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Automatic repeat request

Automatic repeat request (ARQ) is an error-control method employed in data transmission protocols to ensure reliable delivery over unreliable or noisy channels by automatically detecting errors or losses in transmitted packets and requesting their retransmission from the sender. This technique operates at the link layer, using acknowledgments (ACKs) from the receiver to confirm successful receipt and negative acknowledgments (NAKs) or timeouts to trigger retransmissions, thereby minimizing data loss without requiring end-to-end intervention. ARQ is fundamental to link-layer standards such as High-Level Data Link Control (HDLC), while similar mechanisms are integral to transport-layer protocols like Transmission Control Protocol (TCP) for enhancing reliability in error-prone environments. The core mechanism of ARQ involves breaking data into smaller frames or packets, appending error-detection codes such as , and utilizing a for the to inform the sender of the transmission status. Upon detecting an error via integrity checks, the discards the faulty packet and signals for retransmission, which the sender performs from its until an is received or a maximum retry limit is reached. This process provides higher reliability than (FEC) alone, especially in scenarios with variable error rates, though it introduces due to the round-trip time for . ARQ protocols are categorized into types such as stop-and-wait, go-back-N, and selective repeat, based on retransmission strategies that balance efficiency and complexity. These schemes have been surveyed and refined since the early 1970s, influencing link-layer designs in standards and IETF recommendations.

Fundamentals

Definition and Purpose

Automatic repeat request (ARQ) is an error-control method used in protocols to ensure the reliable transmission of information over potentially unreliable channels. In this protocol, the sender transmits data packets, and the inspects them for s using detection mechanisms; if an is detected, the notifies the sender via to request retransmission of the affected packet. This automatic process distinguishes ARQ from simpler discard-based error handling, as it actively recovers lost or corrupted data without manual intervention. The primary purpose of ARQ is to provide reliable data delivery in environments prone to transmission errors, such as or noisy links, by combining detection with selective retransmission. By leveraging , ARQ corrects s on-demand, minimizing the impact of imperfections while adapting to varying rates. This approach enhances overall compared to uncorrected transmission, where errors could propagate and degrade higher-layer performance. Key components of an ARQ system include the sender, which originates and retransmits packets; the receiver, which verifies integrity and generates feedback; the forward channel for data flow; and the reverse channel for acknowledgments (ACKs) confirming successful receipt or negative acknowledgments (NAKs) indicating errors. The basic operation follows a sequential cycle: the sender transmits a packet, the receiver performs error detection and responds with ACK or NAK, and the sender retransmits only if necessary, continuing until acknowledgment is received or a retry limit is exceeded. This feedback-driven loop ensures error recovery without assuming a perfect channel. In contrast to (FEC), which embeds redundant information in the initial transmission to enable receiver-side error repair without feedback, ARQ depends on retransmissions triggered by receiver notifications and avoids upfront bandwidth overhead for redundancy. ARQ principles are employed in protocols like within the TCP/IP suite to maintain end-to-end reliability.

Historical Development

The roots of automatic repeat request (ARQ) protocols trace back to the mid-20th century, emerging from efforts to ensure reliable data transmission amid noise and errors in early electronic communication systems. Initial concepts drew from practices, where manual retransmissions addressed garbled messages, evolving into automated mechanisms in the 1940s and 1950s as advanced. Claude Shannon's seminal 1948 work on provided the theoretical foundation, demonstrating that error-free communication over noisy channels was possible through and principles, which later influenced practical ARQ implementations for robust data delivery. In the , ARQ mechanisms gained formalization during the development of early packet-switching networks, particularly through U.S. Department of Defense-funded projects. Paul Baran's 1964 reports on distributed communications networks introduced with built-in error detection and retransmission strategies to maintain reliability in potentially disrupted environments, laying groundwork for ARQ in decentralized systems. variants appeared in initial designs around 1968-1969, where senders awaited acknowledgments before proceeding, addressing the challenges of variable delays in nascent packet networks. The 1970s and 1980s marked significant advancements in ARQ protocols, integrating them into standardized communication frameworks. and Robert Kahn's 1974 proposal for the (TCP) incorporated ARQ through sequence numbering, acknowledgments, and timeouts for retransmission, enabling reliable end-to-end data transfer across heterogeneous networks. The (ITU-T) standardized X.25 in 1976, employing ARQ-based error recovery in its Link Access Procedure () for packet-switched wide-area networks. By 1979, (HDLC), ratified by the (ISO), formalized go-back-N and selective repeat ARQ options, enhancing efficiency in synchronous data links. ARQ's evolution continued into modern wireless standards, adapting to higher mobility and interference. The standard for wireless local area networks, released in 1997, incorporated ARQ at the (MAC) layer to handle frame errors via acknowledgments and retransmissions, supporting reliable connectivity. In cellular communications, the 3rd Generation Partnership Project () introduced hybrid ARQ (HARQ) in Long-Term Evolution () specifications finalized in 2008, combining with retransmissions for improved throughput in broadband mobile networks.

