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Single-letter information capacity of a finite DMC
Definition
For an input probability vector on (Finite probability vectors), let and . Write for this joint law, using Finite mutual information. The single-letter information capacity is measured in nats per channel use. The finite-dimensional maximum is attained, as proved in Finite DMC information capacity is attained ↗.
Depends on
Used by
- Strict asymptotic separation need not give zero finite-block error Counterexample
- Average-cost fixed-length codes and operational DMC capacity Definition
- Conditional information variance and DMC dispersion Definition
- Finite DMC information density Definition
- A finite-alphabet source-channel rate budget Example
- Capacity of the binary erasure channel Example
- Capacity of the binary symmetric channel Example
- A CAID's information-density variance equals its conditional dispersion Lemma
- An average-cost DMC block input has mutual information at most n C_I(Gamma) Lemma
- Capacity-achieving output laws bound every row divergence Lemma
- Constrained DMC information capacity is attained, nondecreasing, and concave Lemma
- DMC minimum and maximum dispersion are attained Lemma
- Finite DMC information capacity is attained Lemma
- IID DMC information density converges to mutual information Lemma
- Strictly feasible DMC input laws achieve every lower mutual-information rate Lemma
- The capacity-achieving output law is unique Lemma
- The n-letter mutual information of a DMC is at most nC Lemma
- Finite-DMC information deficit controls squared distance to the CAID set Theorem
- Gallager random-coding exponent lower bound Theorem
- Lossless separation for finite IID sources and finite DMCs Theorem
- Lossy separation for finite IID sources and finite DMCs Theorem
- Nondegenerate normal approximation for finite unconstrained DMCs Theorem
- Operational capacity formula for a finite DMC Theorem
- Perfect output feedback does not increase finite DMC capacity Theorem
- Random coding achieves every rate below finite DMC capacity Theorem
- Reliable average-error DMC rates do not exceed capacity Theorem
- Strong converse for finite-alphabet DMCs Theorem
- The error exponent is zero above finite-DMC capacity Theorem
Dependency tree · two levels
10 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 19 §§19.1–19.2 (standard reference, not scraped)
- Robert Gallager, Principles of Digital Communication I, Chapter 8 §§8.7.1–8.7.2, MIT OpenCourseWare (standard reference, not scraped)