List decoding

About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.

Construction of Quasi-Cyclic LDPC Codes for AWGN and Binary Erasure Channels: A Finite Field Approach

Abstract: In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes. This paper shows that finite fields can also be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding. Methods of construction are presented. LDPC codes constructed by these methods are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN), binary random, and burst erasure channels with iterative decoding in terms of bit-error probability, block-error probability, error-floor, and rate of decoding convergence, collectively. Particularly, they have low error floors. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.

Coding Theory: A First Course

Abstract: Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

Channel Coding for Telecommunications

Abstract: From the Publisher: Channel coding is the theory by which codes can be constructed to correct and detect errors. Such errors may be caused by transmission channels and noise.. "This book presents classic theory and techniques for block and convolutional codes with an emphasis on decoding algorithms. Furthermore, the powerful technique of Generalized Concatenated Coding (GCC) is introduced, using illustrative examples.. "The range of topics covered in this book is beneficial to undergraduate and postgraduate students performing research at an advanced level in this subject area, as well as for engineers whose work involves communications error control coding.

Decoding error-correcting codes via linear programming

Abstract: Error-correcting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original information up to the full error-correcting potential of the system is often very complex, especially for modern codes that approach the theoretical limits of the communication channel. In this thesis we investigate the application of linear programming (LP) relaxation to the problem of decoding an error-correcting code. Linear programming relaxation is a standard technique in approximation algorithms and operations research, and is central to the study of efficient algorithms to find good (albeit suboptimal) solutions to very difficult optimization problems. Our new “LP decoders” have tight combinatorial characterizations of decoding success that can be used to analyze error-correcting performance. Furthermore, LP decoders have the desirable (and rare) property that whenever they output a result, it is guaranteed to be the optimal result: the most likely (ML) information sent over the channel. We refer to this property as the ML certificate property. We provide specific LP decoders for two major families of codes: turbo codes and low-density parity-check (LDPC) codes. These codes have received a great deal of attention recently due to their unprecedented error-correcting performance. Our decoder is particularly attractive for analysis of these codes because the standard message-passing algorithms used for decoding are often difficult to analyze. For turbo codes, we give a relaxation very close to min-cost flow, and show that the success of the decoder depends on the costs in a certain residual graph. For the case of rate-1/2 repeat-accumulate codes (a certain type of turbo code), we give an inverse polynomial upper bound on the probability of decoding failure. For LDPC codes (or any binary linear code), we give a relaxation based on the factor graph representation of the code. We introduce the concept of fractional distance, which is a function of the relaxation, and show that LP decoding always corrects a number of errors up to half the fractional distance. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.) (Abstract shortened by UMI.)

Sphere-bound-achieving coset codes and multilevel coset codes

Abstract: A simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array L and its error probability on an additive white Gaussian noise (AWGN) channel. It is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have structure of the kind that has been found to be useful in practice. Capacity curves and design guidance for practical codes are given. Exponential error bounds for coset codes are developed, generalizing Poltyrev's (1994) bounds for lattices. These results are based on the channel coding theorems of information theory, rather than the Minkowski-Hlawka theorem of lattice theory.