Problem 3. Networking in English Letters and bits

Alice transfers information in English alphabets to Bob. There are 26 distinct alphabet letters; only alphabets are treated and capitalization is ignored. Part a uses the letters so that they are equally frequent while Parts d-f use the letters for English language.

b. Alice transforms each letter to bits and transfer the corresponding bits to Bob for each letter. Assuming that Alice cannot send a fraction of bits and she wants to be efficient (the less number of bits the better), how many bits are needed per letter?

c. Alice takes a ten-letter sequence and transforms the sequence to bits, as opposed to transforming them letter-by-letter (as in Part a). Assuming that Alice sends many letters and she wants to be efficient (the less number of bits the better), how many bits are needed per letter?

d. Alice and Bob use the letters for English language. The information entropy for one letter yields the information entropy of X bits. Compare X to the answers in Part a and Part b (it is not required to actually solve for X). Explain why it is bigger, smaller, or the same.