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Functions of the Data Link Layer Provide service interface to the network layer Dealing with transmission errors Regulating data flow Slow receivers not swamped by fast senders

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Functions of the Data Link Layer (2) Relationship between packets and frames.

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Errors in transmission Basics of transmission – variation of (amplitude/phase/frequency) SNR –10 log ((peak signal/(RMS Noise)^2) Regenerative Repeaters Bit Error Ratio (BER) –Optical medium is around 10^-14 –Wireless is around 10^-3 –Copper in between Gaussian Noise/AWGN Burst errors

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Error Detection and Correction Error-Correcting, Error-Detecting Codes Some Basics Msg (m) + Redundant(r) = Code(n) Not all codewords are legal Hamming Distance is the number of positions where two codewords differ If 2 codewords are distance d apart, then it takes d errors to convert one to the other => d+1 distance for d error detection 2d+1 distance for d error correction

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Error Detection and Correction Parity as an EDC 1 bit parity creates a code with distance 2 00 --> 000, 01 --> 011 Suppose we want to correct all single errors in an m bit message. How efficient can such a code be in terms of length ? n bit code => n single bit errors => n+1 codes/valid msg (n+1)2^m <= 2^n or m+r+1 <= 2^r

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Hamming Codes Hamming codes obtain the theoretical lower bounds (perfect parity codes) –In a codeword, powers of 2 are the check bits, and the other bits contain data –The parity of a data bit is checked by several check bits, as directed by the binary representation of its position. Bit 11s parity is checked by 1+2+8 –Reciever “adds” parity bits in error, and this gives the location of the error bit! –Interleaving to detect burst errors

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Error-Correcting Codes Use of a Hamming code to correct burst errors.

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Error Detecting Codes Useful when BERs are low and overhead of ECC is significant compared to Re-Tx. Still use the interleaving idea to convert burst errors into single bit errors Polynomial (CRC) codes –A k+1 bit number is represented as a polynomial of degree k in some dummy variable, with leftmost bit being most significnt. –Sender and receiver agree on the “generator” of the code, another polynomial G(x), with 1s in msb and lsb –Polynomial arithmetic is done modulo 2 (no carries or borrows, GF(2))

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CRC Codes Append a “checksum” to the end of the msg –If G(x) is of degree r, then append r 0s to end of the m msg bits. The new number is now x^rM(x) –Divide this by G(x) modulo 2 –Subtract the remainder from X^rM(x) modulo 2, and let this be T(x). This number is now divisible by G(x) Transmit T(x), and have receiver check if the received data is divisible by G(x) Suppose T(x)+E(x) arrives. (T(x)+E(x)/G(x) ) = E(x)/G(x) Detection whenever E(x)/G(x) != 0

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Error detection in CRC 1 bit error will be caught as long as G has 2 or more terms For 2 isolated bit errors if G(x) does not divide x^k+1 where k = distance between error bits CRC-CCITT 1+x^5 +x^12 +x^16 IEEE 802 (32,26,23,22,16,12,11,10,8,7,5,4,2,1,0) BCH Codes are GF(2^m). Reed-Solomon are BCH codes with block size 2^m Convolution codes (Trellis or Viterbi)

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Error-Detecting Codes Calculation of the polynomial code checksum.

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