The capacity and coding gain of certain checkerboard codes

We define a checkerboard code as a two-dimensional binary code that satisfies some constraint, e.g., every binary one must be surrounded by eight zeros, and then investigate the capacity for each of several different constraints. Using a recursive construction we develop a series of loose bounds on...

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Bibliographic Details
Published in:IEEE transactions on information theory 1998-05, Vol.44 (3), p.1193-1203
Main Authors: Weeks, W., Blahut, R.E.
Format: Article
Language:English
Subjects:
Additive white noise
Binary system
Block codes
Codes
Computer science
Concatenated codes
Cryptography
Error probability
Gain measurement
Gaussian noise
Information science
Iterative decoding
Maximum likelihood decoding
Sufficient conditions
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Summary:We define a checkerboard code as a two-dimensional binary code that satisfies some constraint, e.g., every binary one must be surrounded by eight zeros, and then investigate the capacity for each of several different constraints. Using a recursive construction we develop a series of loose bounds on the capacity. These bounds, in turn, lead to conjecturally precise estimates of the capacity by the use of a numerical convergence-speeding technique called Richardson extrapolation. Finally, using the value of the capacity, we define and compute a measure of coding gain which allows us to compare checkerboard codes to simple coding schemes.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.669282