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Information, Physics, and Computation

Marc Mézard and Andrea Montanari

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and ... More


Statistical Physics of Spin Glasses and Information Processing: An Introduction

Hidetoshi Nishimori

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198509417
eISBN:
9780191709081
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509417.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Spin glasses are magnetic materials with strong disorder. Statistical mechanics has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical ... More


Error-Correcting Codes

Hidetoshi Nishimori

in Statistical Physics of Spin Glasses and Information Processing: An Introduction

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198509417
eISBN:
9780191709081
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509417.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Reliable transmission of information through noisy channels plays a vital role in modern society. Some aspects of this problem have close formal similarities to the theory of spin glasses. Noise in ... More


The random code ensemble

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter studies the simplest error correcting code ensemble, introduced by Shannon, in which codewords are independent random points on the hypercube. This code achieves optimal error correcting ... More


Low-density parity-check codes

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Low-density parity-check (LDPC) codes are among the most efficient error correcting codes in use. This chapter introduces an important family of LDPC ensembles, based on random factor graphs, and ... More


Introduction to information theory

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces some of the basic concepts of information theory, as well as the definitions and notations of probability theory that are used throughout the book. It defines the fundamental ... More


The Mathematics of Various Entertaining Subjects: Research in Recreational Math

Jennifer Beineke and Jason Rosenhouse (eds)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164038
eISBN:
9781400881338
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164038.001.0001
Subject:
Mathematics, History of Mathematics

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, ... More


A maximum entropy approach to structure solution

Christopher J. Gilmore, Kenneth Shankland, and Wei Dong

in Structure Determination from Powder Diffraction Data

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199205530
eISBN:
9780191718076
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205530.003.0014
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes a combined maximum entropy/log-likelihood gain approach to crystal structure determination from powder diffraction data. The approach is described step-by-step, with a ... More


Decoding with belief propagation

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter revisits the problem of decoding low density parity check (LDPC) codes. The maximum a posteriori probability (MAP) decoding of a bit is described as a statistical inference problem, and ... More


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