Wireless networks - Lecture 5: Error detecting and correcting techniques. The main topics covered in this chapter include: block codes; ARQ; hamming code; designed to correct single bit errors; single-error-correcting (SEC) code; multiple error correcting codes; reed-solomon codes;...
Wireless Networks Lecture Error Detecting and Correcting Techniques (Part II) Dr Ghalib A Shah Outlines Review of previous lecture #3 Block Codes ► Hamming ► BCH ► Reed Solmon ARQ ► Sliding window ► Go-back-N Summary of today’s lecture Last Lecture Review Transmission Errors Parity Check ► Single-bit parity ► 2D parity Cyclic Redundancy Check Block Error Code Hamming Code Designed to correct single bit errors Family of (n, k) block errorcorrecting codes with parameters: ► ► ► ► Block length: n = 2m – 1 Number of data bits: k = 2m – m – 1 Number of check bits: n – k = m Minimum distance: dmin = 3 Singleerrorcorrecting (SEC) code ► SEC doubleerrordetecting (SECDED) code Example of Error Detection/Correction C1 C2 1 1 0 0 XOR 1 Hamming distance =3 Received Codeword (Cr) =1 0 1 C1 Cr 1 1 0 1 XOR 0 C2 Cr 0 0 1 0 1 XOR 0 Hamming Code Process Encoding: k data bits + (n k) check bits Decoding: compares received (n k) bits with calculated (n k) bits using XOR ► Resulting (n k) bits called syndrome word ► Syndrome range is between 0 and 2(nk)1 ► Each bit of syndrome indicates a match (0) or conflict (1) in that bit position Example of Hamming Encode Data =00111001 Bit Position Bit Position Bit Position Bit Position Bit Position Pos. Number Pos. Number Pos. Number Pos. Number Pos. Number Trans. Block Trans. Block Trans. Block Trans. Block Trans. Block Check bits 12 12 12 12 11 11 11 10 10 10 999 12 11 10 888 777 666 555 444 33 22 11 Position 1100 1011 1010 1001 1000Code 0111 0110 0101 0100 0011 0010 0001 1100 11001011 1011 10111010 1010 1010 1001 1001 1001 1000 1000 1000 0111 0111 0111 0110 0110 0110 0101 0101 0101 0100 0100 0011 0010 0001 1100 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0011 0010 0010 0001 0001 1010 10 000 000 111 111 0x x 11 11001000 0111 0011 XOR 0111 00 1x x 11 1 X x 1 X X Decoding Hamming Bit Position Pos. Number Trans. Block Trans. Block 12 11 10 1100 1011 Position 1010 1001 1000 0111Code 0110 0101 0100 0011 0010 0001 1010 10 0 0 1 1 0 1 0 1001 0111 0110 0011 XOR 0110 1 1 1 1 BCH Codes BCH Discoverer: Bose, Chaudhuri and Hocquenghem Multiple error correcting codes Generalization of Hamming Code Flexibility in choice of parameters ► Block length, code rate BCH Codes For positive pair of integers m and t, a (n, k) BCH code has parameters: ► Block length: n =2m – ► Number of check bits: n – k =2t +1 Correct combinations of t or fewer errors The generator polynomial can be constructed from the factors of (X2m-1 +1) 10 ReedSolomon Codes Subclass of nonbinary BCH codes Data processed in chunks of m bits, called symbols An (n, k) RS code has parameters: ► Symbol length: m bits per symbol ► Block length: n = 2m – 1 symbols = m(2m – 1) bits ► Data length: k symbols ► Size of check code: n – k = 2t symbols = m(2t) bits ► Minimum distance: dmin = 2t + 1 symbols 11 Automatic Repeat Request Mechanism used in data link control and transport protocols Relies on use of an error detection code (such as CRC) Flow Control Error Control 12 Flow Control Assures that transmitting entity does not overwhelm a receiving entity with data Protocols with flow control mechanism allow multiple PDUs in transit at the same time PDUs arrive in same order they’re sent Slidingwindow flow control ► Transmitter maintains list (window) of sequence numbers allowed to send ► Receiver maintains list allowed to receive 13 Flow Control Reasons for breaking up a block of data before transmitting: ► Limited buffer size of receiver ► Retransmission of PDU due to error requires smaller amounts of data to be retransmitted ► On shared medium, larger PDUs occupy medium for extended period, causing delays at other sending stations 14 Flow Control 15 Error Control Mechanisms to detect and correct transmission errors Types of errors: ► Lost PDU : a PDU fails to arrive ► Damaged PDU : PDU arrives with errors 16 Error Control Requirements Error detection ► Receiver detects errors and discards PDUs Positive acknowledgement ► Destination returns acknowledgment of received, errorfree PDUs Retransmission after timeout ► Source retransmits unacknowledged PDU Negative acknowledgement and retransmission ► Destination returns negative acknowledgment to PDUs in error 17 Go-Back-N Improve Stop-and-Wait by not waiting! Keep channel busy by continuing to send frames Allow a window of up to Ws outstanding frames Use m -bit sequence numbering If ACK for oldest frame arrives before window is exhausted, we can continue transmitting If window is exhausted, pull back and retransmit all outstanding frames Alternative: Use timeout 18 Go-Back-N ARQ frames are outstanding; so go back Go-Back-4: A fr fr fr fr fr fr fr fr fr fr fr fr fr Time fr B A C K Rnext A C K 2 A C K 3 out of sequence frames A C K 4 A C K 5 A C K A C K 6 A C K 8 A C K 9 ► Frame transmission are pipe line d to keep the channel busy ► Frame with errors and subsequent out-of-sequence frames are ignored ► Transmitter is forced to go back when window of is exhausted 19 Window size long enough to cover round trip time Stop-and-Wait ARQ f0 A B Time-out expires A C K Receiver is looking for Rnext=0 Go-Back-N ARQ Time f1 f0 Four frames are outstanding; so go back fr0 f1 f2 f3 f0 f1 f2 f3 f4 f5 f6 Time A B Receiver is Out-oflooking for sequence Rnext=0 frames A C K A C K A C K A C K A C K A C K 20 Go-Back-N with Timeout Problem with Go-Back-N as presented: ► If frame is lost and source does not have frame to send, then window will not be exhausted and recovery will not commence Use a timeout with each frame ► When timeout expires, resend all outstanding frames 21 Go-Back-N Transmitter & Receiver Receiver Transmitter Send Window Frames transmitted S last and ACKed Srecent Buffers Timer Slast Timer Slast+1 Receive Window Slast+Ws-1 oldest unACKed frame Timer Srecent most recent transmission Slast+Ws-1 max Seq # allowed Frames received Rnext Receiver will only accept a frame that is error-free and that has sequence number Rnext When such frame arrives Rnext is incremented by one, so the receive window slides forward by one 22 GobackN ARQ Acknowledgments ► RR = receive ready (no errors occur) ► REJ = reject (error detected) Contingencies ► Damaged PDU ► Damaged RR ► Damaged REJ 23 ... previous lecture #3 Block Codes ► Hamming ► BCH ► Reed Solmon ARQ ► Sliding window ► Go-back-N Summary of today’s lecture Last Lecture Review Transmission Errors Parity Check ► Single-bit... Source retransmits unacknowledged PDU Negative acknowledgement? ?and? ?retransmission ► Destination returns negative acknowledgment to PDUs in? ?error 17 Go-Back-N Improve Stop -and- Wait by not waiting! Keep channel busy... with errors and subsequent out-of-sequence frames are ignored ► Transmitter is forced to go back when window of is exhausted 19 Window size long enough to cover round trip time Stop -and- Wait