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3 Error control digital transmission systems introduce errors applications require certain reliability level data applications require error-free transfer voice & video applications tolerate some errors error control used when transmission system does not meet application requirement error control ensures a data stream is transmitted to a certain level of accuracy despite errors two basic approaches: error detection & retransmission (ARQ) forward error correction (FEC) Principle of error detection transmitter: for a given bit stream M, additional bits (called errordetecting code) are calculated as a function of M and appended to the end of M receiver: for each incoming frame, perform the same calculation and compares the two results. A detected error occurs if there is a mismatch Link Layer 5-9 Link Layer 50 Error detection Parity checks - single bit parity check Sender Data E= f(data) Data 1. Calculate E from received data 2. Compare E and E if identical, no error assumed. otherwise, error detected E Legend: E,E = Error detecting codes f = Error detecting function Data E = f(data) E Compare Receiver add a single bit(parity bit) to each character so that the total number of ones is even (even parity) or odd (odd parity) if di = i-th data bit, then parity bit =d1d2... dn (even parity) d1 d2 d3 d4 d5 d6 d (even parity) single-bit parity checks can only detect odd number of errors Link Layer 51 Link Layer 52

4 Odd-parity : example data parity 1 error 2 errors 3 errors Two dimensional parity check horizontal and vertical parity checks (row and column) Character 1 Data bits d11 d12 ¼ d1n f1r Character parity bits data parity Error detected data parity Error not detected data parity Error detected Single-bit parity check can only detect odd number of errors Character 2 Character m Block check character d21 d22 ¼ d2n f2r ¼ dm1 dm2 ¼ dmn fmr fc1 fc2 ¼ fcn fcr Link Layer 53 Link Layer 54 Error-detecting capability Cyclic Redundancy Check (CRC) One error Three errors Two errors Four errors (undetectable) 1, 2, or 3 errors can always be detected; Not all patterns >4 errors can be detected powerful error detection, easily implemented by hardware logic principle: given a k-bit message (M), the transmitter generates an n-bit sequence (R), so that the resulting frame (T) is exactly divisible by some predetermined (n+1)-bit number (G) use modulo-2 arithmetic: no carries/borrows; add subtract XOR M(k bits) message digits T(k+n bits) R(n bits) check digits CRC : frame Arrows indicate failed check bits Link Layer 55 Link Layer 56

5 CRC calculation M CRC (n bits) (=2 n M) 2 n M/G = Q + R/G Q: quotient R: remainder M CRC (=R) method: 1) append n 0 s to the right of M (initializes CRC bits with zeros) 2) divide the extended message 2 n M by G 3) let CRC be equal to R Link Layer 57 CRC calculation: example generator: (1,0,1,1) G(x) = x 3 + x + 1 message: (1,1,0,0) M(x) = x 3 + x 2 CRC bits: 3 bits (to be calculated) initialization: (1,1,0,0,0,0,0) x 3 M(x) = x 6 + x ) therefore, CRC bits = 010 transmitted codeword: T= (1,1,0,0,0,1,0) T(x) = x 6 + x 5 + x x 3 + x 2 + x x 3 + x + 1 ) x 6 + x 5 x 6 + x 4 + x 3 x 5 + x 4 + x 3 x 5 + x 3 + x 2 x 4 + x 2 x 4 + x 2 + x x Link Layer 58 Undetectable error patterns (transmitter) T(x) (channel) + (receiver) E(x) error polynomial T (x)=t(x)+e(x) E(x) has 1s in error locations & 0s elsewhere receiver divides the received polynomial T (x) by G(x) blindspot: if E(x) is a multiple of G(x), that is, E(x) is a nonzero codeword, then T (x) = T(x) + E(x) = Q(x)G(x) + Q (x)g(x) If an error polynomial is divisible by the generator polynomial, then the error pattern will be undetectable. choose the generator polynomial so that selected error patterns can be detected. Errors detected by CRC all single-bit errors if G(x) has more than one term all double-bit errors, as long as G(x) has a factor with at least three terms any odd number of errors, as long as G(x) contains a factor (x+1) any burst error of length n bits or less, n=degree of the polynomial G(x) Link Layer 59 Link Layer 5-20

