Error Detection EDC Error Detection and Correction bits

Error Detection EDC= Error Detection and Correction bits (redundancy) D = Data protected by error checking, may include header fields • Error detection not 100% reliable! • protocol may miss some errors, but rarely • larger EDC field yields better detection and correction 5: Data. Link Layer 1

Parity Checking Single Bit Parity: Detect single bit errors Two Dimensional Bit Parity: Detect and correct single bit errors 0 0 5: Data. Link Layer 2

Internet checksum Goal: detect “errors” (e. g. , flipped bits) in transmitted segment (note: used at transport layer only) Sender: r treat segment contents as sequence of 16 -bit integers r checksum: addition (1’s complement sum) of segment contents r sender puts checksum value into UDP checksum field Receiver: r compute checksum of received segment r check if computed checksum equals checksum field value: m NO - error detected m YES - no error detected. But maybe errors nonetheless? More later …. 5: Data. Link Layer 3

Checksumming: Cyclic Redundancy Check r view data bits, D, as a binary number r choose r+1 bit pattern (generator), G r goal: choose r CRC bits, R, such that m m m <D, R> exactly divisible by G (modulo 2) receiver knows G, divides <D, R> by G. If non-zero remainder: error detected! can detect all burst errors less than r+1 bits r widely used in practice (ATM, HDCL) 5: Data. Link Layer 4

CRC Example Want: D. 2 r XOR R = n. G equivalently: D. 2 r = n. G XOR R equivalently: if we divide D. 2 r by G, want remainder R R = remainder[ D. 2 r G ] 5: Data. Link Layer 5

Code Division Multiple Access (CDMA) r used in several wireless broadcast channels r r r (cellular, satellite, etc) standards unique “code” assigned to each user; i. e. , code set partitioning all users share same frequency, but each user has own “chipping” sequence (i. e. , code) to encode data encoded signal = (original data) X (chipping sequence) decoding: inner-product of encoded signal and chipping sequence allows multiple users to “coexist” and transmit simultaneously with minimal interference (if codes are “orthogonal”) 5: Data. Link Layer 6

CDMA Encode/Decode sender data bits code Zi, m= di. cm d 0 = 1 -1 -1 -1 1 1 1 -1 -1 -1 slot 1 channel output 1 -1 1 1 1 d 1 = -1 1 channel output Zi, m -1 -1 -1 slot 0 channel output M Di = S Zi, m. cm m=1 received input code receiver 1 1 1 1 -1 -1 -1 1 -1 -1 -1 slot 1 M 1 1 -1 -1 slot 0 d 0 = 1 d 1 = -1 slot 1 channel output slot 0 channel output 5: Data. Link Layer 7

CDMA: two-sender interference 5: Data. Link Layer 8