</small> --- # Outline - Framing - Byte count - Flag bytes with byte stuffing - Flag bits with bit stuffing - Error Control - Error correction - Error detection --- # Frames - Link layer accepts packets from the network layer, and encapsulates them into frames that it sends using the physical layer; reception is the opposite process - The Physical layer (below) is responsible for the transmission of raw sequences of bits --- # Frames </img> --- # Framing Methods - Byte count - Flag bytes with byte stuffing - Flag bits with bit stuffing --- # Framing: Byte count - Frame begins with a count of the number of bytes in it - Simple, but difficult to resynchronize after an error </img> --- # Data Framing – Headers and Trailers - We add a header (e.g. the length of data, etc.) and a trailer (extra data that can be used for e.g. error-detection or error-correction).
</br>
### Open Question: What happens if the flag value is found (i.e. naturally occurs) in the data? --- # Framing: Byte stuffing - Special flag bytes delimit frames; occurrences of flags in the data must be stuffed (escaped) - Longer, but easy to resynchronize after error </img> --- # Framing: Byte stuffing </img> - Byte sequences before and after stuffing for a different special byte - escape! --- # Framing: bit stuffing </img> - The flag is six consecutive ones. Within the data, a zero is stuffed after each five consecutive ones to void instances of the flag in the data.

1. The original data
2. The data as they appear on the line
3. The data as stored by receiver after de-stuffing

--- # Framing: bit stuffing </img> ### Sender: - encloses packet (bit stream) with flag: 0 1 1 1 1 1 1 0 - appends a 0 after each 1 1 1 1 1 in body (bit stuffing) --- # Framing: bit stuffing </img> ### Receiver, upon receiving 0 1 1 1 1 1: - next bit 0: stuffed bit is removed - next bit 1: - if next bit 0 (i.e. 0 1 1 1 1 1 1 0): end of frame marker - if next bit 1 (i.e. 0 1 1 1 1 1 1 1): error --- # Error Detection and Correction (EDC) ### Errors occur during frame transmission ### Two strategies to deal with error: 1. Include enough redundant information to help receivers deduce original data (error correcting) 2. Include enough information to deduce an error occurred (error detecting) - Neither error-correcting codes nor error-detecting codes can handle all possible errors --- # Error Detection and Correction - EDC = Error Detection and Correction bits - D = Data protected by error checking, may include header fields </img> --- # Error Detection and Correction - Error detection not 100% reliable: - a protocol may miss some errors, but rarely ### Example </img> --- # Codewords - A frame consists of m data (message) bits and r redundant (check) bits. - n-bit codewords with n =m+r - ASCII code for “A”: 1000001 - codeword for “A”: 10000010 (r=1) --- # Error Bounds – Hamming distance --- # Error Bounds – Hamming distance #### Example with 2 codewords: - Codeword #1: 1 0 0 0 1 0 0 1 - Codeword #2: 1 0 1 1 0 0 0 1 - Hamming distance is 3. The number of bit positions in which two codewords differ --- # Error Detection and Correction ### Hamming distance Step 1: Ensure the two strings are of equal length. - Codeword #1: 1 0 0 0 1 0 0 1 - Codeword #2: 1 0 1 1 0 0 0 1 --- # Error Detection and Correction ### Hamming distance Step 2: Compare the first two bits in each codeword (XOR them). If they are the same, record a "0" for that bit. If they are different, record a "1" for that bit. Repeat the process for the remaining bits. - Codeword #1: 1 0 0 0 1 0 0 1 - Codeword #2: 1 0 1 1 0 0 0 1 - Record: 0 0 1 1 1 0 0 0 --- # Error Detection and Correction ### Hamming distance Step 3: Add all the ones and zeros in the record together to obtain the Hamming distance. - Hamming distance = 0 + 0 + 1 + 1 + 1 + 0 + 0 + 0 = 3 - OR, count the number of 1s in the record. Three 1 bits in the record. i.e., Hamming distance is 3 --- # Hamming Codes ### Encoding: - We number the data bits starting from one and skipping the powers of two. The powers of two are reserved for parity bits. The rest are for message bits. ### Decoding: - Calculate all parities. If they are all OK, there was no error. If not, add up the positions of the incorrect ones- this gives us the position of the error --- # Error Correction – Hamming code The Hamming code gives a simple way to add check bits and correct up to a single bit error: - Check bits are parity over subsets of the codeword - Recomputing the parity sums (syndrome) gives the position of the error to flip, or 0 if there is no error --- # Error Correction – Hamming code </img> --- # Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

0 0 1 0 1 0 0 1 0 0 1 (received codeword)

--- # Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

- step #1: number the bits

1 2 3 4 5 6 7 8 9 10 11

0 0 1 0 1 0 0 1 0 0&nbsp&nbsp 1&nbsp (received codeword)

--- # Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

- step #2: allocate parity bits and message bits- powers of 2 bits are parity bits and the rest are message bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp (received codeword)

--- # Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

- step #3: finding the parity bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

