Shannon’s Theorem on Noiseless Channels
A noiseless channel is a device which is able to transmit some signals y1, y2, ..., ym (Channel signals) (m ≥ 2) from one place to another one, and the signals do not change during the transmission. The problem starts if we have an information source which emits some signals x1, x2, ..., xn (information signals) (n ≥ 2) which are different from yi’s and we have to transmit xi’s by the channel. The only way to do this is to transform somehow the sequences of xi’s into sequences of yi’s which are transmissible by the channel. This transformations is called encoding. Obviously, it must be such a transformation, that we can uniquely restore the xi’s from the sequence of yi’s. We say in this case that the coding is uniquely decodable. No doubt, these notions require more precise definitions we shall give them later.
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