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Consider the quantizer with and output probabilities indicated in [link] . Straightforward 2-bit encoding requires average bit rate of 2bits/sample, while the variable length code in [link] gives average bits/sample.
output | P k | code |
y 1 | 0.60 | 0 |
y 2 | 0.25 | 01 |
y 3 | 0.10 | 011 |
y 4 | 0.05 | 111 |
Given an arbitrarily complex coding scheme, what is the minimum bits/sample required to transmit (store) the sequence ?
When random process is i.i.d., the minimum average bit rate is
In [link] , a Huffman code was constructed for the output probabilities listed below.Here bits, so that bits/sample (with the i.i.d. assumption). Since the average bit rate for the Huffman code is also bits/sample, Huffman encoding attains R min for this output distribution.
output | P k | code |
y 1 | 0.5 | 0 |
y 2 | 0.25 | 01 |
y 3 | 0.125 | 011 |
y 4 | 0.125 | 111 |
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