THE HULL OF A CHANNEL,
Abstract
A channel is identified, in a natural way, with a subset (the fundamental measures) of the normed linear space of all totally finite signed measures on a given measurable space (the channel output space). With this consideration, it is natural to define the hull of a channel to be the convex hull of the fundamental measures. The hull is said to be generated by the fundamental measures. It is shown that any channel which generates the hull has the same capacity as the hull itself. Finally, it is shown that the coding theorem and the strong converse hold for the hull if and only if they hold for any channel which generates the hull. This immediately proves the coding theorem and the converse for any channel whose hull is finitely generated. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1968
- Accession Number
- AD0680173
Entities
People
- Louis D. Duncan
- Walter B. Miller
Organizations
- Atmospheric Sciences Laboratory