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

Stopping Set Distributions of Some Linear Codes

Stopping sets and stopping set distribution of an low-density parity-check code are used to determine the performance of this code under iterative decoding over a binary erasure channel (BEC). Let $C$ be a binary $[n,k]$ linear code with parity-check matrix $H$, where the rows of $H$ may be dependent. A stopping set $S$ of $C$ with parity-check matrix $H$ is a subset of column indices of $H$ such that the restriction of $H$ to $S$ does not contain a row of weight one. The stopping set distribution $\{T_i(H)\}_{i=0}^n$ enumerates the number of stopping sets with size $i$ of $C$ with parity-check matrix $H$. Note that stopping sets and stopping set distribution are related to the parity-check matrix $H$ of $C$. Let $H^{*}$ be the parity-check matrix of $C$ which is formed by all the non-zero codewords of its dual code $C^{\perp}$. A parity-check matrix $H$ is called BEC-optimal if $T_i(H)=T_i(H^*), i=0,1,..., n$ and $H$ has the smallest number of rows. On the BEC, iterative decoder of $C$ with BEC-optimal parity-check matrix is an optimal decoder with much lower decoding complexity than the exhaustive decoder. In this paper, we study stopping sets, stopping set distributions and BEC-optimal parity-check matrices of binary linear codes. Using finite geometry in combinatorics, we obtain BEC-optimal parity-check matrices and then determine the stopping set distributions for the Simplex codes, the Hamming codes, the first order Reed-Muller codes and the extended Hamming codes.Comment: 33 pages, submitted to IEEE Trans. Inform. Theory, Feb. 201

Integrating protein structural information

Dissertação apresentada para obtenção de Grau de Doutor em Bioquímica,Bioquímica Estrutural, pela Universidade Nova de Lisboa, Faculdade de Ciências e TecnologiaThe central theme of this work is the application of constraint programming and other artificial intelligence techniques to protein structure problems, with the goal of better combining experimental data with structure prediction methods. Part one of the dissertation introduces the main subjects of protein structure and constraint programming, summarises the state of the art in the modelling of protein structures and complexes, sets the context for the techniques described later on, and outlines the main points of the thesis: the integration of experimental data in modelling. The first chapter, Protein Structure, introduces the reader to the basic notions of amino acid structure, protein chains, and protein folding and interaction. These are important concepts to understand the work described in parts two and three. Chapter two, Protein Modelling, gives a brief overview of experimental and theoretical techniques to model protein structures. The information in this chapter provides the context of the investigations described in parts two and three, but is not essential to understanding the methods developed. Chapter three, Constraint Programming, outlines the main concepts of this programming technique. Understanding variable modelling, the notions of consistency and propagation, and search methods should greatly help the reader interested in the details of the algorithms, as described in part two of this book. The fourth chapter, Integrating Structural Information, is a summary of the thesis proposed here. This chapter is an overview of the objectives of this work, and gives an idea of how the algorithms developed here could help in modelling protein structures. The main goal is to provide a flexible and continuously evolving framework for the integration of structural information from a diversity of experimental techniques and theoretical predictions. Part two describes the algorithms developed, which make up the main original contribution of this work. This part is aimed especially at developers interested in the details of the algorithms, in replicating the results, in improving the method or in integrating them in other applications. Biochemical aspects are dealt with briefly and as necessary, and the emphasis is on the algorithms and the code

