Expander Chunked Codes

Chunked codes are efficient random linear network coding (RLNC) schemes with low computational cost, where the input packets are encoded into small chunks (i.e., subsets of the coded packets). During the network transmission, RLNC is performed within each chunk. In this paper, we first introduce a simple transfer matrix model to characterize the transmission of chunks, and derive some basic properties of the model to facilitate the performance analysis. We then focus on the design of overlapped chunked codes, a class of chunked codes whose chunks are non-disjoint subsets of input packets, which are of special interest since they can be encoded with negligible computational cost and in a causal fashion. We propose expander chunked (EC) codes, the first class of overlapped chunked codes that have an analyzable performance,where the construction of the chunks makes use of regular graphs. Numerical and simulation results show that in some practical settings, EC codes can achieve rates within 91 to 97 percent of the optimum and outperform the state-of-the-art overlapped chunked codes significantly.Comment: 26 pages, 3 figures, submitted for journal publicatio

Batched Sparse Codes

Network coding can significantly improve the transmission rate of communication networks with packet loss compared with routing. However, using network coding usually incurs high computational and storage costs in the network devices and terminals. For example, some network coding schemes require the computational and/or storage capacities of an intermediate network node to increase linearly with the number of packets for transmission, making such schemes difficult to be implemented in a router-like device that has only constant computational and storage capacities. In this paper, we introduce BATched Sparse code (BATS code), which enables a digital fountain approach to resolve the above issue. BATS code is a coding scheme that consists of an outer code and an inner code. The outer code is a matrix generation of a fountain code. It works with the inner code that comprises random linear coding at the intermediate network nodes. BATS codes preserve such desirable properties of fountain codes as ratelessness and low encoding/decoding complexity. The computational and storage capacities of the intermediate network nodes required for applying BATS codes are independent of the number of packets for transmission. Almost capacity-achieving BATS code schemes are devised for unicast networks, two-way relay networks, tree networks, a class of three-layer networks, and the butterfly network. For general networks, under different optimization criteria, guaranteed decoding rates for the receiving nodes can be obtained.Comment: 51 pages, 12 figures, submitted to IEEE Transactions on Information Theor

