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2.7. Capacity, redundancy and efficiency of a discrete channel

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Claude Shannon introduced the concept of channel capacity, to measure the efficiency with which information is transmitted, and to find its upper limit.

The capacity C of a channel: (information bit/symbol) is the maximum value of the mutual information I(X, Y) over the set of input symbols probabilities

[2.54]

The maximization of I(X, Y) is performed under the constraints that:


The maximum value of I(X, Y)occurs for some well-defined values of these probabilities, which thus define a certain so-called secondary source.

The capacity of the channel can also be related to the unit of time (bitrate Ct of the channel), in this case, one has:

[2.55]

The channel redundancy Rc and the relative channel redundancy pc are defined by:

[2.56]

[2.57]

The efficiency of the use of the channel is defined by

[2.58]

Digital Communications 1

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