Universal channel coding for general output alphabet
Masahito Hayashi

TL;DR
This paper introduces two universal channel coding schemes suitable for channels with possibly continuous output alphabets, analyzing their error decay and capacity approximation using information spectrum and type methods.
Contribution
It presents novel universal coding strategies for general output alphabets, providing explicit error bounds and capacity approximations with second-order analysis.
Findings
Error probability decays exponentially with explicit bounds
Achieves epsilon-capacity with second-order term characterization
Unified analysis for discrete and continuous output channels
Abstract
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an explicit lower bound on the error exponent. The other class attains the epsilon-capacity the channel and we also identify the second-order term in the asymptotic expansion. The proposed encoder is essentially based on the packing lemma of the method of types. For the decoder, we first derive a R\'enyi-relative-entropy version of Clarke and Barron's formula the distance between the true distribution and the Bayesian mixture, which is of independent interest. The universal decoder is stated in terms of this formula and quantities used in the information spectrum method. The methods contained herein allow us to analyze universal codes for channels with…
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Taxonomy
TopicsCellular Automata and Applications · Wireless Communication Security Techniques · Algorithms and Data Compression
