1.6 Error Control Strategies

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1 1.6 Error Control Strategies Introduction ARQ Data Source Encoder Binary Channel Decoder Data Sink {u} {v} {v'} {u'} encoder, decoder, error control; error control strategies: (simple) error detection; error correction: Forward Error Correction (FEC) at receiver only; FEC Automatic Repeat request (ARQ) error detection (receiver) + eroneous block retransmission (transmitter).

2 If the transmission system is an one-way system (the transmission is strictly in one direction, from transmitter to receiver), the error control must be accomplished using forward error correction (FEC), that is, by employing error-correcting codes that automatically correct errors detected at the receiver (ex. satellites and deep-space transmissions). These codes are used even the channel is not strictly one-way. When the transmission system is two-way, the error control can be accomplished using error detection and retransmission, called automatic repeat request (ARQ). In an ARQ system, when errors are detected at the receiver, a request is sent for transmitter to repeat the message. Note: For ARQ the block sequence numbering is needed each block is identified by a unique sequence number.

3 1.6.2 Error Causes and Consequences Types of errors in data communications (OSI layers 2, 3, 4): change in the packet content: extrinsic causes: noise, non-liniarity, crosstalk, etc; intrinsic causes: inter-symbol interferences, phase jitter in the clock; error occurrence: independent errors; burst errors. solution: encoding at transmitter and detection / correction in receiver. Blocks ordering alteration: loss, duplicate, order change; causes: congestion losses; content errors blocks rejection in network nodes; multiple retransmissions duplicates; connectionless (CL) forwarding order change. solution: data block sequence numbering at transmitter + order check in receiver.

4 1.6.3 Codes used in Data Communications Basics, information bits and control bits Parity check codes; longitudinal and transversal word parity; Block codes (n,k); Polynomial codes; Convolutional codes.

5 1.6.4 Data Sequence Numbering and Administration Goals: checking the data integrity at reception; retransmission; reordering the data sequence; resynchronization; flow control. Numbering types for different transmission data units: data blocks numbering LAPD, HDLC-LAPB, etc; byte numbering TCP, etc. Numbering field (in the block) K bits (=constant) finite set of sequence numbers N=2 K distinct sequence numbers modulo N arithmetic; Examples: HDLC: N=8 or 128 K=3 or 7; TCP: N=2 32.

6 1.6.4 Data Sequence Numbering and Administration (contin.) Data sequence administration variables for transmitter and receiver: Convention V = V mod N (finite set of sequence numbers); VA (at transm.) the number of the oldest transmitted and unconfirmed data unit; VS (at transm.) the number of the next data unit to be transmitted; VR (at rec.) the number of the next data unit to be received. Issue: finite set for N possible misinterpretations at receiver in case of retransmissions; Solution: the use of transmission windows, wt and wr: wt = numbers available for transmission without waiting for confirmation; wr = numbers allowed for reception; Necessary condition: wt + wr N, eliminates the misinterpretation at receiver retransmissions (usually, wt = wr = N / 2). in case of multiple

7 1.6.4 Data Sequence Numbering and Administration (contin.) Infinite numbered data sequence TRS Transm+conf. Transm.+unconf. Possible for transm. Not allowed n VA VS VA+N N REC Received+confirmed VR Allowed for reception Not allowed VR+N n N

8 1.6.5 ARQ Strategies In practice, the number of additional bits required to achieve reliable forward error control increases rapidly as the number of information bits increases. Hence, ARQ method is the predominant method used in data communication and networking systems. There are two basic types of ARQ: idle ARQ (or stop and wait ARQ, SW), which is used with character-oriented data transmission schemes wt = 1, wr = 1; continuous ARQ (wt > 1), which employs a retransmission strategy - go-back-n (GBN) wr = 1; retransmission resumed with VR; - selective repeat (SR) wr > 1; reception buffer for reordering. Note: Continuous ARQ is used primarily with bit-oriented transmission schemes.

9 Stop-and-wait ARQ ARQ Strategies (contin.) the transmitter sends a code word to the receiver and waits for a positive (AK) or negative (NAK) acknowledgement from the receiver. If AK is received (nor errors detected) the transmitter sends the next code word. If NAK is received (errors detected), it resends the preceding code word. Continuous ARQ the transmitter sends code words to the receiver continuously and receiver acknowledgements continuously. When a NAK is received, the transmitter begins a retransmission. Depending on the retransmission type there are two strategies: - Go-back-N ARQ: The code word in error and the words that follow it are retransmitted; - Selective-repeat ARQ: the transmitter may simply resend only those code words that are acknowledged negatively.

