A special word:-
A certain language has the property that all letters occur independently with various probabilities. The Huffman code for this language has average word length L per letter. One special word of length l occurs quite frequently, with probability p. (That is, of 100 words, about 100 Pl will be from the special word.) It is suggested that this word be assigned the symbol 0 and that all other letters be coded with 1 appended by a Huffman code for this group of letters (also of average length L).
(a) For what values of p is this proposal worthwhile?
(b) Does this seem to be a useful strategy for coding English with the special word the, (with a space included) assuming that the Huffman code has length 4 per letter, the word the (with space included) occurs about once every 20 words, and the average word length is five letters?