Optimal decisions. A communications channel has input symbol set {0,1} and output symbol set {a, b,...

 

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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 P{S = 0} = 0.7 and P{S=1} = 0.3 is selected and transmitted. с b 0.7 0.2 0.1 0.3 0.2 0.5 p(rs) a 0 1 It engenders an output symbol R governed by the transition probabilities p(r | s) := P{R = r | S = s} given in the adjacent table. Determine the optimal decision rule p*: {a,b,c} → {0, 1} that minimises the probability of decision error and determine this minimum error probability. 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 P{S = 0} = 0.7 and P{S=1} = 0.3 is selected and transmitted. с b 0.7 0.2 0.1 0.3 0.2 0.5 p(rs) a 0 1 It engenders an output symbol R governed by the transition probabilities p(r | s) := P{R = r | S = s} given in the adjacent table. Determine the optimal decision rule p*: {a,b,c} → {0, 1} that minimises the probability of decision error and determine this minimum error probability.

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