Noisy-channel coding theorem
- 1Establishes a computable maximum rate for error-free data transmission.
- 2Addresses the impact of noise contamination on communication channels.
- 3Introduced by Claude Shannon in 1948.
- 4Incorporates foundational ideas from Harry Nyquist and Ralph Hartley.
In information theory, the noisy-channel coding theorem, establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data nearly error-free up to a computable maximum rate through the channel.
Connections2
Constraint on reliable communication
This theorem defines the channel capacity, which is the maximum rate at which information can be transmitted over a noisy channel, limited by the entropy of the noise.
Core theoretical limit of communication
This theorem defines the maximum rate at which information can be reliably transmitted over a noisy communication channel, a central pillar of information theory.
The noisy-channel coding theorem is a fundamental principle in information theory that defines the limits of data transmission. It establishes that for any communication channel affected by noise contamination, there exists a computable maximum rate at which discrete data can be sent nearly error-free.
Graph showing the proportion of a channel’s capacity ( y -axis) that can be used for payload based on how noisy the channel is (probability of bit flips; x -axis)Wikimedia Commons: File:Noisy-channel_coding_theorem_—_channel_capacity_graph.png Presented by Claude Shannon in 1948, the theorem provides the theoretical basis for reliable digital communication. It was developed by building upon the earlier conceptual work of Harry Nyquist and Ralph Hartley regarding signal transmission and information capacity.