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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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