저밀도 부호의 응용: 묶음 지그재그 파운틴 부호와 WOM 부호

Abstract

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 노종선.This dissertation contains the following two contributions on the applications of sparse codes. Fountain codes Batched zigzag (BZ) fountain codes – Two-phase batched zigzag (TBZ) fountain codes Write-once memory (WOM) codes – WOM codes implemented by rate-compatible low-density generator matrix (RC-LDGM) codes First, two classes of fountain codes, called batched zigzag fountain codes and two-phase batched zigzag fountain codes, are proposed for the symbol erasure channel. At a cost of slightly lengthened code symbols, the involved message symbols in each batch of the proposed codes can be recovered by low complexity zigzag decoding algorithm. Thus, the proposed codes have low buffer occupancy during decoding process. These features are suitable for receivers with limited hardware resources in the broadcasting channel. A method to obtain degree distributions of code symbols for the proposed codes via ripple size evolution is also proposed by taking into account the released code symbols from the batches. It is shown that the proposed codes outperform Luby transform codes and zigzag decodable fountain codes with respect to intermediate recovery rate and coding overhead when message length is short, symbol erasure rate is low, and available buffer size is limited. In the second part of this dissertation, WOM codes constructed by sparse codes are presented. Recently, WOM codes are adopted to NAND flash-based solid-state drive (SSD) in order to extend the lifetime by reducing the number of erasure operations. Here, a new rewriting scheme for the SSD is proposed, which is implemented by multiple binary erasure quantization (BEQ) codes. The corresponding BEQ codes are constructed by RC-LDGM codes. Moreover, by putting RC-LDGM codes together with a page selection method, writing efficiency can be improved. It is verified via simulation that the SSD with proposed rewriting scheme outperforms the SSD without and with the conventional WOM codes for single level cell (SLC) and multi-level cell (MLC) flash memories.1 Introduction 1 1.1 Background 1 1.2 Overview of Dissertation 5 2 Sparse Codes 7 2.1 Linear Block Codes 7 2.2 LDPC Codes 9 2.3 Message Passing Decoder 11 3 New Fountain Codes with Improved Intermediate Recovery Based on Batched Zigzag Coding 13 3.1 Preliminaries 17 3.1.1 Definitions and Notation 17 3.1.2 LT Codes 18 3.1.3 Zigzag Decodable Codes 20 3.1.4 Bit-Level Overhead 22 3.2 New Fountain Codes Based on Batched Zigzag Coding 23 3.2.1 Construction of Shift Matrix 24 3.2.2 Encoding and Decoding of the Proposed BZ Fountain Codes 25 3.2.3 Storage and Computational Complexity 28 3.3 Degree Distribution of BZ Fountain Codes 31 3.3.1 Relation Between $\Psi(x)$ and $\Omega(x)$ 31 3.3.2 Derivation of $\Omega(x)$ via Ripple Size Evolution 32 3.4 Two-Phase Batched Zigzag Fountain Codes with Additional Memory 40 3.4.1 Code Construction 41 3.4.2 Bit-Level Overhead 46 3.5 Numerical Analysis 49 4 Write-Once Memory Codes Using Rate-Compatible LDGM Codes 60 4.1 Preliminaries 62 4.1.1 NAND Flash Memory 62 4.1.2 Rewriting Schemes for Flash Memory 62 4.1.3 Construction of Rewriting Codes by BEQ Codes 65 4.2 Proposed Rewriting Codes 67 4.2.1 System Model 67 4.2.2 Multi-rate Rewriting Codes 68 4.2.3 Page Selection for Rewriting 70 4.3 RC-LDGM Codes 74 4.4 Numerical Analysis 76 5 Conclusions 80 Bibliography 82 초록 94Docto