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A Binary Erasure Channel (BEC) has binary inputs as with the BSC (Binary Symmetric Channel ) . However there are three possible outputs. Given an input of 0, the output is 0 with probability 1 − p1and 2 with probability p1. Given an input of 1, the output is 1 with probability 1−p2and 2 with probability p2. Assume 0 and 1 are equally likely inputs. State the MAP (Maximum A Posteriori Probability) and ML (Maximum Likelihood) decision rules for the BEC when p1 < p2 < ½. How are the decision rules different when p2 < p1 < ½.

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