6.2: Source Entropy
- Page ID
- 50190
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As part of the source model, we assume that each symbol selection is independent of the other symbols chosen, so that the probability \(p(A_i)\) does not depend on what symbols have previously been chosen (this model can, of course, be generalized in many ways). The uncertainty of the identity of the next symbol chosen \(H\) is the average information gained when the next symbol is made known:
\(H = \displaystyle \sum_{i} p(A_i)\log_2\Big(\dfrac{1}{p(A_i)}\Big) \tag{6.3}\)
This quantity is also known as the entropy of the source, and is measured in bits per symbol. The information rate, in bits per second, is \(H • R\) where \(R\) is the rate at which the source selects the symbols, measured in symbols per second.