22 research outputs found
Zigzag Decodable Fountain Codes
This paper proposes a fountain coding system which has lower space decoding
complexity and lower decoding erasure rate than the Raptor coding systems. The
main idea of the proposed fountain code is employing shift and exclusive OR to
generate the output packets. This technique is known as the zigzag decodable
code, which is efficiently decoded by the zigzag decoder. In other words, we
propose a fountain code based on the zigzag decodable code in this paper.
Moreover, we analyze the overhead for the received packets, decoding erasure
rate, decoding complexity, and asymptotic overhead of the proposed fountain
code. As the result, we show that the proposed fountain code outperforms the
Raptor codes in terms of the overhead and decoding erasure rate. Simulation
results show that the proposed fountain coding system outperforms Raptor coding
system in terms of the overhead and the space decoding complexity.Comment: 11 pages, 15 figures, submitted to IEICETransactions, Oct. 201
Cooperative Local Repair in Distributed Storage
Erasure-correcting codes, that support local repair of codeword symbols, have
attracted substantial attention recently for their application in distributed
storage systems. This paper investigates a generalization of the usual locally
repairable codes. In particular, this paper studies a class of codes with the
following property: any small set of codeword symbols can be reconstructed
(repaired) from a small number of other symbols. This is referred to as
cooperative local repair. The main contribution of this paper is bounds on the
trade-off of the minimum distance and the dimension of such codes, as well as
explicit constructions of families of codes that enable cooperative local
repair. Some other results regarding cooperative local repair are also
presented, including an analysis for the well-known Hadamard/Simplex codes.Comment: Fixed some minor issues in Theorem 1, EURASIP Journal on Advances in
Signal Processing, December 201
Storage Codes with Flexible Number of Nodes
This paper presents flexible storage codes, a class of error-correcting codes
that can recover information from a flexible number of storage nodes. As a
result, one can make a better use of the available storage nodes in the
presence of unpredictable node failures and reduce the data access latency. Let
us assume a storage system encodes information symbols over a finite
field into nodes, each of size symbols. The code is
parameterized by a set of tuples ,
satisfying and , such that the information symbols can be reconstructed from any
nodes, each node accessing symbols. In other words, the code
allows a flexible number of nodes for decoding to accommodate the variance in
the data access time of the nodes. Code constructions are presented for
different storage scenarios, including LRC (locally recoverable) codes, PMDS
(partial MDS) codes, and MSR (minimum storage regenerating) codes. We analyze
the latency of accessing information and perform simulations on Amazon clusters
to show the efficiency of presented codes
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μ .This dissertation contains the following two contributions on the applications of sparse codes.
Fountain codes Batched zigzag (BZ) fountain codes
β Two-phase batched zigzag (TBZ) fountain codes
Write-once memory (WOM) codes
β 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 and 31
3.3.2 Derivation of 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
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