While the variance of lengths is an important consideration when choosing between two Huffman codes that have the same average lengths, it is not the only consideration. Another consideration is the ability to recover from errors in the channel. In this problem we will explore the effect of error on two equivalent Huffman codes.
(a) For the source and Huffman, encode the sequence
a2 a1 a3 a2 a1 a2
Suppose there was an error in the channel and the first bit was received as a 0 instead of a 1. Decode the received sequence of bits. How many characters are received in error before the first correctly decoded character?
(b) Repeat using the code in Table.
(c) Repeat parts (a) and (b) with the error in the third bit.
Minimum variance Huffman code
|
Letter
|
Probability
|
Codeword
|
|
a1
|
0.2
|
10
|
|
a2
|
0.4
|
00
|
|
a3
|
0.2
|
11
|
|
a4
|
0.1
|
010
|
|
a5
|
0.1
|
011
|