Information Theory and Coding > Channel Capacity > What is information channel?

What is information channel?

Information Channel is a triple {A, B, P}, where A={a_i : i = 1,2, .. r}  input alphabet and B={ b_j : j = 1,2, … s}  is the output alphabet and P = { P(b_j/a_i) : i = 1,2, .. r; j = 1,2, … s}  is the probability that the output symbol b_j will be received if input symbol a_i is transmitted.

The channel matrix exhibits the following properties and structure:

• Each row of P contains the probabilities of all possible outputs from the same input to the channel
• Each column of P contains the probabilities of all possible inputs to a particular output from the channel
• If we transmit the symbol a_i we must receive an output symbol with probability 1,

that is, the probability terms in each row must sum to 1.

 

Consider a binary source and channel with input alphabet {0,1} and output alphabet {0,1}. If the channel is noiseless there will be no error in transmission, the channel matrix is given by

If the channel is noisy and introduces a bit inversion 1% of the time, then the channel matrix is given by

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