Optimal decisions. A communications channel has input symbol set 0,1 and output

Question

Optimal decisions. A communications channel has input symbol set 0,1 and output symbol set (a, b, c). In a single use of the channel a random input symbol S governed by the a priori probabilities PS 00.7 and PS0.3 is selected and transmitted. p(rIs) | a b c 0.7 0.2 0.1 1 0.3 0.2 0.5 It engenders an output symbol R governed by the transition probabilities p(r s): PR rS s) given in the adjacent table. Determine the optimal decision rule ": {a, b, c} {0, 1} that minimises the probability of decision error and determine this minimum error probability.

Explanation / Answer

The optimal decision can be find when s=0 and value is tend to c=0.3. And when s=1 the value of b should be 0.2. So the optimal return can be reach.

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