What determines ARQ throughput efficiency?

Throughput efficiency depends on the round-trip time (RTT), packet error rate (PER), and the ARQ variant. For Stop-and-Wait, efficiency = (1-PER) / (1 + 2a), where a = propagation delay / packet duration. For GEO satellite links (RTT = 500 ms) with 1 ms packets, a = 250 and efficiency drops below 0.2%, making Stop-and-Wait unusable. Selective Repeat with pipelining achieves efficiency = 1 - PER regardless of RTT, because multiple packets are in flight simultaneously. This is why satellite links always use Selective Repeat or continuous ARQ.

Signal Processing

ARQ

Q: What is the difference between ARQ and FEC?

FEC (Forward Error Correction) adds redundancy to the transmitted data so the receiver can correct errors without requesting retransmission. ARQ detects errors and requests retransmission. FEC works in one direction (no feedback channel needed) and adds constant overhead regardless of channel quality. ARQ adapts naturally: on a clean channel, no retransmissions occur and throughput approaches the raw data rate; on a bad channel, many retransmissions occur and throughput drops. Modern systems combine both: FEC handles the baseline error rate, and ARQ handles residual errors. This combination is called Hybrid ARQ (HARQ), used in LTE, 5G NR, and Wi-Fi.

Q: How does HARQ work in LTE and 5G NR?

LTE and 5G NR use HARQ with soft combining. When a packet fails CRC, the receiver does not discard it. Instead, it stores the soft bits (log-likelihood ratios) and requests retransmission. The retransmitted packet is combined with the stored original before re-decoding. Two combining methods exist: Chase Combining (CC) sends the same coded bits, providing diversity gain; Incremental Redundancy (IR) sends different coded bits from a rate-compatible code, providing coding gain. 5G NR supports up to 16 parallel HARQ processes per carrier, allowing the transmitter to continue sending new data while waiting for ACK/NACK on previous transmissions.

/A-R-Q/ (Automatic Repeat Request)

An error control mechanism where the receiver detects transmission errors (via CRC or checksum), sends a negative acknowledgment (NACK), and the transmitter retransmits the corrupted packet. ARQ converts an unreliable physical link into a reliable data link at the cost of reduced throughput and increased latency. Combined with forward error correction (FEC), it becomes Hybrid ARQ (HARQ), the retransmission engine in LTE, 5G NR, and modern Wi-Fi.

Category: Signal Processing

Abbreviation: Automatic Repeat Request

Modern form: HARQ (Hybrid ARQ)

Understanding ARQ

Every wireless channel introduces errors. FEC coding corrects most of them, but some packets still fail, especially during deep fades or interference events. ARQ is the safety net: the receiver checks each packet (typically with a CRC-16 or CRC-24), and if the check fails, it requests a retransmission. This feedback loop ensures that the upper layers receive error-free data, regardless of the instantaneous channel quality.

The simplest variant, Stop-and-Wait, transmits one packet and waits for an ACK before sending the next. This is straightforward but wastes the channel during the round-trip wait time. Go-Back-N allows multiple packets in flight but requires retransmitting all packets from the point of error. Selective Repeat retransmits only the failed packets, achieving the highest throughput at the cost of receiver reordering complexity.

ARQ Throughput Analysis

Stop-and-Wait Efficiency:
η = (1 − PER) / (1 + 2a), where a = t_prop/t_frame

Go-Back-N Efficiency:
η = (1 − PER) / (1 + 2a × PER) if window ≥ 1+2a

Selective Repeat Efficiency:
η = 1 − PER (independent of RTT)

HARQ gain (soft combining):
After k transmissions, combined SNR ≈ k × SNR_single (Chase Combining)

Example: GEO satellite, RTT=500ms, frame=1ms, PER=0.01. Stop-and-Wait: η=0.2%. Selective Repeat: η=99%.

ARQ Variant Comparison

Variant	Packets in Flight	Retransmit Scope	Receiver Complexity	Best For
Stop-and-Wait	1	1 packet	Minimal	Short-range, low latency links
Go-Back-N	Window (W)	All from error onward	Low (in-order only)	Simple pipelined links
Selective Repeat	Window (W)	Only failed packets	High (reorder buffer)	High-latency links (satellite)
HARQ (Chase)	Multiple processes	Same coded bits	Soft buffer	LTE, 5G NR, Wi-Fi
HARQ (IR)	Multiple processes	New parity bits	Soft buffer + rate matching	5G NR (default)

Common Questions

Frequently Asked Questions

What is the difference between ARQ and FEC?

FEC adds redundancy so the receiver corrects errors without feedback. ARQ detects errors and requests retransmission. FEC adds constant overhead; ARQ adapts naturally (clean channel = no retransmissions). Modern systems combine both as HARQ: FEC handles the baseline error rate, ARQ handles residual errors.

How does HARQ work in LTE and 5G NR?

Failed packets are stored as soft bits, not discarded. Retransmissions are combined with the original before re-decoding. Chase Combining sends the same bits (diversity gain); Incremental Redundancy sends new parity bits (coding gain). 5G NR supports up to 16 parallel HARQ processes per carrier.

What determines ARQ throughput?

RTT, PER, and variant. Stop-and-Wait efficiency collapses on high-latency links (GEO satellite: 0.2% efficiency). Selective Repeat achieves η = 1−PER regardless of RTT because multiple packets fly simultaneously. This is why satellite always uses Selective Repeat.

Related Terms

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ARQ