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# IEEE Transactions on Information Theory

## Filter Results

Displaying Results 1 - 25 of 42
• ### Table of contents

Publication Year: 2011, Page(s):C1 - C4
| PDF (46 KB)
• ### IEEE Transactions on Information Theory publication information

Publication Year: 2011, Page(s): C2
| PDF (42 KB)
• ### The Scientific Legacy of Ralf Koetter

Publication Year: 2011, Page(s):589 - 592
| | PDF (588 KB) | HTML

This special issue is intended as a tribute to the work of Ralf Koetter. Ralf's premature death on February 2, 2009 deprived our community not only of one of its most beloved members, but also of an imaginative individual contributor, valued collaborator, and respected leader who had already had a significant impact on coding theory and practice, and who could have potentially contributed so much ... View full abstract»

• ### Two-Point Coordinate Rings for GK-Curves

Publication Year: 2011, Page(s):593 - 600
Cited by:  Papers (2)
| | PDF (224 KB) | HTML

Giulietti and Korchmáros presented new curves with the maximal number of points over a field of size q6. Garcia, Güneri, and Stichtenoth extended the construction to curves that are maximal over fields of size q2n, for odd n ≥ 3. The generalized GK-curves have affine equations xq+x = yq+1 and yq2-y = zr, for r=(qn+1)/(q+1). We give a new proof for the maximality of the gener... View full abstract»

• ### On Expanded Cyclic and Reed–Solomon Codes

Publication Year: 2011, Page(s):601 - 620
Cited by:  Papers (4)
| | PDF (2035 KB) | HTML

This paper offers new insights into expanded cyclic and Reed-Solomon codes. First, we present a new description of general expanded codes defined over GF(qm). The proposed explicit description of the expanded generator matrix and the expanded parity check matrix reserves the symbol-wise algebraic structure. We reveal that the dual of an expanded code is the symbol-wise dual code expanded by... View full abstract»

• ### Skew-Feedback Shift-Register Synthesis and Decoding Interleaved Gabidulin Codes

Publication Year: 2011, Page(s):621 - 632
Cited by:  Papers (15)
| | PDF (331 KB) | HTML

An efficient algorithm which synthesizes all shortest skew-feedback shift-registers (defined in the paper) generating L sequences of varying length over a field is derived and its correctness is proved. It generalizes the Berlekamp-Massey algorithm and some other algorithms, and has time complexity O(LN2), where N is the length of a longest sequence. The prop... View full abstract»

• ### The Re-Encoding Transformation in Algebraic List-Decoding of Reed–Solomon Codes

Publication Year: 2011, Page(s):633 - 647
Cited by:  Papers (20)
| | PDF (437 KB) | HTML

The main computational steps in algebraic soft-decoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are bivariate polynomial interpolation and factorization. We introduce a computational technique, based upon re-encoding and coordinate transformation, that significantly reduces the complexity of the bivariate interpolation procedure. This re-encoding and coordinate transformation c... View full abstract»

• ### VLSI Architectures for Soft-Decision Decoding of Reed–Solomon Codes

Publication Year: 2011, Page(s):648 - 667
Cited by:  Papers (5)
| | PDF (551 KB) | HTML

Soft-decision decoding of Reed-Solomon codes delivers significant coding gains over classical minimum distance decoding. In this paper, we present architectures for polynomial interpolation and factorization, the two main steps of the soft-decoding algorithm. We introduce an algorithmic transformation for reducing the iterations required in generating the interpolation polynomial and present effic... View full abstract»

• ### On Multiple Decoding Attempts for Reed–Solomon Codes: A Rate-Distortion Approach

Publication Year: 2011, Page(s):668 - 691
Cited by:  Papers (3)  |  Patents (3)
| | PDF (1781 KB) | HTML

One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is based on using multiple trials of a simple RS decoding algorithm in combination with erasing or flipping a set of symbols or bits in each trial. This paper presents a framework based on rate-distortion (RD) theory to analyze these multiple-decoding algorithms. By defining an appropriate distortion measure between an error... View full abstract»

