Wireless Networks Lecture 4 Error Detecting and Correcting

Wireless Networks Ü Lecture 4 Ü Error Detecting and Correcting Techniques Ü Dr. Ghalib A. Shah 1

Outlines Ü Ü Ü Review of previous lecture #3 Transmission Errors Parity Check Cyclic Redundancy Check Block Error Code Summary of today’s lecture 2

Last Lecture Review Ü Multiplexing ► FDM, TDM Ü Transmission Mediums ► Guided media ► Unguided media • • • Microwave Radio waves Infra red Ü Propagation modes ► Ground wave propagation ► Sky-wave propagation ► LOS propagation Ü Multi-path propagation Ü Fading 3

Coping with Transmission Errors Ü Error detection codes ► Detects the presence of an error Ü Error correction codes, or forward correction codes (FEC) ► Designed to detect and correct errors ► Widely used in wireless networks Ü Automatic repeat request (ARQ) protocols ► Used in combination with error detection/correction ► Block of data with error is discarded ► Transmitter retransmits that block of data 4

Error Detection Process Ü Transmitter ► For a given frame, an error-detecting code (check bits) is calculated from data bits ► Check bits are appended to data bits Ü Receiver ► ► Separates incoming frame into data bits and check bits Calculates check bits from received data bits Compares calculated check bits against received check bits Detected error occurs if mismatch 5

Error Detection Transmitter Receiver • Error detection not 100% reliable! • protocol may miss some errors, but rarely • larger EDC field yields better detection and correction 6

Parity Checks Single bit Ü Ü Even or Odd parity Only single bit error detection What about multiple bit errors Use when probability of bit errors is small and independent Ü Errors are usually clustered together The ability of receiver to both detect and correct errors is known as forward error correction (FEC) 7

Examples of parity bit check Adding parity bit 110001011 110001010 Odd parity errors 110101011 110100011 Odd Even error detected error undetected 8

Two-dimensional parity checks Ü Ü Generalization of 1 -bit D bits are divided into i rows and j columns. D 1, 1 D 1, 2 … D 1, j+1 D 2, 2 … D 2, j+1 . . . …. …. …. . Di, 1 Di, 2 … Di, j+1 Di+1, 2 … Di+1, j+1 Ü Receiver can not only detect but correct as well using row, column indices 9

Example of 2 D Odd parity check Ü 1110010101111010 Ü Let i = 4, j = 4 1110 0101 0111 1010 1001 Parity bits 0 1 1 1110 0001 0111 1010 1001 0 1 1 Error detection/correction 1110 0011 0111 1010 1001 0 1 1 Error detection/ no correction 10

Cyclic Redundancy Check (CRC) Ü Transmitter ► For a k-bit block, transmitter generates an (n-k)-bit frame check sequence (FCS) ► Resulting frame of n bits is exactly divisible by predetermined number Ü Receiver ► Divides incoming frame by predetermined number ► If no remainder, assumes no error Ü Algorithm ► Generator: Transmitter and receiver agree on an r + 1 bit pattern P. ► Transmitter chooses r additional bits to append with k data bits. ► Which is remainder of d / P. ► Receiver: if remainder of D / P is 0 , success otherwise error 11

CRC using Modulo 2 Arithmetic Ü Exclusive-OR (XOR) operation Ü Parameters: • • • T = n-bit frame to be transmitted D = k-bit block of data; the first k bits of T F = (n – k)-bit FCS; the last (n – k) bits of T P = pattern of n–k+1 bits; this is the predetermined divisor Q = Quotient R = Remainder 12

CRC using Modulo 2 Arithmetic Ü For T/P to have no remainder, start with Ü Divide 2 n-k. D by P gives quotient and remainder Ü Use remainder as FCS 13

CRC using Modulo 2 Arithmetic Ü Does R cause T/P have no remainder? Ü Substituting, ► No remainder, so T is exactly divisible by P 14

CRC Example Let d = 10111, P=1001 Q 101011 P 1001 `P(X) = X 3 + 1 101110000 1001 1010 1001 D 1100 1001 1010 1001 011 T = 1011 R 15

CRC using Polynomials Ü All values expressed as polynomials ► Dummy variable X with binary coefficients 16

CRC using Polynomials Ü Widely used versions of P(X) ► CRC– 12 • X 12 + X 11 + X 3 + X 2 + X + 1 ► CRC– 16 • X 16 + X 15 + X 2 + 1 ► CRC – CCITT • X 16 + X 12 + X 5 + 1 ► CRC – 32 • 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 17

Wireless Transmission Errors Ü Error detection requires retransmission Ü Detection inadequate for wireless applications ► Error rate on wireless link can be high, results in a large number of retransmissions ► Long propagation delay compared to transmission time 18

Block Error Correction Codes Ü Transmitter ► Forward error correction (FEC) encoder maps each k -bit block into an n-bit block codeword ► Codeword is transmitted; analog for wireless transmission Ü Receiver ► Incoming signal is demodulated ► Block passed through an FEC decoder 19

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FEC Decoder Outcomes Ü No errors present ► Codeword produced by decoder matches original codeword Ü Decoder detects and corrects bit errors Ü Decoder detects but cannot correct bit errors; reports uncorrectable error Ü Decoder detects no bit errors, though errors are present 21

Block Code Principles Ü Hamming distance – for 2 n-bit binary sequences, the number of different bits ► E. g. , v 1=011011; v 2=110001; ► 011011 XOR 110001 = 101010 ► d(v 1, v 2)=3 Ü Redundancy – ratio of redundant bits to data bits Ü Code rate – ratio of data bits to total bits Ü Coding gain – the reduction in the required Eb/N 0 to achieve a specified BER of an error-correcting coded system 22

Block Codes Ü The Hamming distance d of a Block code is the minimum distance between two code words Ü Error Detection: ► Upto d-1 errors Ü Error Correction: ► Upto 23

Example of Block code Ü Let k = 2, n = 5 Data block Codeword 00 01 10 11 00000 00111 11001 11110 Ü Suppose we receive 0 0 1 0 0 pattern Ü Minimum distance is with codeword 0 0 0, so we deduct 0 0 as data bits. 24