Formula for “Code Rate” ?
Number of message bits / Number of encoded bits
Code redundancy (CR)
Number of encoded bits - Number of message bits
Hamming weight w(u)
The number of nonzero elements in u.
Hamming distance d
Denoted d(u,v), is defined by the number of elements in which they differ.
Minimum Hamming distance dmin
Smallest distance between all the codewords
Generator matrix G
Matrix whose rows are equal to the subspace basis vectors.
Systematic block code
Code where the message and parity bits are separated.
Nonsystematic block code
Code where the message and parity bits are not separated but mixed.
Are cyclic codes a part of linear codes ?
Yes.
Are cyclic codes a part of block codes ?
Yes.
Are convolutional codes a part of error correction codes ?
Yes.
Channel coding adds:
A. Redundancy
B. Noise
C. Carriers
D. Images
Answer: A
A codeword contains:
A. Only data
B. Data + redundancy
C. Only parity
D. No message bits
Answer: B
A (7,4) code has:
A. 7 data bits
B. 4 data bits
C. 3 data bits
D. No parity bits
Answer: B
The G matrix is the:
A. Parity-check matrix
B. Generator matrix
C. Demodulation matrix
D. Time matrix
Answer: B
The H matrix is the:
A. Generator
B. Parity-check
C. Encryption key
D. JPEG core
Answer: B
Hamming codes correct:
A. 1-bit errors
B. 2-bit errors
C. No errors
D. Audio noise
Answer: A
Error detection means:
A. Removing errors
B. Discovering errors
C. Adding errors
D. Storing bits
Answer: B
CRC is used for:
A. Error detection
B. Modulation
C. Compression
D. Encryption
Answer: A
A syndrome detects:
A. Correct code
B. Presence of errors
C. Carrier drift
D. Fade depth
Answer: B
Code rate = k/n gives:
A. Signal power
B. Efficiency
C. Noise level
D. Fade margin
Answer: B
A linear (n, k) code contains how many redundancy bits?
A. n
B. k
C. n − k
D. 2k
✅ Answer: C
The parity-check matrix is denoted:
A. G
B. H
C. C
D. P
✅ Answer: B
The syndrome is mainly used for:
A. Synchronization
B. Carrier recovery
C. Error detection and correction
D. Compression
✅ Answer: C
