ECE 380 Introduction to Communication Systems
Homework Assignment 9 Due: 16:00pm Tuesday, April 4, 2023
Problem 1. A source produces X with the following alphabet A = {a1, a2, a3, a4, a5, a6} and the corre- sponding probabilities are {0.1, 0.2, 0.3, 0.05, 0.15, 0.2}, respectively.
(a) Find the entropy of this source.
(b) Compare this entropy with the entropy of a uniformly distributed source with the same alphabet.
Problem 2. Please design the Haffman code for the source X in Problem 1.
Problem 3. Consider Hamming (7,4) code.
(a) Is 0011101 a codeword?
(b) If 0011101 is received, conduct decoding to find the decoded information bits.
(c) The probability of each bit error is 2% and bit errors are independent. If the information bits are 0001, what is the probability that the sequence 0011101 is received?
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