12 — 1:45 PM T Th

Room: BSE 156

The course code for enrolling is #97436

The text, Theory and Practice of Error-Control Codes, by R. E. Blahut (Addison-Wesley 1983) will be available in two parts at the Copy Center in Communications. Master copies for the first 9 chapters (roughly half the book) were being delivered to them yesterday. The first half should be about $8-10, in 8 1/2x 11 form, two book pages/page. (R. Blahut now holds the copyright, and he has granted me permission to make copies without charge.)

For those of you who would like a bound reference text in addition, I can recommend also

Error Control Coding: Fundamentals and Applications, by Shu Lin and Daniel J. Costello, Prentice-Hall, 1983. It is available at about $80, still in print, and amazon.com says that it ships in 24 hrs.

1. a) On Friday, I asked you to write down 16 binary codewords of length 7 that were all distance 3 from each other. For your code, calculate the probability of word error for when you use your code and the complete optimal decoder on a binary symmetric channel with crossover probability p. Is this same as for a [7,4,3] Hamming code?

b) Give a description of the decoding rule that minimizes the probability of word decoding failure (the probability the decoder does NOT output the correct codeword) for a [7,4,3] Hamming code when used on the asymmetric channel in which "1" is changed to "0" with probability p, but "0" is always received correctly. Can you give a better code for this channel than the Hamming code?

c) For the a [7,4,3] Hamming code when used on the asymmetric channel above, would the decoding rule be different if the object was to minimize the probability of bit error? If so how, and why?

2. A length n binary code code with 2^k words and minimum distance 2t+1 is used on a binary symmetric channel with crossover probability p and decoded with a bounded distance decoder. Give the most accurate expression you know for the probability of word error for this system.

3. Blahut 2.7 (Four elements with tables for "+" and "•". Is it a field?)

4. Blahut 2.8

5. Blahut 2.11

6. Blahut 2.13