In Exercises 1 (b) and (c), above, note that the encoding schemes are as short as possible, but not thoughtfully conceived. For instance, in 1(b), the code word for e, the most commonly encountered source letter, is a Hamming distance 2 from the word for c, the least common code word, but a distance 1 from each of the words for b and d. Surely it would increase the reliability R if we interchange the code words representing c and d, or c and b. Verify that this is so. Also, find a fixed-length scheme, of length 3, to replace the scheme in 1(c), which increases the reliability.