7.3.1: Example- Symmetric Binary Channel
- Page ID
- 51266
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For the SBC with bit error probability \(\epsilon\), these formulas can be evaluated, even if the two input probabilities \(p(A_0)\) and \(p(A_1)\) are not equal. If they happen to be equal (each 0.5), then the various information measures for the SBC in bits are particularly simple:
\(I = 1 \;\text{bit} \tag{7.28}\)
\(J = 1 \;\text{bit} \tag{7.29}\)
The errors in the channel have destroyed some of the information, in the sense that they have prevented an observer at the output from knowing with certainty what the input is. They have thereby permitted only the amount of information \(M = I − L\) to be passed through the channel to the output.