CRC and Interfaces-Data Communication-Lecture Slides, Slides of Data Communication Systems and Computer Networks

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Lecture- BS(CIS) Semester-IV

Data Communication

Today’s Lecture

• Revision  Synchronous and Asynchronous Communication  Error Detection using parity,  CRC
• CRC  Using Modulo 2 addition  Polynomial  Digital Logic
• Some important Interfaces  Serial and Parallel Communication Interface  Modem Interface

In case of Error (CRC-Continued)

• In case of remainder error is detected
• Locating Error  Extra bits are required to indicate the error bits (See next topic)
• Correction  Bits in error are XORd with 1  0+1=1 , 1+1=
• Final Equation  Tr=T + E (+ is for XOR) T= Transmitted Tr= Received E = Position of Error Bits

CRC-Polynomial

• All binary values are represented as polynomials  Example D= 110011 D(x)=X^5 + X4 +^ X+ P=11001 P(x)=X^4 + X3 +^ X+  CRC-Calculations Xn-k^ D(x) / P(x) = Q(x)+ R(x) / P(x) T(x) = Xn-k^ D(x) + R(x)
• Error Pattern is represented by E(X)
• An error will remain undetected if E(x) is divisible by P(x)

Error Correction

• Error correction require the knowledge of  Number of errors  Position of each error
• Comparatively greater number of bits required to hold the position of the error (redundancy bits)
• For large chunks of data the number of redundancy bits required are high and inefficient
• Most of the error correction code works for 1, 2, or three bit correction

Single Bit Error Correction

• If 7 bits of data  Number of error locations : 07  Bits required to hold position of one bit error: 03
• Total bits transmitted : 7+3 = 10  Number of error locations = 10  Bits required to hold position of one bit error : 04  Total bits sent for detecting error in 7 bits of data = 11
• To transmit m bits with r redundant bits should be such that 2 r^ ≥ m + r +1 - - - - (1)

Hamming Coding

• Hamming code can be applied to any number of bits using the relation – (1)
• Used to detect 1 and 2 bit error and correct 1 bit error
• Place the r redundancy bits at positions that are powers of 2 i.e. 1,2,4,8 etc
• Place the data bits other than r bits
• Each r bit is parity bit for one of the following combination r1: bits 1 3 5 7 9 11 r2: bits 2 3 6 7 10 11 r3: bits 4 5 6 7 r4: bits 8 9 10 11

Combination for r bits

d d d r d d d r d r r 11 10 9 8 7 6 5 4 3 2 1

1 1 1 1 0 0 0 0 0 0 0

0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0

1 0 1 0 1 0 1 0 1 0 1

11 10 9 8 7 6 5 4 3 2 1

r

r

r r

r

Bit position for parity calculation

Error Detection Correction

• At receiving end the parities are calculated again using the

same r bit combinations for even parity

 Error are detected

• The location of any error is given by the number formed by

the parity bits

 Error bit is inverted , error is corrected

Error Detection Correction

11 10 9 8 7 6 5 4 3 2 1 1 0 0 1 1 0 1

1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 - 0 1 0 0 1 0 1

r1: bits 1 3 5 7 9 11 Parity: 0 (Error )  0111 07

r2: bits 2 3 6 7 10 11 Parity: 1

r3: bits 4 5 6 Parity: 1

r4: bits 8 9 10 11 Parity: 1

..hamming code

• If a bit is inverted at least three bits are changed e.g. if bit 3 is changed (1,2,3) will be effected
• Not all codes are valid for a given distance
• If any invalid code is formed it is easy to detect the invalid code
• A code with distance d ≥ 2t+1 can correct t bit errors
• A code with distance d ≥ 2t can detect t bit errors and can correct errors ≤ t-

Assignment

• Apply hamming code for 1101001
• Apply hamming code for 11 bits and 4 bits

Traditional Configurations

Interfacing

• DTE  Data processing devices (or data terminal equipment, DTE) do not (usually) include data transmission facilities  Reasons - Simple encoding schemes - Transmission distance limitations
• DCE  Need an interface called data circuit terminating equipment (DCE)  e.g. modem, NIC  DCE transmits bits on medium  DCE communicates data and control info with DTE - Done over interchange circuits, Circuits used are termed as (interchange circuits) - Clear interface standards required