|
| related topics |
| {equation, function, exp} |
| {let, theorem, proof} |
| {information, entropy, channel} |
| {error, code, errors} |
| {time, wave, function} |
| {state, algorithm, problem} |
| {algorithm, log, probability} |
| {key, protocol, security} |
| {energy, gaussian, time} |
|
An Application of Renormalization Group Techniques to Classical
Information Theory
Robert R. Tucci
abstract: We apply Renormalization Group (RG) techniques to Classical Information
Theory, in the limit of large codeword size $n$. In particular, we apply RG
techniques to (1) noiseless coding (i.e., a coding used for compression) and
(2) noisy coding (i.e., a coding used for channel transmission). Shannon's
"first" and "second" theorems refer to (1) and (2), respectively. Our RG
technique uses composition class (CC) ideas, so we call our technique
Composition Class Renormalization Group (CCRG). Often, CC's are called "types"
instead of CC's, and their theory is referred to as the "Method of Types". For
(1) and (2), we find that the probability of error can be expressed as an Error
Function whose argument contains variables that obey renormalization group
equations. We describe a computer program called WimpyRG-C1.0 that implements
the ideas of this paper. C++ source code for WimpyRG-C1.0 is publicly
available.
- oai_identifier:
- oai:arXiv.org:quant-ph/0303154
- categories:
- quant-ph
- comments:
- 51 pages (files: 1 .tex, 2 .sty, 10 .eps)
- arxiv_id:
- quant-ph/0303154
- created:
- 2003-03-25
Full article ▸
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