8.5 Binary codes: numerical experiment (huffman codes)

The paragraph below contains Lincoln's Gettysburg Address. Ignore special symbols like periods and ignore the distinction between lowercase and uppercase letters. Compute the relative frequency of occurrence for each of the 26 letters of the alphabet. Write a MATLAB program to generate a binary tree for the Huffman code of the Gettysburg Address. When you have generated the code, compute the average code word length

where $\frac{n_i}{N}$ is the relative frequency for symbol $i$ and $l_i$ is the code word length for symbol $i$ . Compare $L$ with the entropy

and compare $L$ to ${log}_{2}26$ . Interpret your findings.

Gettysburg address