can achieve excellent error-correcting performance. Hence, the performance of conventional linear diversity combining techniques are derived. Then the SNRs of these linear combiners are compared and the relationship of the noise power between different linear combiners is obtained. Nonlinear detectors have been shown to achieve better performance than linear combiners hence, optimal and sub-optimal detectors are also presented and compared. A non-linear detector based on the bi-parameter Cauchy-Gaussian mixture model is used and shows near-optimal performance with a significant reduction in complexity when compared with the optimal detector. Furthermore, we show how to apply density evolution of LDPC codes for different combining techniques on these channels and an estimation of the waterfall performance of LDPC codes is derived that reduces the gap between simulated and asymptotic performance. In conclusion, the work presented in this thesis provides a framework to evaluate the performance of communication systems in the presence of additive impulsive noise, with and without spatial diversity at the receiver. For the first time, bounds on the BEP performance of LDPC codes on channels with impulsive noise have been derived for optimal and sub-optimal receivers, allowing other researchers to predict the performance of LDPC codes in these type of environments without needing to run lengthy computer simulations

Initial Synchronisation in the Multiple-Input Multiple-Output Aided Single- and Multi-Carrier DS-CDMA as well as DS-UWB Downlink

In this thesis, we propose and investigate code acquisition schemes employing both colocated and cooperative Multiple Input/Multiple Output (MIMO) aided Single-Carrier (SC) and Multi-Carrier (MC) Code Division Multiple Access (CDMA) DownLink (DL) schemes. We study their characteristics and performance in terms of both Non-Coherent (NC) and Differentially Coherent (DC) MIMO scenarios. Furthermore, we also propose iterative code acquisition schemes for the Direct Sequence-Ultra WideBand (DS-UWB) DL. There is a paucity of code acquisition techniques designed for transmit diversity aided systems. Moreover, there are no in-depth studies representing the fundamental characteristics of code acquisition schemes employing both co-located and cooperative MIMOs. Hence we investigate both NC and DC code acquisition schemes in the co-located and cooperative MIMO aided SC and MC DS-CDMA DL, when communicating over spatially uncorrelated Rayleigh channels. The issues of NC initial and post-initial acquisition schemes as well as DC schemes are studied as a function of the number of co-located antennas by quantifying the attainable correct detection probability and mean acquisition time performances. The research of DS-UWB systems has recently attracted a significant interest in both the academic and industrial community. In the DS-UWB DL, initial acquisition is required for both coarse timing as well as code phase alignment. Both of these constitute a challenging problem owing to the extremely short chip-duration of UWB systems. This leads to a huge acquisition search space size, which is represented as the product of the number of legitimate code phases in the uncertainty region of the PN code and the number of legitimate signalling pulse positions. Therefore the benefits of the iterative code acquisition schemes are analysed in terms of the achievable correct detection probability and mean acquisition time performances. Hence we significantly reduce the search space size with the aid of a Tanner graph based Message Passing (MP) technique, which is combined with the employment of beneficially selected generator polynomials, multiple receive antennas and appropriately designed multiple-component decoders. Finally, we characterise a range of two-stage iterative acquisition schemes employing iterative MP designed for a multiple receive antenna assisted DS-UWB DL scenario

Initial synchronisation in the multiple-input multiple-output aided single- and multi-carrier DS-CDMA as well as DS-UWB downlink

In this thesis, we propose and investigate code acquisition schemes employing both colocated and cooperative Multiple Input/Multiple Output (MIMO) aided Single-Carrier (SC) and Multi-Carrier (MC) Code Division Multiple Access (CDMA) DownLink (DL) schemes. We study their characteristics and performance in terms of both Non-Coherent (NC) and Differentially Coherent (DC) MIMO scenarios. Furthermore, we also propose iterative code acquisition schemes for the Direct Sequence-Ultra WideBand (DS-UWB) DL. There is a paucity of code acquisition techniques designed for transmit diversity aided systems. Moreover, there are no in-depth studies representing the fundamental characteristics of code acquisition schemes employing both co-located and cooperative MIMOs. Hence we investigate both NC and DC code acquisition schemes in the co-located and cooperative MIMO aided SC and MC DS-CDMA DL, when communicating over spatially uncorrelated Rayleigh channels. The issues of NC initial and post-initial acquisition schemes as well as DC schemes are studied as a function of the number of co-located antennas by quantifying the attainable correct detection probability and mean acquisition time performances. The research of DS-UWB systems has recently attracted a significant interest in both the academic and industrial community. In the DS-UWB DL, initial acquisition is required for both coarse timing as well as code phase alignment. Both of these constitute a challenging problem owing to the extremely short chip-duration of UWB systems. This leads to a huge acquisition search space size, which is represented as the product of the number of legitimate code phases in the uncertainty region of the PN code and the number of legitimate signalling pulse positions. Therefore the benefits of the iterative code acquisition schemes are analysed in terms of the achievable correct detection probability and mean acquisition time performances. Hence we significantly reduce the search space size with the aid of a Tanner graph based Message Passing (MP) technique, which is combined with the employment of beneficially selected generator polynomials, multiple receive antennas and appropriately designed multiple-component decoders. Finally, we characterise a range of two-stage iterative acquisition schemes employing iterative MP designed for a multiple receive antenna assisted DS-UWB DL scenario.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Performance analysis of protograph low-density parity-check codes for Nakagami-m fading relay channels

NSF of China [61271241, 61001073, 61102134]; European Union [294923]; Fundamental Research Funds for the Central Universities [201112G017]In this study, the authors investigate the error performance of the protograph (low-density parity check) codes over Nakagami-m fading relay channels. The authors first calculate the decoding thresholds of the protograph codes over such channels with different fading depths (i.e. different values of m) by exploiting the modified protograph extrinsic information transfer (PEXIT) algorithm. Furthermore, based on the PEXIT analysis and using Gaussian approximation, the authors derive the bit-error-rate (BER) expressions for the error-free (EF) relaying protocol and decode-and-forward (DF) relaying protocol. The authors finally compare the threshold with the theoretical BER and the simulated BER results of the protograph codes. It reveals that the performance of DF protocol is approximately the same as that of EF protocol. Moreover, the theoretical BER expressions, which are shown to be reasonably consistent with the decoding thresholds and the simulated BERs, are able to evaluate the system performance and predict the decoding threshold with lower complexity as compared with the modified PEXIT algorithm. As a result, this work can facilitate the design of the protograph codes for the wireless communication systems