- Finding p1: - Count one bit and skip one, starting from p1 but not including p1 value. - Add the 1s. If the result is even then p1 parity is 0, if the result is odd then p1 parity is 1. - p1 is? 1 1 0 0 1 → 1 --- # Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

- step #3: finding the parity bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

- Finding p2: - Count two bits and skip two, starting from p2 but not including p2 value. - Add up the result. If the result is even then p2 parity is 0, if the result is odd then p2 parity is 1 - p2 is? 1 0 0 0 1 → 0 --- # Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

- step #3: finding the parity bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

- Finding p4: - Count four bits and skip four, starting from p4 but not including p4 value. - Add up the result. If the result is even then p4 parity is 0, if the result is odd then p4 parity is 1. - p4 is ? 1 0 0 - - → 1 --- # Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

- step #3: finding the parity bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

- Finding p8: - Count eight bits and skip eight, starting from p8 but not including p8 value. - Add up the result. If the result is even then p8 parity is 0, if the result is odd then p8 parity is 1. - p8 is ? 0 0 1 - - → 1 --- # Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

- step #4: compare our result with the received parity bits.

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

- p1 is 0 1 1 0 0 1 → 1 ✘ - p2 is 0 1 0 0 0 1 → 0 ✔ - p4 is 0 1 0 0 - - → 1 ✘ - p8 is 1 0 0 1 - - → 1 ✔ - p1+p4 → in position 5 --- # Error Detection ### Three types of error detection codes: 1. Parity 2. Checksums 3. Cyclic redundancy codes --- # Error Detection – Parity - Parity bit is added as the modulo 2 sum of data bits - Equivalent to XOR; this is an odd parity - Ex: 1100110 → 11001101 - Detection checks if the sum is wrong (an error) --- # Error Detection – Parity - A sends a packet of 8 bits to B - 1 bit (the third bit) is flipped from 0 to 1 due to some noise or interference in the channel - How can we detect that the bit is flipped? </img> --- # Error Detection – Parity - Parity is used to detect the error by appending a “parity bit” to the data. - Example: A protocol between two hosts using odd parity for error detection </img> --- # Error Detection – Parity - Parity is used to detect the error by appending a “parity bit” to the data. - Example: A protocol between two hosts using even parity for error detection </img> --- # Parity Checking </img> --- # Error Detection – Checksum ### The sender: 1. Data is divided into k segment each of m bits (normally 16-bits integers) and summed. 3. The 1s complement of the sum forms the checksum 4. The checksum segment is sent along with the data segments --- # Error Detection – Checksum ### Sending four segments: - k = 4 m=8 - Segment #1 1 0 1 1 0 0 1 1 - Segment #2 1 0 1 0 1 0 1 1 - Segment #3 0 1 0 1 1 0 1 0 - Segment #4 1 1 0 1 0 1 0 1 --- # Error Detection – Checksum - 10110011 segment #1 - 10101011 segment #2 XOR them ---- - 01011110 ( 1 carry over) ---- - 01011111 sum - 01011010 segment #3 ---- - 10111001 - 11010101 segment #4 --- # Error Detection – Checksum ---- - 10001110 ( 1 carry over) ---- 10001111 sum ---- 01110000 Checksum --- # Error Detection – Checksums ### The receiver: 1. All received segments are added 2. The sum is complemented 3. If the result is zero, the received data is OK; otherwise wrong --- # Error Detection – Checksums - 10110011 segment #1 - 10101011 segment #2 ----------------------------- - 01011110 ( 1 carry over) ----------------------------- - 01011111 sum - 01011010 segment #3 ------------------------------ - 10111001 - 11010101 segment#4 -------------------------- - 10001110 (1 carry over) --- # Error Detection – Checksums -------------------------- - 10001111 - 01110000 Checksum ------------------------------ - 11111111 sum - 00000000 complement - Data is accepted --- # Error Detection - CRC --- # Error Detection - CRC - One of the most commonly used error detection codes ### Basic approach: - Let M1 be the message of n-bits - M1 is padded with CRC code and send it - CRC is generated using a given polynomial P1 (or Divisor) - P1 is agreed between sender and receiver - Receiver gets M1 + CRC and extracts the M1 using P1 --- # CRC – error detection and correction </img> --- # Error Detection – CRC (example) #### Example: encoding / sender side M1 = 1 0 1 0</br> P1 (Divisor) = 1 0 1 1 #### Generate CRC: 1. Add the degree of P1 (P1 length – 1) to M1 as zeros </br> P1 length - 1 = 4 – 1 = 3 2. Add 3 zeros to M1 </br> 1 0 1 0 0 0 0 3. Divide M1 by P1 using XOR --- # Error Detection – CRC (example) Transmitted frame: 1 0 1 0 0 1 1 </img> --- # Error Detection – CRC #### Example: decoding / receiver side Message: 1 0 1 0 0 1 1 Divisor: 1 0 1 1 - Divide the received message by the divisor - If the result is 0, message is correct. Otherwise, message is incorrect. --- # Error Detection – CRC (example) </img> --- # Summary - Link layer services - Data Framing - Error detection and correction