For a (6, 3) systematic linear block code, the codeword comprises of m0,m1,m2 as the message bits and p0,p1,p2 as the parity bits. The coded bits are given as: c0=m0⊕m1, c1=m0⊕m2, c2=m1⊕m2. Which of the statement(s) is/are correct? The error-correcting capability of the code is 1. The error-detecting capability of the code is 2. The error-correcting capability of the code is 2. The error-detecting capability of the code is 3
Question
For a (6, 3) systematic linear block code, the codeword comprises of m0,m1,m2 as the message bits and p0,p1,p2 as the parity bits. The coded bits are given as:
c0=m0⊕m1,
c1=m0⊕m2,
c2=m1⊕m2.
Which of the statement(s) is/are correct? The error-correcting capability of the code is 1. The error-detecting capability of the code is 2. The error-correcting capability of the code is 2. The error-detecting capability of the code is 3
Solution
The error-correcting capability of a code is determined by its Hamming distance. The Hamming distance of a code is the minimum number of bit changes needed to go from one valid codeword to another. In this case, the Hamming distance is 1, because each parity bit is the XOR of two message bits. Therefore, the error-correcting capability of the code is 1.
The error-detecting capability of a code is determined by its ability to detect errors. In this case, the code can detect up to two errors. This is because if one bit is flipped, the parity check will fail, indicating an error. If two bits are flipped, the parity check will also fail, indicating an error. However, if three bits are flipped, the parity check may not fail, and the error may not be detected. Therefore, the error-detecting capability of the code is 2.
So, the correct statements are:
- The error-correcting capability of the code is 1.
- The error-detecting capability of the code is 2.
Similar Questions
A message comprises a set of symbols which are to be mapped onto binary code words for transmission. The code word set is {000000, 000111, 010010, 100001, 110011, 111000}. How many bit errors in a code word can be reliably detected? (Type a number only - no units.)
Determine all the code words of the code if Generator matrix for a (7,4) block code is as given below. Also if transmitted code word C=1011is received as 1111, use syndrome to correct this error.1 & 0 & 0 & 0 & : & 0 & 1 & 1 \\0 & 1 & 0 & 0 & : & 1 & 0 & 1 \\0 & 0 & 1 & 0 & : & 1 & 1 & 0 \\0 & 0 & 0 & 1 & : & 1 & 1 & 1 \\\end{bmatrix} \]
Linear block code
What is the relationship between the distance between parity bits and their error detection and correction capability in Hamming Code?Closer parity bits provide higher error correction capabilityCloser parity bits provide lower error correction capabilityDistance between parity
Which of the following statement(s) is/are true: The strength of binary code depends on the hamming distance between codewords The strength of binary code does not depend on the hamming distance between codewords The minimum distance of linear block code is the minimum distance of its codewords The minimum distance of linear block code is the maximum distance of its codewords.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.