An important problem in communications is the efficient representation of data generated by a

discrete source. The process by which this representation is accomplished is called source

encoding. Table below shows a set of symbols with their respective probabilities. These symbols

are sent through a communication channel. Analyse the set of symbols to obtain the appropriate

code using Huffman code algorithm.

Symbol xi X$1$ X$2$ X$3$ X$4$ X$5$ X$6$

Probability p$($xi$)0\mathrm{.}10\mathrm{.}40\mathrm{.}060\mathrm{.}10\mathrm{.}040\mathrm{.}3$

Based on the developed code, calculate the code efficiency and entropy of the second$-$order

extension of the source.