9 Channel partitioning: FDMA FDMA: frequency division multiple access channel spectrum divided into frequency bands each station assigned fixed frequency band unused transmission time in frequency bands go idle example: 6-station LAN, 1,3,4 have pkt, frequency bands 2,5,6 idle FDM cable frequency bands Channel partitioning: CDMA CDMA: code division multiple access 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 allows multiple users to coexist and transmit simultaneously with minimal interference (if codes are orthogonal ) encoded signal = (original data) X (chipping sequence) decoding: inner-product of encoded signal and chipping sequence Link Layer 5-33 Link Layer 5-34 CDMA encode/decode CDMA: two-sender interference sender data bits code d 1 = d 0 = slot 1 slot 0 Z i,m = d i. cm channel output Z i,m slot 1 channel output slot 0 channel output Sender 1 Sender 2 channel sums together transmissions by sender 1 and 2 received input receiver code slot 1 slot 0 M D i = Z. i,m cm m=1 M d 1 = slot 1 channel output d 0 = 1 slot 0 channel output using same code as sender 1, receiver recovers sender 1 s original data from summed channel data! Link Layer 5-35 Link Layer 5-36

10 Random access protocols when node has packet to send transmit at full channel data rate R. no a priori coordination among nodes two or more transmitting nodes collision, random access MAC protocol specifies: how to detect collisions how to recover from collisions (e.g., via delayed retransmissions) examples of random access MAC protocols: ALOHA CSMA, CSMA/CD, CSMA/CA ALOHA ALOHA protocol was developed for a radio (wireless) LAN at the University of Hawaii in early 1970 talk when you please scheme original ALOHA protocol is called pure ALOHA each station whenever it has a new frame to send: 1. immediately transmits the frame 2. waits for a round-trip interval for ACK 3. if ACK is not received, waits for a random amount of time and repeats the step 1 Link Layer 5-37 Link Layer 5-38 Collisions in pure ALOHA Vulnerable time in pure ALOHA Link Layer 5-39 Link Layer 5-40

11 Slotted ALOHA In 1972, Robert published a method for doubling the capacity of an ALOHA system time is divided into fixed slots corresponding to one frame for each slot nodes can transmit only at the beginning of the next slot nodes need to be synchronized Collisions in slotted ALOHA Link Layer 5-41 Link Layer 5-42 Vulnerable time in slotted ALOHA Carrier Sense Multiple Access (CSMA) carrier sensing is useful to reduce the possibility that a new transmission will collide with an ongoing transmission listen before talk scheme: If channel sensed idle, transmit entire frame If channel sensed busy, defer transmission CSMA can improve performance over the ALOHA because no station begins to transmit when it senses the channel busy three CSMA schemes: Non-persistent CSMA 1-persistent CSMA p-persistent CSMA Link Layer 5-43 Link Layer 5-44

12 Collisions in CSMA collisions can still occur: propagation delay means two nodes may not hear each other s transmission collision: entire frame transmission time wasted Vulnerable time in CSMA B s C s Link Layer 5-45 Link Layer 5-46 Three CSMA schemes CSMA with Collision Detection (CSMA/CD) listen while talk scheme: listen before transmission until the channel is free additionally continue to monitor channel during transmission if collision is detected, immediately abort transmission and then, retransmit after a random amount of time collisions can be detected by looking at the power of the received signal and comparing it to the transmitted signal CSMA/CD is used on Ethernet (IEEE 802.3) LANs Link Layer 5-47 Link Layer 5-48

13 Collision and abortion in CSMA/CD Frame size for collision detection in the worst case, a station cannot detect a collision during 2, where is the propagation delay from end to end. minimum frame size >= 2 + safety margin. Link Layer 5-49 Link Layer 5-50 Ethernet CSMA/CD algorithm Taking turns MAC protocols 1. NIC receives datagram from network layer, creates frame 2. If NIC senses channel idle, starts frame transmission. If NIC senses channel busy, waits until channel idle, then transmits. 3. If NIC transmits entire frame without detecting another transmission, frame transmission is done! 4. If NIC detects another transmission while transmitting, aborts and sends jam sequence 5. After aborting, NIC enters binary (exponential) backoff: after mth collision, NIC chooses K at random from {0,1,2,, 2 m }. NIC waits K 512 bit times, returns to Step 2 longer backoff interval with more collisions polling: master node invites slave nodes to transmit in turn typically used with dumb slave devices concerns: polling overhead latency single point of failure (master) data slaves data poll master Link Layer 5-51 Link Layer 5-52

14 Taking turns MAC protocols token passing: control token passed from one node to next sequentially. token message concerns: token overhead latency single point of failure (token) (nothing to send) T T Summary of MAC protocols channel partitioning, by time, frequency or code TDMA, FDMA, CDMA random access (dynamic) ALOHA, S-ALOHA, CSMA, CSMA/CD collision detection: easy in some technologies (wire), hard in others (wireless) CSMA/CD used in Ethernet CSMA/CA used in (WiFi) taking turns polling from central site token passing: FDDI, token ring (802.5) data Link Layer 5-53 Link Layer 5-54

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