For the bellow Alphabet, construct the Tunstall code and draw the tree (step by step with completely explanation). Limit the final coding table to the size , M8, (n=3). Calculate the average length of the code per symbol.

Alphabet Prob.

16 0.6

24 0.3

32 0.1

Hint: Tunstall Code The idea is to construct a fixed-length code for encoding a variable-length sequence of input symbols. These codes are called " variable-to-fixed" (or "variable to-block") codes in contrast to the variable-length codes a.k.a. fixed-to-variable codes. This is a joint coding (recall Huffman for sequences), but not for all combinations of symbols of the original alphabet, but rather for most probable ones. The condition for constructing such codes is that symbols are to be iid. Given an alphabet of size N, construct a new alphabet whose size M is limited by the available bit budget per symbol, n; M>N, and M2n . The code is a prefix code by design. It is similar to the Huffman code, and it makes and optimal use of bits per symbol. The algorithm for designing the code is described below: Start with the root and all Level 1 nodes as leaves. the leaves correspond to the original alphabet symbols. Pick a highest probability leaf; make it intermediate, and grow N leaves on it by concatenating all the symbols in the original alphabet. If the number of leaves