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Two-user discrete memoryless multiple-access channel
Definition
A two-user finite discrete memoryless multiple-access channel (DM-MAC) consists of finite nonempty input alphabets , a finite nonempty output alphabet , and a stochastic kernel from to in the convention of Finite stochastic kernels. Its length- conditional law is .
Facts & Assumptions
Given: Finite nonempty alphabets and a two-input stochastic kernel.
Finite stochastic kernels: a finite stochastic kernel has nonnegative entries and each row sums to one.
Proof
For each input pair, is a probability vector by [F1].
Summing the product law over factors into row sums, each equal to one; therefore is a stochastic kernel and the block law is well-defined.
Depends on
Used by
- Lossless transmission of two correlated IID sources over a DM-MAC Definition
- No-feedback independent-private-message DM-MAC code Definition
- Two-user DM-MAC code with perfect causal output feedback Definition
- A correlated binary source is sent uncoded over an adder MAC Example
- Conditional type packing bounds for source-indexed DM-MAC codebooks Lemma
- Cover-El Gamal-Salehi sufficient condition for correlated sources over a DM-MAC Theorem
- Cover-Leung inner bound for the two-user DM-MAC with feedback Theorem
- Independent-private-message DM-MAC capacity region Theorem
Dependency tree · two levels
2 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
- Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, 2nd ed., Chapter 15, §15.3 (standard reference, not scraped)
- Abbas El Gamal and Young-Han Kim, Network Information Theory, Lecture Notes 4, Multiple Access Channels (standard reference, not scraped)