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

Hideki Yagi, Te Sun Han, Ryo Nomura

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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 languageEnglish
Article number7479457
Pages (from-to)4395-4412
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number8
Publication statusPublished - 2016 Aug
Externally publishedYes


  • $\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


Dive into the research topics of 'First- and second-order coding theorems for mixed memoryless channels with general mixture'. Together they form a unique fingerprint.

Cite this