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Finite DMC with a nonnegative input cost and feasible budget
Definition
Let be a finite DMC with nonempty finite input alphabet (Finite discrete memoryless channels). A letter cost is a supplied function with finite real values. Define for each input probability vector (Finite probability vectors). A real number is a feasible cost budget when . Costs and budgets are per channel use; all logarithms and rates in this pair use natural units The natural logarithm as the inverse of the exponential function.
Depends on
Used by
- An inactive DMC cost constraint recovers ordinary capacity Corollary
- Average-cost fixed-length codes and operational DMC capacity Definition
- Causal feedback codes for a finite cost-constrained DMC Definition
- Cost-constrained capacity of a binary identity channel with feedback Example
- An average-cost DMC block input has mutual information at most n C_I(Gamma) Lemma
- Constrained DMC information capacity is attained, nondecreasing, and concave Lemma
- Strictly feasible DMC input laws achieve every lower mutual-information rate Lemma
- Average-cost capacity formula for a finite DMC Theorem
- Causal feedback does not increase finite DMC capacity under average cost Theorem
Dependency tree · two levels
6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Yury Polyanskiy and Yihong Wu, Information Theory: From Coding to Learning, Chapter 20 §20.1 (standard reference, not scraped)
- Yury Polyanskiy, MIT 6.441 Information Theory, Chapter 17 §17.1, Channels with Input Constraints (standard reference, not scraped)