Algorithmic Results in List Decoding introduces and motivates the problem of list decoding, and discusses the central algorithmic results of the subject, culminating with the recent results on achieving "list decoding capacity." The main technical focus is on giving a complete presentation of the recent algebraic results achieving list decoding capacity, while pointers or brief descriptions are provided for other works on list decoding. Algorithmic Results in List Decoding is intended for scholars and graduate students in the fields of theoretical computer science and information theory. The author concludes by posing some interesting open questions and suggests directions for future work.
This book presents some spectacular new results in the area of decoding algorithms for error-correcting codes.
This text offers both "classical" coding theory-such as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codes-as well as modern codes and decoding methods, including turbo codes, LDPC codes, repeat-accumulate codes, space time ...
Foundations of Software Technology and Theoretical Computer Science FSTTCS 2005. LNCS, vol. ... 11(2), 109–125 (1981) Parameterized Matching 1993; Baker MOSHE LEWENSTEIN Department of Computer Science, Bar-Ilan University, Ramat-Gan, ...
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Proposes a new way of looking at arithmetic codes with forbidden symbols.
... algorithms, and show that under some mild conditions property testers for Boolean functions can be transformed into this canonical form. Our first main result shows, roughly speaking, that every ... Boolean Function Properties Introduction.
M. Kisin, Potentially semi-stable deformation rings, J. AMS, 21, 513–546, ... R. Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. ... Modular elliptic curves and Fermat's last theorem, Ann. of Math.
Based on the encoding process, arithmetic codes can be viewed as tree codes and current proposals for decoding arithmetic codes with forbidden symbols belong to sequential decoding algorithms and their variants.
This book introduces and motivates locally decodable codes, and discusses the central results of the subject. It will benefit computer scientists, electrical engineers, and mathematicians with an interest in coding theory.
MACKAY , D. J. C. , and NEAL , R. M. ( 1995 ) Good codes based for blind source separation . In ICA : Principles and Practice , ed . by S. Roberts and R. Everson . Cambridge Univ . Press . on very sparse matrices .