2.4 Error Detection Bit errors in a frame will occur. How do we detect (and then. (or both) frames contains an error. This is inefficient (and not

Transcription

1 CS475 Networks Lecture 5 Chapter 2: Direct Link Networks Assignments Reading for Lecture 6: Sections Homework 2: 2.1, 2.4, 2.6, 2.14, 2.18, 2.31, Due Thursday, Sept Error Detection Bit errors in a frame will occur. How do we detect (and then recover) from them? We look at error detection first. We detect errors by adding redundant information. We could transmit duplicate frames. If the frames differ on reception, one (or both) frames contains an error. This is inefficient (and not that reliable). We will look at the two-dimensional parity,, and cyclic redundancy check (CRC) error detection methods Two-Dimensional Parity Two-dimensional parity is often used with 7-bit codes ( ). It requires the addition of a parity byte (and 1 parity bit per word). Two-dimensional parity catches all 1, 2, and 3 bit errors (and most 4 bit errors). Fig 2.14: 2D Parity (Even Parity) PC serial port hardware can be configured to transmit and receive using 1-D parity. The settings must be identical on both ends of the link. Windows Serial Port Properties Window 09/08/2011 Page 1 of 6

2 2.4.2 Checksums Checksums are not used at the link layer, but are used at the higher layers in the TCP/IP stack. The checksum algorithm is easy to implement in software. In the checksum algorithm, data is treated as 16-bit integers. The integers are added using ones complement arithmetic. The ones complement of the sum is sent as the checksum. In ones complement addition any carry out of the most significant bit is added back in at the least significant position. Example: Compute the 8-bit check sum of , , using the Internet checksum algorithm Checksum is At the receiver all words are added (including the checksum) extra bits (16 for a message of any size), but it is relatively weak. using ones complement arithmetic. If there are no errors the sum Experience has shown that the algorithm is sufficient as long as will be all 1s ( in the previous example). stronger error detection ( ) is used at the link layer. The Internet checksum algorithm uses only a small number of Cyclic Redundancy Check The CRC algorithm is based on polynomial division. The bits in the message are treated as of a polynomial. For example, the four bit message 1011 represents: M(x) = 1 x x x = x 3 + x + 1 Note that most messages are thousands of bits long and would represent polynomials of high degree. To calculate a CRC, the sender and receiver agree on a divisor polynomial, C(x) Standard divisor polynomials are known to give good results. ( uses CRC-32). CRC C(x) CRC-8 x 8 + x 2 + x + 1 CRC-10 x 10 + x 9 + x 5 + x 4 + x + 1 CRC-12 x 12 + x 11 + x 3 + x CRC-16 x 16 + x 12 + x CRC-CCITT x 16 + x 12 + x 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 /08/2011 Page 2 of 6

3 To compute the k-bit CRC: 1) Multiply M(x) by x k (add k zeros at the end of the message). Call this message T(x). 2) Divide T(x) by C(x) and find the remainder. In performing the division, exclusive-or is used instead of subtraction. Polynomials of equal order can always be divided. The result is the original message followed by the in step 2). 3) Subtract the remainder from T(x). Consider computing the 3-bit CRC for the message M(x) = using C(x) = ) Message The transmitted signal is If this polynomial is divided by 1101 at the receiver, the remainder should be 0. If it is not, then an has occurred. Although the CRC calculation appears complex, it can be computed in using a shift register and exclusive-or gates. Fig. 2.16: CRC calc. using a shift register Division by x3 + x Reliable Transmission A link-level protocol that wants to deliver frames reliably must recover frames that have errors. This is usually done by using some combination of acknowledgments (ACKs) and timeouts. Recovery algorithms that use ACKs and timeouts are known as automatic repeat request ( ) algorithms. We will examine three such algorithms Stop-and-Wait The simplest ARQ scheme is the stop-and-wait algorithm. After transmitting one frame the sender waits for an acknowledgment before transmitting the next frame. If the ACK does not arrive after a certain interval, the sender retransmits the original frame. 09/08/2011 Page 3 of 6

4 If there are no errors the timeline is as shown below. (If an error If a frame is lost, the sender automatically retransmits the frame is detected in the received frame, the receiver does not return an after the timer has.. It waits for the frame to be retransmitted. Fig. 2.17: ACK received Fig. 2.17: Lost frame If the ACK is lost, the sender automatically retransmits the frame If the ACK is delayed, the sender automatically retransmits the after the timer has expired. The receiver can discard the duplicate frame, but must still send an ACK. frame after the timer has expired. The receiver can discard the duplicate frame, but must still send an ACK. Fig. 2.17: Lost ACK Fig. 2.17: Slow ACK 09/08/2011 Page 4 of 6

5 To simplify detection of frames, the frame header includes a bit that alternates between 0 and 1. If two consecutive 0 (or 1) frames are received, the receiver knows that the second frame is a duplicate. The main problem with the stop-and-wait algorithm is that it does not use the link to its full capacity. A 1.5 Mbps link with a 45 ms RTT has a delay x BW product of 67.5 kb (8 kb). Assuming a 1 kb frame, stop-and-wait would only allow a throughput of Fig. 2.18: Stop and wait with 1-bit sequence number. 1 kb x 8 b/b / 45 ms = This is only 1/8 of the link BW! Sliding Window To fully utilize the available BW we allow the sender to transmit frames in sequence. On the 1.5 Mbps link from the previous slide we want the sender to transmit 8 frames and be ready to send the 9th as soon as the ACK for the first frame is received. Fig. 2.19: Sliding Window Timeline The sender assigns a sequence number, SeqNum, to each frame. The sender has to maintain three variables related to the sliding window algorithm: SWS, the send window, LFS, the seq. num. of the last frame sent A new frame is sent (and LFS ) only if: LFS LAR SWS LAR, the seq. num. of the last acknowledgment received, Fig. 2.20: Sliding window on the sender. The receiver maintains the following three variables: 09/08/2011 Page 5 of 6

6 RWS, the receive window size, LAF LFR RWS LAF, the sequence number of the largest frame, LFR, the seq. num. of the last frame received The receiver maintains the following invariant: Fig. 2.21: Sliding window on the receiver. If the SeqNum of a received frame satisfies LFR < SeqNum LAF, the frame is accepted. If all frames with seq. numbers less than SeqNum have been ACKed then this frame is ACKed, LFR is set to SeqNum and LAF is set to LFR + RWS. When frames are received the details are a bit more complicated. See the text for details Concurrent Logical Channels ARPANET used a variation of stop-and-wait while still keeping the pipe full. It worked by using multiple logical channels and running stop-and-wait on each channel. The of each frame contained a 1-bit sequence number and the number of the logical channel. 09/08/2011 Page 6 of 6