Question

Design a Shannon-Fano code and sketch the corresponding coding tree where the alphabet is {a,b,c,d,e,f} with corresponding probabilities {0.4, 0.3, 0.15, 0.1, 0.03, 0.02} .

Answer 1

To design a Shannon-Fano code, you start by listing the symbols and their corresponding probabilities in descending order. Then, you divide the list into two groups, assigning a 0 prefix to the symbols in the first group and a 1 prefix to the symbols in the second group. Repeat this process recursively until all symbols are assigned unique codes.

Step-by-step explanation:

A Shannon-Fano code is a variable-length prefix code that provides an efficient way to compress data. To design a Shannon-Fano code, you start by listing the symbols (a, b, c, d, e, f) and their corresponding probabilities (0.4, 0.3, 0.15, 0.1, 0.03, 0.02) in descending order.

Next, you divide the list into two groups, ensuring that the sum of probabilities in each group is as close as possible to 0.5. You assign a 0 prefix to the symbols in the first group and a 1 prefix to the symbols in the second group.

Repeat this process recursively for each group until all symbols are assigned unique codes. The resulting coding tree will have the symbols at the leaves and the corresponding codes along the paths from the root to each leaf.

Here is an example of a Shannon-Fano code: