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Shannon's theorem was outlined in his 1948 master's thesis. The first rigorous proof was by Feinstein (2). In this tutorial, we have introduced the theorem and gave visual demonstrations of several key results and definitions. In doing so, we have limited ourselves to demonstrations using a binary alphabet, but it is important to note that Shannon's formulation applies equally well to all finite alphabets.
Shannon also outlines a version of the channel coding theorem that applies to continuous channels. In the basic model, these are channels that transmit a continuous function of one variable, but that function is limited in power and bandwidth. This approach requires decomposing such functions into a finite basis using an interval sampling technique.
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