Opportunistic Routing with Network Coding in Powerline Communications

Opportunistic Routing (OR) can be used as an alternative to the legacy routing (LR) protocols in networks with a broadcast lossy channel and possibility of overhearing the signal. The power line medium creates such an environment. OR can better exploit the channel than LR because it allows the cooperation of all nodes that receive any data. With LR, only a chain of nodes is selected for communication. Other nodes drop the received information. We investigate OR for the one-source one-destination scenario with one traffic flow. First, we evaluate the upper bound on the achievable data rate and advocate the decentralized algorithm for its calculation. This knowledge is used in the design of Basic Routing Rules (BRR). They use the link quality metric that equals the upper bound on the achievable data rate between the given node and the destination. We call it the node priority. It considers the possibility of multi-path communication and the packet loss correlation. BRR allows achieving the optimal data rate pertaining certain theoretical assumptions. The Extended BRR (BRR-E) are free of them. The major difference between BRR and BRR-E lies in the usage of Network Coding (NC) for prognosis of the feedback. In this way, the protocol overhead can be severely reduced. We also study Automatic Repeat-reQuest (ARQ) mechanism that is applicable with OR. It differs to ARQ with LR in that each sender has several sinks and none of the sinks except destination require the full recovery of the original message. Using BRR-E, ARQ and other services like network initialization and link state control, we design the Advanced Network Coding based Opportunistic Routing protocol (ANChOR). With the analytic and simulation results we demonstrate the near optimum performance of ANChOR. For the triangular topology, the achievable data rate is just 2% away from the theoretical maximum and it is up to 90% higher than it is possible to achieve with LR. Using the G.hn standard, we also show the full protocol stack simulation results (including IP/UDP and realistic channel model). In this simulation we revealed that the gain of OR to LR can be even more increased by reducing the head-of-the-line problem in ARQ. Even considering the ANChOR overhead through additional headers and feedbacks, it outperforms the original G.hn setup in data rate up to 40% and in latency up to 60%.:1 Introduction 2 1.1 Intra-flow Network Coding 6 1.2 Random Linear Network Coding (RLNC) 7 2 Performance Limits of Routing Protocols in PowerLine Communications (PLC) 13 2.1 System model 14 2.2 Channel model 14 2.3 Upper bound on the achievable data rate 16 2.4 Achieving the upper bound data rate 17 2.5 Potential gain of Opportunistic Routing Protocol (ORP) over Common Single-path Routing Protocol (CSPR) 19 2.6 Evaluation of ORP potential 19 3 Opportunistic Routing: Realizations and Challenges 24 3.1 Vertex priority and cooperation group 26 3.2 Transmission policy in idealized network 34 3.2.1 Basic Routing Rules (BRR) 36 3.3 Transmission policy in real network 40 3.3.1 Purpose of Network Coding (NC) in ORP 41 3.3.2 Extended Basic Routing Rules (BRR) (BRR-E) 43 3.4 Automatic ReQuest reply (ARQ) 50 3.4.1 Retransmission request message contents 51 3.4.2 Retransmission Request (RR) origination and forwarding 66 3.4.3 Retransmission response 67 3.5 Congestion control 68 3.5.1 Congestion control in our work 70 3.6 Network initialization 74 3.7 Formation of the cooperation groups (coalitions) 76 3.8 Advanced Network Coding based Opportunistic Routing protocol (ANChOR) header 77 3.9 Communication of protocol information 77 3.10 ANChOR simulation . .79 3.10.1 ANChOR information in real time .80 3.10.2 Selection of the coding rate 87 3.10.3 Routing Protocol Information (RPI) broadcasting frequency 89 3.10.4 RR contents 91 3.10.5 Selection of RR forwarder 92 3.10.6 ANChOR stability 92 3.11 Summary 95 4 ANChOR in the Gigabit Home Network (G.hn) Protocol 97 4.1 Compatibility with the PLC protocol stack 99 4.2 Channel and noise model 101 4.2.1 In-home scenario 102 4.2.2 Access network scenario 102 4.3 Physical layer (PHY) layer implementation 102 4.3.1 Bit Allocation Algorithm (BAA) 103 4.4 Multiple Access Control layer (MAC) layer 109 4.5 Logical Link Control layer (LLC) layer 111 4.5.1 Reference Automatic Repeat reQuest (ARQ) 111 4.5.2 Hybrid Automatic Repeat reQuest (HARQ) in ANChOR 114 4.5.3 Modeling Protocol Data Unit (PDU) erasures on LLC 116 4.6 Summary 117 5 Study of G.hn with ANChOR 119 5.1 ARQ analysis 119 5.2 Medium and PHY requirements for “good” cooperation 125 5.3 Access network scenario 128 5.4 In-home scenario 135 5.4.1 Modeling packet erasures 136 5.4.2 Linear Dependence Ratio (LDR) 139 5.4.3 Worst case scenario 143 5.4.4 Analysis of in-home topologies 145 6 Conclusions . . . . . . . . . . . . . . . 154 A Proof of the neccessity of the exclusion rule 160 B Gain of ORPs to CSRPs 163 C Broadcasting rule 165 D Proof of optimality of BRR for triangular topology 167 E Reducing the retransmission probability 168 F Calculation of Expected Average number of transmissions (EAX) for topologies with bi-directional links 170 G Feedback overhead of full coding matrices 174 H Block diagram of G.hn physical layer in ns-3 model 175 I PER to BER mapping 17

