This paper deals with Extended Huffman Codes. For instance, for a source emitting two symbols A and B, the second order extension involves coding messages AA, AB, BA and BB (2^2 in number). The third order extension involves messages such as AAA,AAB, etc. (2^3 in number). The probabilities of such strings are computed by multiplying the individual probabilities. Calculate third, fourth and fifth order extensions of a source message. 1. Choose an alphabet a set of at least six (6) symbols with assigned probabilities. It can be assigned as

[ A=0.3; B= 0.7; C=0.1;D=0.2;E=0.5;F=0.15].

2. Compute the third, fourth and fifth order extension probabilities.

3. Using the built-in algorithm, derive the Huffman Code for each extension.

4. Compute the following quantities: (i) Average length of the codeword; (ii) The code efficiency; (iii) The Compression Ratio.

Note: I am assuming but needs to be verified that if we need are using 6 symbols A to F. 6^3=216, the 6 to the third power comes from the third extension and so on. AAA, AAB,ABB,AAA, AAF and so on and then AAA=0.3 * 0.3 * 0.3 to get the probability.

HAND CALCULATION OR EXCEL