Question E8C08:
How does ARQ accomplish error correction?  

Choices:  
A: Special binary codes provide automatic correction  
B: Special polynomial codes provide automatic correction  
C: If errors are detected, redundant data is substituted  
D: If errors are detected, a retransmission is requested    

Correct Answer is  D: If errors are detected, a retransmission is requested  

ARQ (Automatic Repeat reQuest) is an error-control method that relies on error detection plus retransmission, not on correcting the errors in place.

1) Why D is correct
- In ARQ, the receiver checks each block with an error-detecting code (often a CRC).
- If no errors are found, it sends an ACK; if errors are detected, it sends a NAK or stays silent.
- The sender then retransmits the block until it is received without errors.
- Therefore: If errors are detected, a retransmission is requested.

2) Why the other choices are incorrect
- A: “Special binary codes provide automatic correction” describes Forward Error Correction (FEC) schemes (e.g., Hamming, BCH). ARQ does not correct errors locally; it resends.
- B: “Special polynomial codes provide automatic correction” also points to FEC such as Reed–Solomon (polynomial-based). CRCs are polynomial-based but provide detection, not automatic correction. ARQ relies on detection + repeat, not correction.
- C: “If errors are detected, redundant data is substituted” describes redundancy-based FEC where the receiver reconstructs the data from extra bits. ARQ does not substitute; it requests a repeat.

3) Useful formulas / rules of thumb
- Let $p$ be the probability a frame is received in error.
  - Probability of success on any given try: $1 - p$.
  - Expected number of transmissions per successful frame:
    $$E[N] = \frac{1}{1 - p}$$
- Rough efficiency (ignoring protocol overhead) decreases with higher $p$ because more retransmissions are needed.
- ARQ vs FEC rule of thumb:
  - ARQ: error detection + retransmission (good when latency is acceptable and channels are bursty).
  - FEC: error correction without retransmission (good when retransmission is costly or impossible).