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IEEE International Symposium on Information Theory (ISIT)

作者： Cadambe, Viveck R. Huang, Cheng Li, Jin Univ Calif Irvine Irvine CA 92697 USA Microsoft Res Commun Collaborat & Syst Grp Redmond WA USA

ISBN: (纸本)9781457705953

We consider exact repair of failed nodes in maximum distance separable (MDS) code based distributed storage systems. It is well known that an (n, k) MDS code can tolerate failure (erasure) of up to n - k storage disks, when the code is used to store k information elements over n distributed storage disks. The focus of this paper is optimal recovery, in terms of repair bandwidth - the amount of data to be downloaded to repair a failed node - for a single failed node. When a single node fails, it has been previously shown by Dimakis et. al. that the amount of repair bandwidth is at least L(n - 1)/n - k units, when each storage disk stores L units of data. The achievability of this lower bound of L(n - 1)/n - k units, for arbitrary values of (n, k);has been shown previously using asymptotic code constructions based on asymptotic interference alignment. However, the existence of finite codes satisfying this lower bound has been shown only for specific regimes of (n, k) and their existence for arbitrary values of (n, k) remained open. In this paper, we provide the first known construction of a finite code for arbitrary (n, k), which can repair a single failed systematic node by downloading exactly L(n - 1)/n - k units of data. The code that we construct is based on permutation matrices and hence termed the permutation code.

关键词： Bandwidth Equations Interference cancellation Maintenance engineering Redundancy Systematics asymptotic code constructions asymptotic interference alignment codes computational complexity distributed storage disks distributed storage systems finite codes information elements matrix algebra maximum distance separable code optimal exact-repair permutation code permutation matrices single failed systematic node

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Fragile watermarking with permutation code for content-leakage in digital rights management system

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MULTIMEDIA SYSTEMS 2016年第5期22卷 603-615页

作者： Ta Minh Thanh Iwakiri, Munetoshi Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku 2-12-2 Ookayama Tokyo 1528552 Japan Le Quy Don Tech Univ Dept Network Secur 236 Hoang Quoc Viet Hanoi Vietnam Natl Def Acad Dept Comp Sci 1-10-20 Hashirimizu Yokosuka Kanagawa 2398686 Japan

In this paper, we present a new scheme of digital rights management (DRM) system employing the fragile watermarking with permutation code for the image distribution via network. General DRM systems are designed to protect the copyright of contents and to trace the source of the illegal distributors based on the user-side watermarking. However, in the typical DRM systems, the original digital contents are temporarily disclosed without the watermarking information inside user's system by the decryption process. Therefore, the user can copy the leaked original content inside the system and illegally redistribute via network without the permission of the content providers. Our work describes the idea of a DRM method which is composed of the incomplete cryptography based on permutation codes and user identification mechanism to control the quality of digital contents. There are two fundamental steps in our proposed cryptography: incomplete encoding and incomplete decoding. These two steps will create the scrambled content that is used as trial content and the watermarked content that is used to prevent unauthorized duplication or business of digital contents, respectively. Experimental results show that the proposed method is suitable for DRM in the network distribution system.

关键词： Digital rights management (DRM) Incomplete cryptography Invisible fragile watermarking permutation code

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permutation codes invariant under isometries

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DESIGNS codeS AND CRYPTOGRAPHY 2015年第3期75卷 497-507页

作者： Janiszczak, Ingo Lempken, Wolfgang Ostergard, Patric R. J. Staszewski, Reiner Univ Duisburg Essen Inst Expt Math D-45326 Essen Germany Aalto Univ Sch Elect Engn Dept Commun & Networking Aalto 00076 Finland

The symmetric group on letters is a metric space with respect to the Hamming distance. The corresponding isometry group is well known to be isomorphic to the wreath product . A subset of is called a permutation code or a permutation array, and the largest possible size of a permutation code with minimum Hamming distance is denoted by . Using exhaustive search by computer on sets of orbits of isometry subgroups we are able to determine serveral new lower bounds for for . The codes are given by the group and representatives of the U-orbits.

关键词： Backtrack search Bounds Isometry permutation code

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permutation-Based Block code for Short Packet Communication Systems

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SENSORS 2022年第14期22卷 5391-5391页

作者： Faure, Emil Shcherba, Anatoly Makhynko, Mykola Stupka, Bohdan Nikodem, Joanna Shevchuk, Ruslan Cherkasy State Technol Univ Fac Informat Technol & Syst UA-18006 Cherkassy Ukraine State Sci & Res Inst Cybersecur Technol & Informa UA-03142 Kiev Ukraine GoodLabs Studio Inc Toronto ON M5H 3E5 Canada Univ Bielsko Biala Dept Comp Sci & Automat PL-43309 Bielsko Biala Poland

This paper presents an approach to the construction of block error-correcting code for data transmission systems with short packets. The need for this is driven by the necessity of information interaction between objects of machine-type communication network with a dynamically changing structure and unique system of commands or alerts for each network object. The codewords of a code are permutations with a given minimum pairwise Hamming distance. The purpose of the study is to develop a statistical method for constructing a code, in contrast to known algebraic methods, and to investigate the code size. An algorithm for generating codewords has been developed. It can be implemented both by enumeration of the full set of permutations, and by enumeration of a given number of randomly selected permutations. We have experimentally determined the dependencies of the average and the maximum values of the code size on the size of a subset of permutations used for constructing the code. A technique for computing approximation quadratic polynomials for the determined code size dependencies has been developed. These polynomials and their corresponding curves estimate the size of a code generated from a subset of random permutations of such a size that a statistically significant experiment cannot be performed. The results of implementing the developed technique for constructing a code based on permutations of lengths 7 and 11 have been presented. The prediction relative error of the code size did not exceed the value of 0.72% for permutation length 11, code distance 9, random permutation subset size 50,000, and permutation statistical study range limited by 5040.