Protocol Types

Stop-and-Wait ARQ

Stop-and-Wait ARQ is the most basic automatic repeat request , in which the sender transmits a data or packet and then halts transmission until it receives a positive (ACK) from the confirming successful receipt, or a negative acknowledgment (NAK) indicating an error. If neither is received within a predefined timeout period—typically set to account for delays and processing—the sender assumes the was lost or corrupted and retransmits it. This mechanism ensures reliable delivery over potentially erroneous channels by combining error detection with selective retransmission of only the problematic . The operational sequence begins with the sender encapsulating data into a , appending error-detection information such as a , and transmitting it over the channel while simultaneously starting a retransmission . Upon receipt, the verifies the 's ; if valid, it discards any duplicates using sequence numbers (typically 0 or 1) and sends an back to the sender. If invalid or if no frame arrives within an expected , the sends a NAK or simply times out, prompting the sender to retransmit upon expiration or NAK arrival. This stop-and-wait cycle repeats for each , maintaining strict sequencing and flow control without buffering multiple outstanding frames. A primary advantage of lies in its simplicity, requiring minimal buffering (only one at a time) and low computational overhead, which makes it suitable for resource-constrained devices and channels with low bit error rates where retransmissions are infrequent. It is particularly effective in half-duplex environments, as the forward data path and reverse acknowledgment path can operate alternately without complex . However, the protocol suffers from significant inefficiencies on high-bandwidth or high-latency links, as the sender remains idle during the round-trip time for acknowledgments, leading to underutilization of the channel and increased —especially pronounced in scenarios like communications where are substantial. The throughput of , which measures the effective data rate as a fraction of the , is derived considering both and probabilities. In an -free , the time to successfully transmit one includes the frame transmission time t_f plus the round-trip time $2 t_p (from to and back for the ). Thus, the efficiency \eta is the ratio of useful transmission time to total cycle time: \eta = \frac{t_f}{t_f + 2 t_p} = \frac{1}{1 + 2a} where a = \frac{t_p}{t_f} is the normalized propagation delay factor, representing the bandwidth-delay product impact. To incorporate errors, assume each frame has an independent error probability P_e, requiring on average \frac{1}{1 - P_e} transmissions per successful delivery (since the probability of success is $1 - P_e). The expected cycle time scales by this factor, yielding the full throughput formula: \eta = \frac{1 - P_e}{1 + 2a} This derivation assumes negligible ACK transmission time and processing delays, ACKs are error-free or protected separately, and errors lead to retransmission without cumulative effects. The formula highlights how errors reduce throughput linearly while delays amplify idleness, limiting applicability to low-a and low-P_e channels. An illustrative example of in practice is its use in early modem-based protocols like XMODEM, developed in the late for systems, where the sender would transmit fixed-size blocks (128 bytes) over dial-up telephone lines and wait for /NAK before the next, ensuring reliability despite noisy analog connections.

Go-Back-N ARQ

is an extension of basic ARQ protocols that employs a sliding window mechanism to improve efficiency by allowing the sender to transmit up to N unacknowledged before awaiting confirmation. The receiver operates with a single-frame and sends cumulative acknowledgments (s), each specifying the sequence number of the next expected frame in order, thereby acknowledging all prior correctly received frames. This approach enables pipelined transmission, where multiple frames are outstanding on the channel simultaneously. In operation, the sender assigns sequence numbers to frames using modulo-M arithmetic, where M is determined by the number of bits k allocated for sequencing (e.g., numbers cycling from 0 to M-1). The sender advances its as ACKs arrive, sliding it forward to allow new transmissions. The receiver accepts only in-order frames; upon detecting an error (via failure) or an out-of-sequence frame, it discards the erroneous frame and any subsequent ones, without buffering them, and continues sending ACKs for the last correctly received frame. If the sender experiences a timeout for any unacknowledged frame or receives a negative acknowledgment (NAK), it performs a "go-back" by retransmitting all frames from the point of the lost or errored frame onward, resetting the accordingly. To prevent ambiguity in distinguishing new frames from retransmissions, the maximum window size is constrained by the sequence number space: N \leq 2^k - 1, where k is the number of bits used for sequence numbers. For instance, with 3-bit sequence numbers (k=3), N \leq 7, ensuring the sender does not wrap around the sequence space before resolving all potential ACKs. This limitation arises because the cannot differentiate between a new frame with a repeated sequence number and a retransmission if the window exceeds half the sequence space. Go-Back-N ARQ offers improved efficiency over stop-and-wait protocols on channels with high bandwidth-delay products, as it minimizes idle time by keeping the link utilized with multiple in-flight frames, achieving throughput closer to the under low error rates. However, it inefficiently retransmits correctly received frames following an error, wasting and reducing overall performance in noisy environments where errors are frequent. An example of implementation is in the (HDLC) protocol, standardized for bit-oriented synchronous data transmission over point-to-point links, where the sender window size defaults to 7 (for 3-bit sequence numbers) or optionally extends to 127 (for 7-bit sequence numbers) to balance efficiency and ambiguity avoidance.