Characterizing Spoken Discourse in Individuals with Parkinson Disease Without Dementia

Background: The effects of disease (PD) on cognition, word retrieval, syntax, and speech/voice processes may interact to manifest uniquely in spoken language tasks. A handful of studies have explored spoken discourse production in PD and, while not ubiquitously, have reported a number of impairments including: reduced words per minute, reduced grammatical complexity, reduced informativeness, and increased verbal disruption. Methodological differences have impeded cross-study comparisons. As such, the profile of spoken language impairments in PD remains ambiguous. Method: A cross-genre, multi-level discourse analysis, prospective, cross-sectional between groups study design was conducted with 19 PD participants (Mage = 70.74, MUPDRS-III = 30.26) and 19 healthy controls (Mage = 68.16) without dementia. The extensive protocol included a battery of cognitive, language, and speech measures in addition to four discourse tasks. Two tasks each from two discourse genres (picture sequence description; story retelling) were collected. Discourse samples were analysed using both microlinguistic and macrostructural measures. Discourse variables were collapsed statistically to a primal set of variables used to distinguish the spoken discourse of PD vs. controls. Results: Participants with PD differed significantly from controls along a continuum of productivity, grammar, informativeness, and verbal disruption domains including total words F(1,36) = 3.87, p = .06; words/minute F(1,36) = 7.74, p = .01 , % grammatical utterances F(1,36) = 11.92, p = .001, total CIUs F(1,36) = 13.30, p = .001, % CIUs (Correct Information Units) F(1,36) = 9.35, p = .004, CIUs/minute F(1,36) = 14.06, p = .001, and verbal disruptions/100 words F(1,36) = 3.87, p = .06 (α = .10). Discriminant function analyses showed that optimally weighted discourse variables discriminated the spoken discourse of PD vs. controls with 81.6% sensitivity and 86.8% specificity. For both discourse genres, discourse performance showed robust, positive, correlations with global cognition. In PD (picture sequence description), more impaired discourse performance correlated significantly with more severe motor impairment, more advanced disease staging, and higher doses of PD medications. Conclusions: The spoken discourse in PD without dementia differs significantly and predictably from controls. Results have both research and clinical implications

The Computational Attitude in Music Theory

Music studies’s turn to computation during the twentieth century has engendered particular habits of thought about music, habits that remain in operation long after the music scholar has stepped away from the computer. The computational attitude is a way of thinking about music that is learned at the computer but can be applied away from it. It may be manifest in actual computer use, or in invocations of computationalism, a theory of mind whose influence on twentieth-century music theory is palpable. It may also be manifest in more informal discussions about music, which make liberal use of computational metaphors. In Chapter 1, I describe this attitude, the stakes for considering the computer as one of its instruments, and the kinds of historical sources and methodologies we might draw on to chart its ascendance. The remainder of this dissertation considers distinct and varied cases from the mid-twentieth century in which computers or computationalist musical ideas were used to pursue new musical objects, to quantify and classify musical scores as data, and to instantiate a generally music-structuralist mode of analysis. I present an account of the decades-long effort to prepare an exhaustive and accurate catalog of the all-interval twelve-tone series (Chapter 2). This problem was first posed in the 1920s but was not solved until 1959, when the composer Hanns Jelinek collaborated with the computer engineer Heinz Zemanek to jointly develop and run a computer program. Recognizing the transformation wrought on modern statistics and communications technology by information theory, I revisit Abraham Moles’s book Information Theory and Esthetic Perception (orig. 1958) and use its vocabulary to contextualize contemporary information-theoretic work on music that various evokes the computational mind by John. R. Pierce and Mary Shannon, Wilhelm Fucks, and Henry Quastler (Chapter 3). I conclude with a detailed look into a score-segmentation algorithm of the influential American music theorist Allen Forte (Chapter 4). Forte was a skilled programmer who spent several years at MIT in the 1960s, with cutting-edge computers and the company of first-rank figures in the nascent fields of computer science and artificial intelligence. Each one of the researchers whose work is treated in these case studies—at some stage in their relationship with music—adopted what I call the computational attitude to music, to varying degrees and for diverse ends. Of the many questions this dissertation seeks to answer: what was gained by adopting such an attitude? What was lost? Having understood these past explorations of the computational attitude to music, we are better suited ask of ourselves the same questions today