1. 1 Wireless Networks Lecture 5 Error Detecting and Correcting Techniques (Part II) Dr. Ghalib A. Shah

2. 2 Outlines  Review of previous lecture #3  Block Codes ►Hamming ►BCH ►Reed Solmon  ARQ ►Sliding window ►Go-back-N  Summary of today’s lecture

3. 3 Last Lecture Review  Transmission Errors  Parity Check ►Single-bit parity ►2D parity  Cyclic Redundancy Check  Block Error Code

4. 4 Hamming Code  Designed to correct single bit errors  Family of (n, k) block error-correcting codes with parameters: ► Block length:n = 2 m – 1 ► Number of data bits: k = 2 m – m – 1 ► Number of check bits: n – k = m ► Minimum distance: d min = 3  Single-error-correcting (SEC) code ► SEC double-error-detecting (SEC-DED) code

5. 5 Example of Error Detection/Correction 1 1 0 1 1 0 0 0 0 1 1 1 0 1 0 C1 C2 XOR Hamming distance = 3 Received Codeword (Cr) = 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 C1 Cr XOR 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 C2 Cr XOR

6. 6 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 (n-k) -1 ► Each bit of syndrome indicates a match (0) or conflict (1) in that bit position

7. 7 Example of Hamming Encode  Data = 00111001 Bit Position 121110987654321 Pos. Number 110010111010100110000111011001010100001100100001 Trans. Block Bit Position 121110987654321 Pos. Number 110010111010100110000111011001010100001100100001 Trans. Block xxxX Bit Position 121110987654321 Pos. Number 110010111010100110000111011001010100001100100001 Trans. Block 0011 x 100 x 1 xX Bit Position 121110987654321 Pos. Number 110010111010100110000111011001010100001100100001 Trans. Block 0011 x 100 x 1 xX Bit Position 121110987654321 Pos. Number 110010111010100110000111011001010100001100100001 Trans. Block 0011x100x1XX Check bits 0111 Bit Position 121110987654321 Pos. Number 110010111010100110000111011001010100001100100001 Trans. Block 001101001111 PositionCode 10 1010 9 1001 7 0111 3 0011 XOR 0111

8. 8 Decoding Hamming Bit Position 121110987654321 Pos. Number 110010111010100110000111011001010100001100100001 Trans. Block 001101101111 PositionCode 10 1010 9 1001 7 0111 6 0110 3 0011 XOR 0110 Bit Position 121110987654321 Pos. Number 110010111010100110000111011001010100001100100001 Trans. Block 001101001111

9. 9 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

10. 10 BCH Codes  For positive pair of integers m and t, a (n, k) BCH code has parameters: ►Block length: n = 2 m – 1 ►Number of check bits: n – k <= mt ►Minimum distance:d min >= 2t + 1  Correct combinations of t or fewer errors  The generator polynomial can be constructed from the factors of (X 2m-1 +1)

11. 11 Reed-Solomon 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 = 2 m – 1 symbols = m(2 m – 1) bits ► Data length: k symbols ► Size of check code: n – k = 2t symbols = m(2t) bits ► Minimum distance: d min = 2t + 1 symbols

12. 12 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

13. 13 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  Sliding-window flow control ► Transmitter maintains list (window) of sequence numbers allowed to send ► Receiver maintains list allowed to receive

14. 14 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

15. 15 Flow Control

16. 16 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

17. 17 Error Control Requirements  Error detection ► Receiver detects errors and discards PDUs  Positive acknowledgement ► Destination returns acknowledgment of received, error-free PDUs  Retransmission after timeout ► Source retransmits unacknowledged PDU  Negative acknowledgement and retransmission ► Destination returns negative acknowledgment to PDUs in error

18. 18 Go-Back-N  Improve Stop-and-Wait by not waiting!  Keep channel busy by continuing to send frames  Allow a window of up to W s 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

19. 19 ►Frame transmission are pipelined 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 4 is exhausted Go-Back-N ARQ A B fr 0 Time fr 1 fr 2 fr 3 fr 4 fr 5 fr 6 fr 3 ACK1ACK1 out of sequence frames Go-Back-4: 4 frames are outstanding; so go back 4 fr 5 fr 6 fr 4 fr 7 fr 8 fr 9 ACK2ACK2 ACK3ACK3 ACK4ACK4 ACK5ACK5 ACK6ACK6 ACK7ACK7 ACK8ACK8 ACK9ACK9 R next 0 1 2 3 3 4 5 6 7 8 9

20. 20 A B fr0 Time f1f2 f3 f0 Receiver is looking for R next =0 Out-of- sequence frames Four frames are outstanding; so go back 4 f2 f3 f1 f4f5f6 Go-Back-N ARQ ACK1ACK1 ACK2ACK2 ACK3ACK3 ACK4ACK4 ACK5ACK5 ACK6ACK6 Window size long enough to cover round trip time A B Time f0 Time-out expires f1 ACK1ACK1 Stop-and-Wait ARQ Receiver is looking for R next =0

21. 21 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

22. 22 Receiver Receive Window R next Frames received Receiver will only accept a frame that is error-free and that has sequence number R next When such frame arrives R next is incremented by one, so the receive window slides forward by one Timer S last S last +1 S recent S last +W s -1 Timer Transmitter... Buffers S last S last +W s -1... Send Window S recent Frames transmitted and ACKed... most recent transmission oldest un- ACKed frame max Seq # allowed Go-Back-N Transmitter & Receiver

23. 23 Go-back-N ARQ  Acknowledgments ► RR = receive ready (no errors occur) ► REJ = reject (error detected)  Contingencies ► Damaged PDU ► Damaged RR ► Damaged REJ