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IEEE 54th Annual Symposium on Foundations of Computer Science (FOCS)

作者： Guruswami, Venkatesan Kopparty, Swastik Carnegie Mellon Univ Dept Comp Sci Pittsburg KS USA Rutgers State Univ Dept Math & Comp Sci Piscataway NJ USA

ISBN: (纸本)9780769551357

A subspace design is a collection {H-1, H-2,..., H-M} of subspaces of F-q(m) with the property that no low-dimensional subspace W of F-q(m) intersects too many subspaces of the collection. Subspace designs were introduced by Guruswami and Xing (STOC 2013) who used them to give a randomized construction of optimal rate list-decodable codes over constant-sized large alphabets and sub-logarithmic (and even smaller) list size. Subspace designs are the only non-explicit part of their construction. In this paper, we give explicit constructions of subspace designs with parameters close to the probabilistic construction, and this implies the first deterministic polynomial time construction of list-decodable codes achieving the above parameters. Our constructions of subspace designs are natural and easily described, and are based on univariate polynomials over finite fields. Curiously, the constructions are very closely related to certain good list-decodable codes (folded RS codes and univariate multiplicity codes). The proof of the subspace design property uses the polynomial method (with multiplicities): Given a target low-dimensional subspace W, we construct a nonzero low-degree polynomial P-W that has several roots for each H-i that non-trivially intersects W. The construction of P-W is based on the classical Wronskian determinant and the folded Wronskian determinant, the latter being a recently studied notion that we make explicit in this paper. Our analysis reveals some new phenomena about the zeroes of univariate polynomials, namely that polynomials with many structured roots or many high multiplicity roots tend to be linearly independent.

关键词： algebraic coding List-decoding Polynomial Method Pseudorandomness Reed-Solomon codes

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Fundamental bounds on power reduction during data-retention in standby SRAM

Fundamental bounds on power reduction during data-retention ...

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IEEE International Symposium on Circuits and Systems

作者： Kumar, A. Qin, H. Ishwar, P. Rabaey, J. Ramchandran, K. Univ Calif Berkeley EECS Berkeley CA 94720 USA Boston Univ ECE Boston MA 02215 USA

ISBN: (纸本)9781424409204

We study leakage-power reduction in standby random access memories (SRAMs) during data-retention. An SRAM cell requires a minimum critical supply voltage (DRV) above which it preserves the stored-bit reliably. Due to process-variations, the intra-chip DRV exhibits variation with a distribution having a diminishing tail. In order to minimize leakage power while preserving data reliably, existing low-power design methods use a worst-case standby supply voltage. This worst-case voltage is larger than the highest DRV among all cells in an SRAM. In contrast, our approach uses aggressive voltage reduction and counters the ensuing unreliability by an error-control code based memory architecture. Using this approach, we explore fundamental trade-offs between power reduction and redundancy present in the SRAM. We establish fundamental bounds on the power reduction in terms of the DRV-distribution using techniques from information theory and algebraic coding theory. For an experimental test-chip DRV-distribution in the 90nm CMOS technology, we show that 49% power reduction with respect to (w.r.t.) the worst-case is a fundamental lower bound while 40% power reduction w.r.t. the worst-case is achievable by using a practical algebraic coding scheme. We also study the power reduction as a function of the block-length for low-latency codes since most applications using SRAM are latency constrained. We propose a reliable low-power memory architecture based on the Hamming code for the next test-chip implementation with a predicted power reduction of 33% while accounting for coding overheads.