10 1.6.5 ARQ Strategies (contin.) Stop-and-wait ARQ (SW) T t T t Transmitter (T) I(N) I(N+1) I(N+1) AK(N+1) NAK(N+1) Time Receiver (R) t p t ie t r1 t ce t p t r2 I(N) I(N+1) I(N+1) t p propagation time; t ie information block emission time; t r1 time for information block processing at R station and for reversing the transmission way; t ce confirmation block emission time; t r2 time for confirmation block processing at primary station and for reversing the transmission way; T t total block transmission time; MSC diagrams (Message Sequence Chart)

11 Continuous ARQ ARQ Strategies (contin.) t ie t RTT Transmitter N N+1 N+m AK(N) Time Receiver N t p t ce t p t RTT = 2 t p + t ce ; condition: m t ie t RTT

12 1.6.5 ARQ Strategies (contin.) problem = the loss of AK / NAK acknowledgements (or only AKs are used) solution = using a timer at transmitter to limit the acknowledgement waiting time. The timer is fixed to a value (at least the = round trip time - RTT) and is started when each new block is transmitted (countdown). When the time expires (timer to 0) the last block is retransmitted automatically. Example: SW Timer expired T t T t RTT Transmitter I(N) I(N+1) I(N+1) AK(N+1) Time Receiver I(N) I(N+1)

13 1.6.5 ARQ Strategies (contin.) Exercise ARQ error control example Let s consider: A communication between 2 stations A B, using modulo-16 numbering, error control with AKs and NAKs, the receiver buffer size B r =1. At the moment t 0 the system state is defined by: VS=3 VA=14. At the moment t 0 there is 1 unsent data block. VR=0 Requirements: a. Draw the transmission MSC assuming no errors, pointing out the moments t 0 and t 1, where t 1 is fixed immediately after the transmission of the positive confirmation for the unsent block at moment t 0 ; b. Draw and explain the circular diagram at moments t 0 and t 1 for no errors; c. Draw the MSC at moment t 1 for the case when the last block being transmitted at moment t 0 is lost; d. Draw and explain the circular diagram at moment t 1 for the case when the last block being transmitted at moment t 0 is lost.

14 1.6.5 ARQ Strategies (contin.) Exercise ARQ error control example (contin.) Comments: B r =1 means that the receiver cannot save more than one block (1 buffer location) reordering the data sequence is not possible no selective retransmissions (SREJ) are possible only GBN can be used. For the MSC drawing the blocks being on the way at initial moment have to be identified: VS=3, VR=0 means that I(3) is the next to be sent and I(15) is the last received block, thus the blocks being on the way are I(0), I(1) si I(2). VA=14 means that the transmitter received the confirmation AK(14); VR=0 means that the receiver sent AK(0), thus the confirmations being on the way are AK(0) and AK(15). The MSC is drawn such that the moment t 0 overlaps with the blocks being on the way.

15 Exercise ARQ error control example (contin.) Solution: a. the MSC for the no errors case A N = 16 VS= 3 VA=14 VS= 4 VA=2 VS= 4 VA=4 I(13) I(14) I(15) I(0) I(1) I(2) I(3) t B AK(14) AK(15) AK(0) AK(1) AK(2) AK(3) AK(4) t 0 t 1 VR=0 VR=4 VR=4 t

16 Exercise ARQ error control example (contin.) Solution: b. the circular diagram at moment t 0 for the no errors case Transm. Rec. VA=14 VR= VS= t 0 Note: The arrow inside the transmitter diagram covers the current transmission window size (which is the number of transmitted and unconfirmed data blocks), while the arrow inside the receiver diagram represents the receiver buffer size.

17 Exercise ARQ error control example (contin.) Solution: b. the circular diagram at moment t 1 for the no errors case Transm. Rec. VA= VS= VR=4 t 1

18 Exercise ARQ error control example (contin.) Solution: c. the MSC for the case when the last block being transmitted at moment t 0 is lost N = 16 VS= 3 VA=14 VS= 4 VA=2 VS= 4 VA= 4 A t I(14) I(0) I(2) AK(1) AK(2) NAK(2) I(2) I(3) AK(4) B t t 0 t 1 VR=0 VR=4 VR=4

19 Exercise ARQ error control example (contin.) Solution: d. the circular diagram at moment t 1 for the case when the last block being transmitted at moment t 0 is lost Transm. Rec. VA= VS= VR=4 t 1

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