Consider a systematic (8.4) code whose parity equations are: r

p0 = al + a2 + a3 

p1 = a0 + al + a2 

p2 = a0 + al + a3 

p3 = a0 + a2 + a3 

where a0, a1, a2, a3 are the message digits and p0, p1. p2. p3 are parity-check digits. The codewords are in the format (a0, a1, a2. a3, p0, p1. p2, p3). 

1. Find all valid codewords for this scheme. 

2. Use an example to show how this coding scheme can detect a 3-bit error but not a 4-bit error. 

3. Use an example to show how this coding scheme can correct a single-bit error but not a double-bit error. 

4. Assuming that parts (2) and (3) are correct in all cases, what is the minimum Hamming distance of this coding scheme?r

Answer rating: 100% (QA)

1 if p0 0 then a0 a1 a2 a3 0 if p1 0 then a0 a1 a2 0 if p2 0 then a0 a1 a3 0 if p3 0 ... View the full answer