# First- and second-order coding theorems for mixed memoryless channels with general mixture

Hideki Yagi, Te Sun Han, Ryo Nomura

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

This paper investigates the first- and second-order maximum achievable rates of codes with/without cost constraints for mixed channels whose channel law is characterized by a general mixture of (at most) uncountably many stationary and memoryless discrete channels. These channels are referred to as mixed memoryless channels with general mixture and include the class of mixed memoryless channels of finitely or countably memoryless channels as a special case. For the mixed memoryless channels with general mixture, the first-order coding theorem which gives a formula for the $\varepsilon$ -capacity is established, and then a direct part of the second-order coding theorem is provided. A subclass of mixed memoryless channels whose component channels can be ordered according to their capacity is introduced, and the first- and second-order coding theorems are established. It is shown that the established formulas reduce to several known formulas for restricted scenarios.

Original language English 7479457 4395-4412 18 IEEE Transactions on Information Theory 62 8 https://doi.org/10.1109/TIT.2016.2573310 Published - 2016 Aug 1 Yes

coding
scenario
Law
costs
Costs

### Keywords

• $\varepsilon$ -capacity
• Channel coding
• cost constraint
• information spectrum
• mixed channel
• second-order coding rate

### ASJC Scopus subject areas

• Information Systems
• Computer Science Applications
• Library and Information Sciences

### Cite this

First- and second-order coding theorems for mixed memoryless channels with general mixture. / Yagi, Hideki; Han, Te Sun; Nomura, Ryo.

In: IEEE Transactions on Information Theory, Vol. 62, No. 8, 7479457, 01.08.2016, p. 4395-4412.

Research output: Contribution to journalArticle

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