关键词： secure channel coding scheme permutation codeword factorial code block error-correcting code permutation code code size

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Proof of a conjecture of Klove on permutation codes under the Chebychev distance

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DESIGNS codeS AND CRYPTOGRAPHY 2017年第3期83卷 685-690页

作者： Guo, Victor J. W. Yang, Yiting Huaiyin Normal Univ Sch Math Sci Huaian 223300 Jiangsu Peoples R China Tongji Univ Dept Math Shanghai 200092 Peoples R China

Let d be a positive integer and x a real number. Let A(d,x) be a d x 2d matrix with its entries a(i, j) = {x for 1 <= j <= d + 1 - i, 1 for d + 2 - i <= j <= d + i, 0 for d + 1 + i <= j <= 2d. Furthe... 详细信息

Let d be a positive integer and x a real number. Let A(d,x) be a d x 2d matrix with its entries a(i, j) = {x for 1 <= j <= d + 1 - i, 1 for d + 2 - i <= j <= d + i, 0 for d + 1 + i <= j <= 2d. Further, let R-d be a set of sequences of integers as follows: R-d = {(rho(1), rho(2), ... , rho(d))vertical bar 1 <= rho(i) <= d + i, 1 <= i <= d, and rho(r) not equal rho(s) for r not equal s}. and define Omega(d)(x) = Sigma(rho is an element of Rd) alpha 1(,rho 1) alpha(2,rho 2) ... alpha(d,rho d). In order to give a better bound on the size of spheres of permutation codes under the Chebychev distance, Klove introduced the above function and conjectured that Omega(d)(x) = Sigma(d)(m=0) ( [GRAPHICS] )(m + 1)(d) (x - 1)(d-m). In this paper, we settle down this conjecture positively.

关键词： permutation code Chebychev distance Permanent

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SELF-DUAL permutation codeS OVER FORMAL POWER SERIES RINGS AND FINITE PRINCIPAL IDEAL RINGS

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Acta Mathematica Scientia 2013年第6期33卷 1695-1710页

作者：张光辉刘宏伟 School of Mathematical Sciences Luoyang Normal University School of Mathematics and Statistics Central China Normal University

In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.

关键词： self-dual code group code permutation code formal power series ring finiteprincipal ideal ring

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Low-complexity maximum-likelihood decoding of shortened enumerative permutation codes for holographic storage

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2001年第4期19卷 783-790页

作者： King, BM Neifeld, MA Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA Univ Arizona Ctr Opt Sci Tucson AZ 85721 USA

Volume holographic memories (VHM) are page-oriented optical storage systems whose pages commonly contain on the order of one million pixels. Typically, each stored data page is composed of an equal number of binary pixels in either a low-contrast ("off") state or a high-contrast ("on") state. By increasing the number of "off" pixels and decreasing the number of "on" pixels per page, there is an associated gain in VHM system storage capacity. When grayscale pixels are used, a further gain is possible by similarly controlling the fraction of pixels at each gray level. This paper introduces a constant-weight, nonbinary, shortened enumerative permutation modulation block code to produce pages that exploit the proposed capacity advantage. Tn addition to the code description, we present an encoder and a low-complexity maximum-likelihood (ML) decoder For the shortened permutation code. A proof verifies our claim of ML decoding. Applying this class of code to VHMs predicts a 49% increase in storage capacity when recording modulation coded 3-bit (eight gray level) pixels compared with a VHM using a binary signaling alphabet and equal-probable (unbiased) data.

关键词： DC codes enumeration code holographic data storage low weight codes modulation coding optical data storage page-oriented memories permutation code sparse codes

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ON SELF-DUAL permutation codeS

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Acta Mathematica Scientia 2008年第3期28卷 633-638页

作者：樊恽袁媛 School of Mathematics and Statistics Central China Normal University School of Informatics Guangdong University of Foreign Studies

permutation codes over finite fields are introduced, some conditions for existence or non-existence of self-dual permutation codes are obtained.

关键词： Finite field group code permutation code self-dual code

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New Lower Bounds for permutation codes Using Linear Block codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第7期66卷 4019-4025页

作者： Micheli, Giacomo Neri, Alessandro Univ S Florida Dept Math Tampa FL 33620 USA INRIA Saclay Ile de France F-91120 Palaiseau France

In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an [n,k,d](q) linear block code, we are able to prove the existence of a permutation code in the symmetric group of degree n, having minimum distance at least d and large cardinality. With our technique, we obtain new lower bounds for permutation codes that enhance the ones in the literature and provide asymptotic improvements in certain regimes of length and distance of the permutation code.

关键词： Parity check codes Hamming distance Hamming weight Generators Linear codes Symmetric matrices permutation code powerline communications linear block code maximum distance separable (MDS) code almost MDS code permutation array

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Bounds on permutation codes of distance four

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JOURNAL OF ALGEBRAIC COMBINATORICS 2010年第1期31卷 143-158页

作者： Dukes, P. Sawchuck, N. Univ Victoria Dept Math & Stat Victoria BC V8W 3R4 Canada

A permutation code of length n and distance d is a set I" of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x,yaI" is at least d. In this note, we determine some new results on the maximum size of a permutation code with distance equal to 4, the smallest interesting value. The upper bound is improved for almost all n via an optimization problem on Young diagrams. A new recursive construction improves known lower bounds for small values of n.

关键词： Symmetric group permutation code permutation array Characters Young diagram Linear programming

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