关键词： CMOS memory circuits Hamming codes SRAM chips algebraic codes error correction codes low-power electronics CMOS technology SRAM cell algebraic coding data retention error-control code information theory leakage-power reduction standby suppl

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Bounds on Cardinality of Multicomponent Network Codes 14

Bounds on Cardinality of Multicomponent Network Codes

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XIV Int Symposium Problems Redundancy Inform Control Syst

作者： Afanassiev, Valentin B. Gabidulin, Ernst M. Pilipchuk, Nina I. Russian Acad Sci Inst Informat Transmiss Problems Moscow Russia State Univ Moscow Inst Phys & Technol Dolgoprudnyi Russia

Network coding is a new direction of communications and information theory. algebraic coding in this area is based on Grassmann metric known also as subspace metric. The paper is devoted to some bounds on cardinality ... 详细信息

ISBN: (纸本)9781479940509

关键词： algebraic codes network coding Grassmann metric algebraic coding code cardinality communication theory information theory multicomponent network code subspace metric Control systems Measurement Network coding Redundancy Upper bound Vectors algebraic codes Network coding Communication Theory Information Theory control systems base number Upper bound redundancy Network Code

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Private-key cryptosystem for CD and DVD

Private-key cryptosystem for CD and DVD

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Conference on Mathematics of Data/Image coding, Compression, and Encryption

作者： Jiawook, RN Obducat AB S-20125 Malmo Sweden

ISBN: (纸本)0819429112

Symmetric code cryptosystems are particularly suitable when large data sets have to be transmitted or stored at high rate. The existing algebraic code based cryptosystems are time consuming and the encoding/decoding speed depends on the key length. They were mainly designed for communications and magnetic media, which have an expected lifetime of up to only a few years. As for transmission there is virtually no lifetime of the transferred information, since the data vanishes by itself. The data that is stored on CD or DVD can not be changed, and must remain secure for the lifetime of the sensitive/classified information or the media, which might extend to 100 years or more. This paper proposes a private-key cryptosystem based on algebraic coding theory, uses a simple code such as Reed-Solomon code. This new approach is ideal for use in optical media applications. It incorporates with the CD and DVD encoding system, and increases the power of the error correction as a by-product. The system appears to be secure and very efficient because of the low overhead for encryption and decryption.

关键词： private-key cryptosystem algebraic coding symmetric coding CD DVD optical storage optical media

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Efficient Reduction Algorithms for Special Gaussian Integer Moduli 29

Efficient Reduction Algorithms for Special Gaussian Integer ...

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29th IEEE Symposium on Computer Arithmetic (ARITH)

作者： Safieh, Malek De Santis, Fabrizio Siemens AG Technol Munich Germany

ISBN: (数字)9781665478274

ISBN: (纸本)9781665478274

Gaussian integers are a subset of the complex numbers with integers as real and imaginary parts. When Gaussian integers are equipped with modulo operations, they form Gaussian integer rings or fields, depending on the specific choice of the modulus. Arithmetic on Gaussian integers can offer advantages in terms of operand size and improved parallelism, due to independent calculation of the real and imaginary parts. However, although Gaussian integer modulo reduction is the fundamental operation to enable computations in finite Gaussian integer rings and fields, efficient algorithms for Gaussian integer modulo reduction have not been widely investigated so far. In this work, we fill this gap and present efficient reduction algorithms for Gaussian integer moduli of special forms. Indeed, we demonstrate that there exist different classes of Gaussian integer moduli allowing for very fast reductions. Finally, we show that the computational complexity of the proposed algorithm is significantly reduced compared with generic Gaussian integer reduction methods known to date, e.g., Montgomery-based reduction for Gaussian integers.

关键词： Gaussian Integers Modular Arithmetic Modulo Reduction Cryptography algebraic coding

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A Lightweight Secure Network coding Scheme against Wiretapping

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Wuhan University Journal of Natural Sciences 2014年第2期19卷 156-160页

作者： LIU Guangjun LIU Ximeng XIONG Jinbo ZHOU Hang School of Mathematics and Computer Engineering Xi'an University of Arts and Science School of Telecommunication Engineering Xidian University School of Software Fujian Normal University School of Science Engineering University of the ChinesePeople's Armed Police Force

Existing works for securing network coding against wiretapping either incur high coding complexity or bring large bandwidth overhead. For exploiting the lightweight security mechanism for resource-constrained networks, an efficient secure coding scheme is proposed in conjunction with the inherent mix- ing characteristic of network coding. The key idea is to minimize the randomizing operations to the entire plaintext data. The pro- posed scheme is shown to have properties of lightweight security complexity and lower communication overhead compared with the existing traditional solutions, and can be easy in implementation and combination with classical cryptography techniques.