비동일 분포 병렬 채널을 위한 폴라 부호 기법과 인덱스 코드를 위한 연계 폴라 부호 설계 기법

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 8. 이정우.본 논문은 Part I의 비동형 대칭 이진 이산 무기억 채널에서 채널 용량을 달성 하는 폴라 부호의 설계 기법 및 증명과 Part II의 비동형 이진 독립 무기억 채널에서 인덱스 부호와 폴라 부호의 연계기법을 통한 최적의 전송률을 달성하는 연계 기법에 대한 설계로 구성된다. Part I에서는 먼저 각 채널의 통계적 특성을 대변하는 채널 파라미터가 결정적인 형태로 부호기와 복호기에 주어지는 경우대 대해 다루며, 두번째로 이 파라미터들이 결정적이 아닌 랜덤한 값으로써 주어지는 경우에 대하여 적합한 폴라 부호 기법에 대해 기술한다. 후자는 다시 두가지의 하위 경우로 나뉘는데 하나는 모든 파라미터들이 단 하나의 확률 분포에 대한 실현값인 경우이고, 또다른 한가지는 각 파라미터들이 각각의 서로 다른 확률 분포의 실현값인 경우이다. 폴라 부호를 이용하여 결정적인 경우와 랜덤한 실현값으로 주이지는 모든 경우에 대하여 평균 채널 용량을 달성 할수있음을 증명한다. 이에 더해 결정적 채널 파라미터가 가정된 시스템에서 채널 입력으로 사용되는 정보 벡터의 치환 연산의 중요성에 대하여 논한다. 적절한 치환 연산을 이론적 상한값인 채널용량에 대한 수렴속도를 향상 시킬수 있음을 예시를 통해 보이고 휴리스틱 치환 알고리즘을 개발하여 달성 전송률 또는 시스템 신뢰도를 향상 시킬수 있음을 보인다. Part II에서는 폴라 부호와 인덱스 부호를 접합시켜 일종의 연계된 소스-채널 부호 설계 기법을 개발하고 제안된 기법이 최적의 전송률을 달성함을 보인다. 먼저 인덱스 부호에서 수신노드에서 송신노드로 전달되는 부가정보를 통해 그려지는 그래프가 완전그래프일때 항상 최적의 달성 기법이 존재함을 보이고, 이를 임의의 부가정보 패턴이 주어지는 경우로 확장한다. 완전 그래프가 그려지는 경우와 달리 임의의 패턴으로 주어지는 경우는 부가정보들이 특정 조건을 만족하는 경우에 한하여 최적 전송률을 달성하게됨을 보이고 이를 만족하는 인덱스-폴라 부호 설계 기법을 제안한다. 마지막으로 부가정보가 결정적으로 주어지지 않고 존재성을 표현하는 확률로써 주어지는 경우 제안된 연계기법을 이용한 평균 전송률에 대하여 논한다.Abstract i Contents iv List of Figures viii List of Tables xii I Polar codes for Non i.i.d. Parallel channels 1 Chapter 1 Introduction 1.1 Backgrounds 1.2 Scope and Organization Chapter 2 Polar codes with deterministic non-identically distributed channels 2.1 Non-identical channels with deterministic CP 2.1.1 The evolution of Symmetric Capacities 2.1.2 Achievable Scheme based on the symmetric capacity 2.1.3 The evolution of Bhattacharayya Parameters 2.1.4 Supermartingale Zn 2.1.5 Convergence of Zn 2.2 Channel mapping via the Interleaver Q 2.2.1 Exhaustive Search Method with Grouping 2.2.2 Heuristic method 2.3 Link failures: Puncturing operation 2.4 Polarizations on non-independent channels 2.5 Summary Chapter 3 Non-identical Binary Erasure Channels with random Erasure probabilities with Single distribution 3.1 Non-identical Binary Erasure Channels with random Erasure probabilities with Single distribution 3.1.1 Proof of Theorem 2 3.1.2 The Achievable Polar coding scheme 3.2 Random Erasure probabilities with non-identical distributions 3.2.1 Case1: Variable coding structure 3.2.2 Case2: Fixed coding structure 3.3 Summary II Polar codes schemes for Index Coded Systems Chapter 4 Nested Polar codes structures for Index codes 4.1 Introduction to Index codes 4.2 Nested structures for NC and Polar codes 4.3 ICPC for fully connected SI 4.3.1 General channel setting 4.3.2 Degraded channel setting 4.3.3 IC gain analysis 4.4 ICPC for Arbitrary SI 4.4.1 Proof of the Lemma 6 4.4.2 Proof of the Theorem 5 4.4.3 Achievable ICPC scheme for degraded structures 4.4.4 Proof of the Corollary 2 4.4.5 The ICPC scheme 4.4.6 Example: Partially Perfect Graph 4.5 ICPC for Probabilistic Side Information 4.5.1 Random ICPC for non-identical B-DMCs 4.5.2 Expected rate maximization 4.5.3 Expected achievable rate via Random graph 4.6 Summary Chapter 5 Conclusions 121 Appendix A A.1 Proof of (2.25) A.2 Proof of (2.36) A.3 Proof of (2.37) A.4 Proof of the number of equivalent channel combinations Bibliography Abstract in Korean 138Docto

Automatic Extraction and Assessment of Entities from the Web

The search for information about entities, such as people or movies, plays an increasingly important role on the Web. This information is still scattered across many Web pages, making it more time consuming for a user to find all relevant information about an entity. This thesis describes techniques to extract entities and information about these entities from the Web, such as facts, opinions, questions and answers, interactive multimedia objects, and events. The findings of this thesis are that it is possible to create a large knowledge base automatically using a manually-crafted ontology. The precision of the extracted information was found to be between 75–90 % (facts and entities respectively) after using assessment algorithms. The algorithms from this thesis can be used to create such a knowledge base, which can be used in various research fields, such as question answering, named entity recognition, and information retrieval