December 2020
Intermediate to advanced
336 pages
5h 49m
English
Content preview from Digital Communications 2
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2 Baseband Digital Transmission: Problems 16 to 26
2.1. Problem 16 – Entropy and information to signal source coding
We consider the problem of long-distance transmission over low cost electric cable of a compressed information source S from a video signal compression ystem. The compression system used makes sure that the source S delivers words s a a dictionary with only five words: [s1, s2, s3, s4, s5] . The probabilities of issuing symbols are given in Table 2.1.
Table 2.1. Probability of emission of source S
| s | s1 | s2 | s3 | s4 | s5 |
| Pr(s) | 0.11 | 0.19 | 0.40 | 0.21 | 0.09 |
The symbols are delivered by the source with a rate of 13.5 × 106 symbols per second.
- 1) Determine the entropy H (S) of the source S. Deduce the entropy rate per second. What would be the efficiency η1 of a fixed-length code C1, its length L1, and the bitrate per second, denoted D1?
- 2) Construct the Huffman code C2 generating the codeword Si associated with each of the symbols si
NOTE.– In the design of the code C2, the coding suffix associated with the element of lower probability will be systematically set to 1.
Deduce the average length L2 of the codeword C2, its efficiency η2 and the bitrate per second D2
- 3) It is considered here that the source S delivers the following time sequence SS of symbols s:
Deduce the corresponding sequence SB of bits obtained at the output of the Huffman coding C2 . SB is of ...
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