关键词： network coding security wiretapping algebraic coding pseudo-random function

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Network Error Correction, II: Lower Bounds

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Communications in Information & Systems 2006年第1期6卷 37-54页

作者： Ning Cai Raymond W. Yeung

In Part I of this paper, we introduced the paradigm of network error correction as a generalization of classical link-by-link error correction. We also obtained the network generalizations of the Hamming bound and the Singleton bound in classical algebraic coding theory. In Part II, we prove the network generalization of the Gilbert-Varshamov bound and its enhancement. With the latter, we show that the tightness of the Singleton bound is preserved in the network setting. We also discuss the implication of the results in this paper.

关键词： 94B60 94A05 algebraic coding error correction Gilbert bound multicast Network coding Singleton bound Varshamov bound

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Network Error Correction, I: Basic Concepts and Upper Bounds

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Communications in Information & Systems 2006年第1期6卷 19-35页

作者： Raymond W. Yeung Ning Cai

Error correction in existing point-to-point communication networks is done on a link-by-link basis, which is referred to in this paper as classical error correction . Inspired by network coding, we introduce in this two-part paper a new paradigm called network error correction . The theory thus developed subsumes classical algebraic coding theory as a special case. In Part I, we discuss the basic concepts and prove the network generalizations of the Hamming bound and the Singleton bound in classical algebraic coding theory. By studying a few elementary examples, the relation between network error correction and classical error correction is investigated.

关键词： 94B60 94A05 algebraic coding error correction Hamming bound multicast Network coding Singleton bound

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SEQUENCING 2 DNA TEMPLATES IN 5 CHANNELS BY DIGITAL COMPRESSION

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 1993年第5期90卷 1647-1651页

作者： NELSON, M ZHANG, YP STEFFENS, DL GRABHERR, R VANETTEN, JL UNIV NEBRASKA DEPT PLANT PATHOL LINCOLN NE 68583 USA LI COR INC LINCOLN NE 68504 USA

By applying algebraic coding methods to the Sanger dideoxynucleotide procedure, DNA sequences of two templates can be determined simultaneously in only five reactions and data channels. A 5:2 data compression is accomplished by instantaneous source coding of nucleotide sequence pairs into one set of 5-bit block codes. A general algebraic expression, 2n - 1 greater-than-or-equal-to 4f, describes conditions under which f DNA templates can be sequenced using n channels. Such compression sequencing is accurate and efficient, as demonstrated by manual S-35 autoradiographic detection and automated on-line analysis using fluorescent-labeled primers. Symmetric 5:2 compression is especially useful when comparing two closely related sequences.

关键词： INFORMATION THEORY algebraic coding

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Low-complexity Secure Network coding Against Wiretapping Using Intra-/Inter-generation coding

Low-complexity Secure Network Coding Against Wiretapping Usi...

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第八届中国可信计算与信息安全学术会议

Existing solutions against wiretapping attacks for network coding either bring significant bandwidth overhead or incur a high computational *** order to reduce the security overhead of the existing solutions for securing network coding,a novel securing network coding paradigm is presented relying on two coding models:intra-generation coding and intergeneration *** basic idea to secure network coding using intra-generation coding is to limit the encryption operations for each generation,and then subject the scrambled and the remaining original source vectors to a linear *** method is then generalized seamlessly using intergeneration coding by further exploiting the algebraic structure of network *** show that the proposed schemes have properties of low-complexity security,little bandwidth consumption,and high efficiency in integrating with the existing security techniques effectively.

关键词： Index Terms-network coding security wiretapping attacks algebraic coding encryption

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