Due February 25
1. Compute the Kraft number for the following sets of lengths using the
radix indicated by r. In each case, indicate whether a uniquely
decodable code exits. If there is a possble code, write a decoding tree.
- with r = 2: lengths = 2,2,3,3,4,4,4,4
- with r = 4: lengths = 1,1,1,2,2,2,3,3,3,3
- with r = 3: lengths = 1,1,1,2,2,2,3,3,3,3
- with r = 3: lengths = 1,1,2,2,2,2
2. For a block of bits with probability of error p=0.02:
- find the probability of zero errors in a block of 20 bits
- fing the probability of exactly 4 errors in a block of 12 bits
- find the expected number of errors in a block of 100 bits
- find the probability of a undetectable error in a block of 50 bits, where
there is a single parity check
- find the maximum block size that will give a undetected error probability
of less than .006. (suggestion: use a spreadsheet or a program)
3. Compute the check character (fill in the "?") for the ISBN code 0-471-14338-?
4. Use the rectangular and triangular error-correction methods to encode the
15-bit message 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1. Give the efficiency of each code.