Abstract
Upper bounds are derived on the probability of error that can be achieved by using block codes on general time-discrete memoryless channels. Both amplitude-discrete and amplitude-continuous channels are treated, both with and without input constraints. The major advantages of the present approach are the simplicity of the derivations and the relative simplicity of the results; on the other hand, the exponential behavior of the bounds with block length is the best known for all transmission rates between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</tex> and capacity. The results are applied to a number of special channels, including the binary symmetric channel and the additive Gaussian noise channel.
Keywords
Channel (broadcasting)Probability of errorBinary numberMathematicsGaussianCoding (social sciences)Binary symmetric channelSimple (philosophy)Discrete mathematicsAlgorithmUpper and lower boundsBlock (permutation group theory)SimplicityChannel capacityGaussian noiseAmplitudeChannel codeComputer scienceCombinatoricsDecoding methodsStatisticsTelecommunicationsMathematical analysisArithmetic
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Publication Info
- Year
- 1965
- Type
- article
- Volume
- 11
- Issue
- 1
- Pages
- 3-18
- Citations
- 688
- Access
- Closed
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Cite This
Robert G. Gallager
(1965).
A simple derivation of the coding theorem and some applications.
IEEE Transactions on Information Theory
, 11
(1)
, 3-18.
https://doi.org/10.1109/tit.1965.1053730
Identifiers
- DOI
- 10.1109/tit.1965.1053730