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Advances in Visual Data Compression and Communication
book

Advances in Visual Data Compression and Communication

by Feng Wu
July 2014
Intermediate to advanced content levelIntermediate to advanced
513 pages
16h 40m
English
Auerbach Publications
Content preview from Advances in Visual Data Compression and Communication
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18 1 Information Theory
For example, if x = [0,0,1,1], the codeword is
y = [0,0,1, 1,0,1,0] + [0, 0, 0,1,1,0, 1] = [0,0,1,0, 1,1,1].
All codewords for this code are
[0,0,0,0, 0,0,0], [1, 1,0,1,0, 0, 0],[0,1, 1,0,1,0,0] ,[1,0,1,1, 1,0,0]
[0,0,1,1, 0,1,0], [1, 1,1,0,0, 1, 0],[0,1, 0,1,1,1,0] ,[1,0,0,0, 1,1,0]
[0,0,0,1, 1,0,1], [1, 1,0,0,1, 0, 1],[0,1, 1,1,0,0,1] ,[1,0,1,0, 0,0,1]
[0,0,1,0, 1,1,1], [1, 1,1,1,1, 1, 1],[0,1, 0,0,0,1,1] ,[1,0,0,1, 0,1,1]
. (1.60)
It can be verified that the number of different bits between any two codewords is 3.
This is known as Hamming distance. Therefore, Hamming (7,4) codes can detect up
to two bits of error and correct up to one bit of error.
Every (n,k) linear block code has associated with a (n k) ×n matrix
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Publisher Resources

ISBN: 9781482234138