• ### Identifying Traitors Using the Koetter–Vardy Algorithm

Publication Year: 2011, Page(s):692 - 704
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This paper deals with the use of the Koetter-Vardy soft-decision decoding algorithm to perform identification of guilty users in traitor tracing and fingerprinting schemes. In these schemes, each user is assigned a copy of an object with an embedded codeword. Placing different codewords in different copies makes each copy unique and at the same time allows unique identification of each user. The w... View full abstract»

• ### Soft Decoding, Dual BCH Codes, and Better List-Decodable $varepsilon$-Biased Codes

Publication Year: 2011, Page(s):705 - 717
Cited by:  Papers (2)
| | PDF (325 KB) | HTML

Explicit constructions of binary linear codes that are efficiently list-decodable up to a fraction (1/2 - ε) of errors are given. The codes encode k bits into n = poly(k/ε) bits and are constructible and list-decodable in time polynomial in k and 1/ε (in particular, ε need not be constant and can even be polynomially small in n). These results give the best known polyno... View full abstract»

• ### On the List-Decodability of Random Linear Codes

Publication Year: 2011, Page(s):718 - 725
Cited by:  Papers (5)
| | PDF (234 KB) | HTML

The list-decodability of random linear codes is shown to be as good as that of general random codes. Specifically, for every fixed finite field Fq, p ∈ (0,1 - 1/q) and ε >; 0, it is proved that with high probability a random linear code C in Fqn of rate (1-Hq(p)-ε) can be list decoded from a frac... View full abstract»

• ### Minimal Realizations of Linear Systems: The “Shortest Basis” Approach

Publication Year: 2011, Page(s):726 - 737
Cited by:  Papers (8)
| | PDF (262 KB) | HTML

Given a discrete-time linear system C, a shortest basis for C is a set of linearly independent generators for C with the least possible lengths. A basis B is a shortest basis if and only if it has the predictable span property (i.e., has the predictable delay and degree properties, and is non-catastrophic), or alternatively if and only if it has the subsystem basis prop... View full abstract»

• ### Linear Tail-Biting Trellises: Characteristic Generators and the BCJR-Construction

Publication Year: 2011, Page(s):738 - 751
Cited by:  Papers (10)
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This paper investigates the constructions of tail-biting trellises for linear block codes as introduced by Koetter and Vardy (2003) and Nori and Shankar (2006). For a given code, the sets of characteristic generators are defined slightly more generally than by Koetter and Vardy. In particular, they are not uniquely determined by the code. The effect of the choice of characteristic generators on th... View full abstract»

• ### Normal Factor Graphs and Holographic Transformations

Publication Year: 2011, Page(s):752 - 763
Cited by:  Papers (27)
| | PDF (421 KB) | HTML

This paper stands at the intersection of two distinct lines of research. One line is “holographic algorithms,” a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is “normal factor graphs,” an elegant framework proposed by Forney for representing codes defined on graphs. We introduce the notion of holographic tr... View full abstract»

• ### The Dynamics of Message Passing on Dense Graphs, with Applications to Compressed Sensing

Publication Year: 2011, Page(s):764 - 785
Cited by:  Papers (185)  |  Patents (1)
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“Approximate message passing” (AMP) algorithms have proved to be effective in reconstructing sparse signals from a small number of incoherent linear measurements. Extensive numerical experiments further showed that their dynamics is accurately tracked by a simple one-dimensional iteration termed state evolution. In this paper, we provide rigorous foundation to state evolution. We pro... View full abstract»

• ### Divide and Concur and Difference-Map BP Decoders for LDPC Codes

Publication Year: 2011, Page(s):786 - 802
Cited by:  Papers (11)
| | PDF (1947 KB) | HTML

The “Divide and Concur” (DC) algorithm introduced by Gravel and Elser can be considered a competitor to the belief propagation (BP) algorithm, in that both algorithms can be applied to a wide variety of constraint satisfaction, optimization, and inference problems. We show that DC can be interpreted as a message-passing algorithm on a “normal” factor graph. The “... View full abstract»

• ### Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform So Well over the BEC

Publication Year: 2011, Page(s):803 - 834
Cited by:  Papers (260)  |  Patents (3)
| | PDF (1020 KB) | HTML

Convolutional low-density parity-check (LDPC) ensembles, introduced by Felström and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed to date, all of which share the good performance characteristics of convolutional LDPC ensembles. We describe the fundamental mechanism ... View full abstract»

• ### Deriving Good LDPC Convolutional Codes from LDPC Block Codes

Publication Year: 2011, Page(s):835 - 857
Cited by:  Papers (61)  |  Patents (4)
| | PDF (1403 KB) | HTML

Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper, we discuss several graph-cover-based methods for deriving families of time-invariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional code constructions can be presented within th... View full abstract»

• ### Enumerators for Protograph-Based Ensembles of LDPC and Generalized LDPC Codes

Publication Year: 2011, Page(s):858 - 886
Cited by:  Papers (36)
| | PDF (893 KB) | HTML

Protograph-based LDPC and generalized LDPC (G-LDPC) codes have the advantages of a simple design procedure and highly structured encoders and decoders. The design of such “protograph-based codes” relies on what is effectively a computer-based search. As such, following Gallager, it is prudent to restrict the search to a “good ensemble,” for example, an ensemble whose mi... View full abstract»

• ### LP Decoding of Regular LDPC Codes in Memoryless Channels

Publication Year: 2011, Page(s):887 - 897
Cited by:  Papers (12)
| | PDF (544 KB) | HTML

We study error bounds for linear programming decoding of regular low-density parity-check (LDPC) codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly exponential in the girth of the factor graph. For memoryless binary-input AWGN channel, we prove lower bounds on the threshold for regular LDPC codes whose factor graphs h... View full abstract»

• ### Lifting the Fundamental Cone and Enumerating the Pseudocodewords of a Parity-Check Code

Publication Year: 2011, Page(s):898 - 909
Cited by:  Papers (2)
| | PDF (257 KB) | HTML

The performance of message-passing iterative decoding and linear programming decoding depends on the Tanner graph representation of the code. If the underlying graph contains cycles, then such algorithms could produce a noncodeword output. The study of pseudocodewords aims to explain this noncodeword output. We examine the structure of the pseudocodewords and show that there is a one-to-one corres... View full abstract»

• ### On the Number of Errors Correctable with Codes on Graphs

Publication Year: 2011, Page(s):910 - 919
Cited by:  Papers (9)
| | PDF (269 KB) | HTML

We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum distance of codes in these ensembles grows linearly with the code length. We show that these codes can correct a linearly growing number of errors under simple ... View full abstract»

• ### Turbo Equalization: An Overview

Publication Year: 2011, Page(s):920 - 952
Cited by:  Papers (85)
| | PDF (951 KB) | HTML

Turbo codes and the iterative algorithm for decoding them sparked a new era in the theory and practice of error control codes. Turbo equalization followed as a natural extension to this development, as an iterative technique for detection and decoding of data that has been both protected with forward error correction and transmitted over a channel with intersymbol interference (ISI). In this paper... View full abstract»

• ### The Error-Pattern-Correcting Turbo Equalizer: Spectrum Thinning at High SNRs

Publication Year: 2011, Page(s):953 - 971
Cited by:  Papers (2)
| | PDF (1251 KB) | HTML

The error-pattern correcting code (EPCC) is a code designed to correct frequently observed error cluster patterns of the intersymbol interference (ISI) channel. This paper focuses on developing theoretical understanding of the performance of serial concatenation of the EPCC with an outer recursive systematic convolutional code (RSCC) in ISI channel environments. To analyze the performance of this ... View full abstract»

## Aims & Scope

IEEE Transactions on Information Theory publishes papers concerned with the transmission, processing, and utilization of information.

Full Aims & Scope

## Meet Our Editors

Editor-in-Chief
Prakash Narayan

Department of Electrical and Computer Engineering