Calculate the word decoding error probability, Operation Management

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Calculate the word decoding error probability

Assignment:

Consider a block binary code with encoding map

μ_c(00) = 0000, μ_c(01) = 0111, μ_c(10) = 1011, μ_c(11) = 1110

a) Find the maximum number of errors that can be detected in any received word.

b) Find the information efficiency of the code, assuming the information symbols are the output of a memoryless source with PMD

p_b(0) = 1/4, p_b(1) = 3/4

c) Calculate the word decoding error probability, conditioned on the transmitted word b = [00], for a memoryless BSC channel with P_bit = 0.1 and minimum distance decoding.

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