Digital Communications 2

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. 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. 2) Construct the Huffman code C₂ generating the codeword S_i associated with each of the symbols s_i

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

1. 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 ...