CRC Encoding Efficiency Explained | Generated by AI
Question: In cyclic redundancy check (CRC), if the codeword has k information bits and r redundancy bits are added during encoding, what is the encoding efficiency?
Answer:
The correct answer is D. k/(k+r).
Explanation:
Encoding efficiency (also called code rate or information rate) measures how much of the total transmitted bits actually carry useful information.
- Information bits (payload): k bits
- Redundancy bits (check bits, parity bits): r bits
- Total codeword length: k + r bits
Therefore, the encoding efficiency is defined as:
Efficiency = (number of information bits) / (total number of bits in the codeword) = k / (k + r)
This matches option D.
Quick memory tip (as provided):
“信息位k，总长k+r，效率k/(k+r)”
Why the other options are incorrect:
- A. r/(r+k) → This would be the redundancy ratio, not the efficiency.
- B. 1/(k+r) → This has no meaningful interpretation in this context.
- C. r/k → This is the relative redundancy, opposite of efficiency.
So the correct choice is indeed D.
References:
- None (standard coding theory definition, no external reference required)