Arbitrarily varying channel

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (August 2024) (Learn how and when to remove this message)

An arbitrarily varying channel (AVC) is a communication channel model used in coding theory, and was first introduced by Blackwell, Breiman, and Thomasian. This particular channel has unknown parameters that can change over time and these changes may not have a uniform pattern during the transmission of a codeword. ${\displaystyle \textstyle n}$ uses of this channel can be described using a stochastic matrix ${\displaystyle \textstyle W^{n}:X^{n}\times }$ ${\displaystyle \textstyle S^{n}\rightarrow Y^{n}}$, where ${\displaystyle \textstyle X}$ is the input alphabet, ${\displaystyle \textstyle Y}$ is the output alphabet, and ${\displaystyle \textstyle W^{n}(y|x,s)}$ is the probability over a given set of states ${\displaystyle \textstyle S}$, that the transmitted input ${\displaystyle \textstyle x=(x_{1},\ldots ,x_{n})}$ leads to the received output ${\displaystyle \textstyle y=(y_{1},\ldots ,y_{n})}$. The state ${\displaystyle \textstyle s_{i}}$ in set ${\displaystyle \textstyle S}$ can vary arbitrarily at each time unit ${\displaystyle \textstyle i}$. This channel was developed as an alternative to Shannon's Binary Symmetric Channel (BSC), where the entire nature of the channel is known, to be more realistic to actual network channel situations.