Selective Repeat ARQ

Selective Repeat ARQ is a highly efficient protocol that retransmits only identified as erroneous, while the buffers correctly received out-of-order frames to maintain upon delivery to higher layers. Unlike simpler ARQ variants, it employs individual acknowledgments for each frame, enabling the sender to proceed with new transmissions without halting for cumulative confirmations. This approach minimizes redundant data transfer, particularly in channels with sporadic errors. The protocol operates using a sliding mechanism where the sender transmits up to a predefined window size of numbered . Upon receipt, the inspects each : correctly received prompt a selective (SACK) specifying the frame's sequence number, while errored frames elicit a negative acknowledgment (NAK). The stores valid out-of-order in a until all preceding frames arrive, at which point it reassembles and forwards the complete sequence. The sender, upon receiving a NAK or experiencing a timeout for an unacknowledged , retransmits solely that frame, advancing the window as positive ACKs arrive. This selective process ensures continuous flow while isolating error recovery. To prevent ambiguity between new frames and potential duplicates from retransmissions, Selective Repeat ARQ requires a number space at least twice the maximum size. For a k-bit number field, this limits the window to at most $2^{k-1} frames, ensuring the can uniquely identify frames within the current without overlap from prior cycles. The primary advantages of Selective Repeat ARQ include optimal utilization through minimal retransmissions—only errored frames are resent—and superior in high-latency or error-prone environments compared to protocols that discard entire blocks. However, these benefits come with increased implementation complexity, as both sender and receiver must maintain buffers for out-of-order frames and track individual /NAK states, demanding more memory and processing resources. The efficiency \eta of Selective Repeat ARQ is \eta = 1 - P_e, where P_e is the frame error rate, assuming a sufficiently large window size to cover the and error-free acknowledgments. This formula indicates near-channel-capacity performance in low-error conditions by minimizing redundant transmissions. An practical example of Selective Repeat principles in action is the protocol's Selective Acknowledgment () option, introduced in RFC 2018, which permits receivers to report multiple non-contiguous blocks of successfully received data. This allows senders to retransmit only missing segments, reducing recovery time from multiple losses without invoking full window reductions.

Operational Mechanisms

Error Detection Methods

In Automatic Repeat reQuest (ARQ) protocols, error detection plays a pivotal role by identifying transmission errors in received data frames, which precedes the generation of feedback signals to initiate retransmissions. These detection methods are typically appended to the data frames as redundant check information, enabling the receiver to verify integrity without correcting errors. One common method is the , a simple arithmetic technique that computes the one's complement sum of 16-bit words from the and appends the result modulo $2^{16} to detect inconsistencies. For instance, the used in IPv4 headers sums all 16-bit segments and takes the one's complement of the result, providing basic protection against single-bit and some multi-bit errors in ARQ-enabled networks. Cyclic Redundancy Check (CRC) offers more robust detection through polynomial division in GF(2), particularly effective for burst errors up to the degree of the generator polynomial. The CRC-32 variant, employing a 32-bit polynomial such as x^{32} + x^{26} + x^{23} + x^{22} + x^{16} + x^{12} + x^{11} + x^{10} + x^{8} + x^{7} + x^{5} + x^{4} + x^{2} + x + 1, is a standard in protocols like Ethernet for ARQ error verification. Parity bits provide a rudimentary approach by adding a single bit to ensure an even or odd number of 1s in the data word, capable of detecting single-bit errors but ineffective against even-numbered errors or bursts. Their use in ARQ is limited due to low detection capability, often serving as a lightweight option in simple systems. Modern lightweight hash-based methods, such as the , compute two running sums modulo 65535 over 16-bit blocks to produce a 32-bit value, balancing efficiency and detection strength as an alternative to in resource-constrained ARQ implementations. These methods detect various error patterns, including single-bit flips, burst errors (for CRC, all bursts shorter than the polynomial degree), and random multi-bit errors, with extremely low undetected error probabilities—on the order of $2^{-n} for an n-bit check where undetected errors are negligible in practice. For CRC computation, consider a message M(x) of degree k and generator polynomial G(x) of degree n. The transmitter forms M(x) \cdot x^n, performs modulo-2 division by G(x) to obtain remainder R(x), and transmits T(x) = M(x) \cdot x^n + R(x). The receiver divides T(x) by G(x); a zero remainder confirms no errors. \begin{align*} &\text{Transmitted frame: } T(x) = M(x) \cdot x^n + R(x) \\ &\text{Where } R(x) \text{ is the remainder of } \frac{M(x) \cdot x^n}{G(x)} \\ &\text{Receiver check: } T(x) \mod G(x) = 0 \text{ (error-free)} \end{align*}

