Homework 8:  Error Correction and Data Compression

1. Assume you're transmitting/receiving information using the codes in Table 10.2 in the chapter on Coding Information; also assume that at most one error per "word" will occur. What would you do if you receive the message 1111001 ?

2. Consider the following (5,3) binary linear code. (Be sure you understand what that means!) The first check digit is calculated as the parity bit for all three data bits; the second check digit is the parity bit for the first two data bits.
   1. Show the table containing all the "code words".
   2. What is the weight of this code?
   3. How many errors can this code detect?
   4. How many errors can this code correct?

3. Consider the "DNA" data compression scheme in the book.
   1. How would the string TACGTTGCA be represented using this scheme?
   2. Does this require more or less space than the simpler 2-bit-per-symbol scheme?
   3. Does this mean that this compression scheme is bogus? Explain.

4. Consider this alternative to the book's DNA scheme:

    A -> 1     C -> 00     T -> 01     G -> 101

   Is this better? Worse? Equivalent? Explain.