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Suppose an information source X represents a weighted coin toss with probability of heads equal to 0.9, and probability of tails equal to 0.1. (a) Construct a Huffman code for this source, encoding one message at a time. (This is a very simple code.) How does the average code word length compare to the entropy of the source? 1 (b) Construct a Huffman code for this source, encoding two messages at a time. (Hint: you need four codewords.) How does the average code word length (per message X) compare to the entropy of the source X?

Suppose an information source X represents a weighted coin toss with probability of heads equal to 0.9, and probability of tails equal to 0.1. (a) Construct a Huffman code for this source, encoding one message at a time. (This is a very simple code.) How does the average code word length compare to the entropy of the source? 1 (b) Construct a Huffman code for this source, encoding two messages at a time. (Hint: you need four codewords.) How does the average code word length (per message X) compare to the entropy of the source X?

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Suppose an information source X represents a weighted coin toss with probability of heads equal to 0.9, and probability of tails equal to 0.1. (a) Construct a Huffman code for this source, encoding one message at a time. (This is a very simple code.) How does the average code word length compare to the entropy of the source? 1 (b) Construct a Huffman code for this source, encoding two messages at a time. (Hint: you need four codewords.) How does the average code word length (per message X) compare to the entropy of the source X? (c) Construct a Huffman code for this source, encoding three messages at a time. (Hint: you need eight codewords.) How does the average code word length (per message X) compare to the entropy of the source X?
Transcribed Image Text:Suppose an information source X represents a weighted coin toss with probability of heads equal to 0.9, and probability of tails equal to 0.1. (a) Construct a Huffman code for this source, encoding one message at a time. (This is a very simple code.) How does the average code word length compare to the entropy of the source? 1 (b) Construct a Huffman code for this source, encoding two messages at a time. (Hint: you need four codewords.) How does the average code word length (per message X) compare to the entropy of the source X? (c) Construct a Huffman code for this source, encoding three messages at a time. (Hint: you need eight codewords.) How does the average code word length (per message X) compare to the entropy of the source X?
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