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# information theory

## Analysis of the Transfer of Messages through Channels

A message proceeds along a channel from the source to the receiver; information theory defines for any given channel a limiting capacity or rate at which it can carry information, expressed in bits per second. In general, it is necessary to process, or encode, information from a source before transmitting it through a given channel. For example, a human voice must be encoded before it can be transmitted by telephone. An important theorem of information theory states that if a source with a given entropy feeds information to a channel with a given capacity, and if the source entropy is less than the channel capacity, a code exists for which the frequency of errors may be reduced as low as desired. If the channel capacity is less than the source entropy, no such code exists.

The theory further shows that noise, or random disturbance of the channel, creates uncertainty as to the correspondence between the received signal and the transmitted signal. The average uncertainty in the message when the signal is known is called the equivocation. It is shown that the net effect of noise is to reduce the information capacity of the channel. However, redundancy in a message, as distinguished from redundancy in a source, makes it more likely that the message can be reconstructed at the receiver without error. For example, if something is already known as a certainty, then all messages about it give no information and are 100% redundant, and the information is thus immune to any disturbances of the channel. Using various mathematical means, Shannon was able to define channel capacity for continuous signals, such as music and speech.

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