Question: A symmetric binary channel has error probability 1/4. A source emits words w1, w2, w3, w4, w5 with probabilities 1/2, 1/4, 1/8, 1/16, 1/16. These

A symmetric binary channel has error probability 1/4. A source emits words w1, w2, w3, w4, w5 with probabilities 1/2, 1/4, 1/8, 1/16, 1/16. These words are Huffman-encoded as 0, 10, 110, 1110, 1111, respectively. What is the probability that there will be at least one (undetected!) error transmission of a word? Now add a parity-check bit, giving codewords 00, 100, 1100, 11101, 11110. What is the probability that there is an undetected error in transmission of a word?

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