The Least Degraded and the Least Upgraded Channel with respect to a Channel Family
Wei Liu, S. Hamed Hassani, and Ruediger Urbanke
TL;DR
This paper identifies the most degraded and least upgraded channels within a family of binary-input memoryless output-symmetric channels with fixed capacity, providing explicit characterizations and capacity formulas.
Contribution
It introduces explicit characterizations and formulas for the extremal degraded and upgraded channels within a given BMS channel family.
Findings
Explicit characterization of the least upgraded and most degraded channels.
Formulas for the capacities of these extremal channels.
Applicable to fixed-capacity BMS channel families.
Abstract
Given a family of binary-input memoryless output-symmetric (BMS) channels having a fixed capacity, we derive the BMS channel having the highest (resp. lowest) capacity among all channels that are degraded (resp. upgraded) with respect to the whole family. We give an explicit characterization of this channel as well as an explicit formula for the capacity of this channel.
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