Acknowledgment and Retransmission Processes

In Automatic Repeat Request (ARQ) protocols, acknowledgments serve as feedback mechanisms to confirm data reception or indicate errors, enabling the sender to decide on retransmissions. Positive acknowledgments (ACKs) are sent by the receiver upon successful receipt of a data unit, signaling the sender to proceed with the next transmission. Some ARQ protocols use negative acknowledgments (NAKs) to notify the sender of detected errors in the received data, prompting retransmission of the affected unit; others rely on the absence of ACKs and timeouts. These acknowledgment types can be cumulative, where an ACK confirms all data units up to a specified sequence number, or selective, which explicitly identifies only the successfully received units while implying others need retransmission. Timing mechanisms in ARQ ensure timely retransmissions by incorporating retransmission based on estimated round-trip time (RTT). The starts upon sending a data unit and expires if no arrives within the calculated interval, triggering a retransmission; this interval is often derived from smoothed RTT measurements to adapt to network variability. For handling duplicates—arising from delayed or lost s—sequence numbers are assigned to data units, allowing the to discard redundant transmissions and send cumulative s to advance the sender's . may adjust the on repeated timeouts to mitigate congestion. Retransmission policies dictate the response to : upon receiving a NAK, the immediately retransmits the erroneous unit, while timeouts lead to delayed retransmissions of unacknowledged units. In cumulative schemes, an error may prompt retransmission of the errored unit and all subsequent units in the ; selective policies limit retransmissions to only the erroneous units for efficiency. Flow control integrates with these policies through adjustments based on ACKs, where the advertises its capacity to prevent and regulate throughput. To optimize in bidirectional links, ARQ employs , where ACKs or NAKs are embedded in reverse-direction data packets rather than sent as standalone messages, reducing protocol overhead without delaying . This technique is particularly effective in full-duplex environments, combining reliability signaling with ongoing data exchange. ARQ mechanisms rely briefly on prior error detection outcomes to generate appropriate ACKs or NAKs. A representative example is the Transmission Control Protocol (TCP), which implements ARQ-like reliability through its three-way handshake for initial sequence number synchronization: the client sends a SYN segment with its initial sequence number, the server responds with SYN-ACK confirming the client's number and providing its own, and the client finalizes with an ACK of the server's number. Subsequent data transfers use cumulative ACKs and RTT-based timers for retransmissions, with sequence numbers handling duplicates and window scaling for flow control.

