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Information, Physics, and Computation$
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Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

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The random code ensemble

The random code ensemble

Chapter:
(p.107) 6 The random code ensemble
Source:
Information, Physics, and Computation
Author(s):

Marc Mézard

Andrea Montanari

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570837.003.0006

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 performances, and offers a constructive proof of the ‘direct’ part of the channel coding theorem: it is possible to communicate with vanishing error probability as long as the communication rate is smaller than the channel capacity. It is also very closely related to the Random Energy Model.

Keywords:   error correcting code, random code, code ensemble, channel coding theorem, Random Energy Model

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