Channel capacity

The capacity of a discrete memoryless channel is

C = max_{P_{X}} I (X; Y) .

Table of contents
- Weakly symmetric channel capacity Channel capacity
  - Binary symmetric channel capacity Weakly symmetric channel capacity
  - Ternary symmetric channel capacity Weakly symmetric channel capacity

Weakly symmetric channel capacity

If every row of an

m

-output channel matrix is a permutation of every other row and all column sums agree, the uniform input achieves a uniform output and

C = lo g_{2} m - H (one row) .

Binary symmetric channel capacity

A binary symmetric channel with crossover probability

p

has capacity

C = 1 - h_{2} (p)

bits per channel use.

Ternary symmetric channel capacity

For diagonal transition probability

1 - 2 α

and each off-diagonal probability

α

,

C = lo g_{2} 3 + (1 - 2 α) lo g_{2} (1 - 2 α) + 2 α lo g_{2} α,

with

0 lo g 0 = 0

.

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Channel capacity by

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Channel capacity is a fundamental concept in information theory that represents the maximum rate at which information can be reliably transmitted over a communication channel. More specifically, it refers to the highest data rate (measured in bits per second, bps) that can be achieved without significant errors as the length of transmission approaches infinity. The concept was introduced by Claude Shannon in his seminal 1948 paper "A Mathematical Theory of Communication.

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