Applications and Performance

Use in Communication Protocols

Automatic Repeat Request (ARQ) is integral to the suite, where the Transmission Control Protocol () implements ARQ mechanisms through sequence numbers for ordering, acknowledgments (ACKs) to confirm receipt, and retransmissions for lost or corrupted segments, ensuring reliable end-to-end delivery over unreliable networks. This approach, specified in the foundational TCP document from 1981, operates as a go-back-N variant, retransmitting all outstanding segments upon timeout or duplicate ACKs to handle errors without higher-layer intervention. At the link layer, protocols such as (HDLC) employ to manage frame retransmissions in synchronous environments, using sequence numbers and supervisory frames for error recovery in point-to-multipoint scenarios. Similarly, the (PPP), which leverages HDLC-like framing for encapsulation, incorporates ARQ through its Link Control Protocol (LCP) options for negotiated error detection and optional retransmission capabilities over serial links. In wireless personal area networks, adopts selective repeat ARQ at the layer for asynchronous connection-less () links, allowing individual packet retransmissions based on negative acknowledgments (NAKs) to optimize throughput in interference-prone short-range communications, as defined in its core specifications since the early . Wireless local area networks utilize hybrid ARQ in (Wi-Fi) standards, combining (FEC) in the with ARQ retransmissions at the MAC layer via block acknowledgments, enabling efficient recovery from packet losses in contention-based environments. For cellular networks, Long-Term Evolution (LTE) and 5G New Radio (NR) employ Hybrid ARQ (HARQ), which integrates ARQ with incremental redundancy FEC; upon decoding failure, receivers request retransmissions that provide additional parity bits for soft combining, significantly improving in high-mobility scenarios as outlined in 3GPP technical specifications. In satellite communications, ARQ is applied alongside standards to mitigate errors over long-delay links, where adaptive coding and modulation (ACM) pairs with higher-layer ARQ protocols to request retransmissions for uncorrectable frames, enhancing reliability in hybrid satellite-terrestrial systems without relying solely on FEC due to propagation delays. Emerging (IoT) protocols like incorporate lightweight ARQ variants based on , using optional per-frame acknowledgments and up to three retransmission attempts with to balance low power consumption and reliability in mesh topologies for sensor networks. A notable case study is ARQ in Voice over IP (VoIP) over UDP, where the Real-time Transport Protocol (RTP) adds reliability through application-layer mechanisms like negative acknowledgments (NACKs) and selective retransmissions as per RTP extensions, avoiding TCP's full overhead while correcting critical packet losses to maintain conversational quality without excessive latency.

Efficiency and Limitations

The throughput efficiency of Automatic Repeat Request (ARQ) protocols is influenced by factors such as the channel error rate P_e, propagation delay, and window size, which determine how effectively the available bandwidth is utilized for successful data transmission. In general, efficiency decreases as P_e increases because more retransmissions are required, reducing the proportion of useful data relative to total transmissions. For instance, in the stop-and-wait variant, the efficiency can be approximated as \eta = \frac{1 - P_e}{1 + 2a}, where a = \frac{t_p}{t_f} is the ratio of one-way propagation delay t_p to frame transmission time t_f, assuming negligible acknowledgment time; this highlights how higher delays (larger a) or error rates degrade performance by idling the sender during round-trip times. Larger window sizes in protocols like go-back-N or selective repeat mitigate delay impacts up to the bandwidth-delay product limit, allowing pipelined transmission to approach full channel utilization in low-error scenarios. Latency in ARQ systems arises from the inherent round-trip time (RTT) for acknowledgments plus additional delays from retransmissions, leading to end-to-end delays that scale with the average number of transmission attempts per frame. The average number of attempts is \frac{1}{1 - P_e}, so total latency per frame is approximately t_f + \text{RTT} \times \frac{1}{1 - P_e}, which becomes prohibitive in high-latency environments like satellite links where frequent errors amplify waiting periods. This added delay contrasts with forward error correction (FEC), which avoids retransmissions but incurs constant overhead. Key limitations of ARQ include the bandwidth overhead from frequent acknowledgments (ACKs), which consume resources even on error-free links—typically 1-5% of depending on frame size—and vulnerability to errors in the , potentially triggering unnecessary retransmissions or frame losses if negative ACKs (NAKs) are corrupted. In scenarios with perfect forward channels but noisy reverse links, this can halve effective throughput by causing duplicate transmissions. Additionally, ARQ performs poorly in asymmetric or broadcast settings lacking reliable . Compared to FEC, ARQ offers superior in low-error-rate environments (e.g., P_e < 10^{-3}) by transmitting only uncoded data initially and retransmitting selectively, achieving near-100% utilization when errors are rare, whereas FEC imposes a fixed penalty of 20-50% regardless of conditions. However, in high-error channels (P_e > 10^{-2}), ARQ's repeated attempts lead to excessive and reduced throughput due to cumulative retransmissions, making FEC preferable for its ability to correct errors in a single pass without dependency. ARQ-FEC schemes these trade-offs by combining incremental redundancy with retransmissions. To address these limitations, adaptive ARQ strategies dynamically switch operational modes based on estimated quality, such as transitioning from go-back-N to selective repeat in poor conditions or adjusting window sizes via on , thereby maintaining higher throughput (up to 20-30% improvement) across varying P_e. For example, in a with 1% (P_e = 0.01) and 100 ms RTT where transmission time equals RTT (i.e., a = 0.5), stop-and-wait efficiency drops to approximately 50% due to idling and one expected retransmission per 100 frames.

References

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