Error Detection & Message Flow Control. Oswald Jumira Stellenbosch University

Transcription

1 Error Detection & Message Flow Control Oswald Jumira Stellenbosch University

2 Channel Coding Class of signal transformations designed to improve communications performances by enabling the transmitted signals to better withstand the effects of channel impairments e.g. Noise, Interference and Fading. Trade-off exist for accomplishing desired systems e.g. Error performance vs bandwidth Channel coding techniques have managed to provide as much as 10dB performance improvement (less costs other than using higher power transmitters and larger antennas)

3 Waveform Coding deals with transforming waveform into better waveforms to make detection process less subject to errors Structured Sequences transforming data sequences into better sequences having structured redundancy (redundant bits used for error detection and correction)

4 Types of Error Control Error detection and retransmission utilises parity bits to detect errors and receiver does not attempt to correct errors but requests a retransmission (2 way comms required) Forward Error Correction- parity bits designed for both detection and correction of errors (requires a one way link) NB. Not all error patterns can be corrected, error-correcting codes are classified according to their error correcting capabilities

5 Redundancy and Efficiency When we expect errors might occur during transmission we add redundancy (parity bits and CRC) Example 1 Tradeoff: Essential redundancy Vs Reduced efficiency

6 Parity Encoding and Checking Widely used method for error detection 1-bit error detection with parity Add an extra bit to a code to ensure an even or odd number of 1s Every code word has an even or odd number of 1s Single error detection no correction Two flipped around bits will result in passed parity Parity bit can be corrupted Retransmission requested since no correction Total Efficiency = 8/9 = 89%

7 Parity Array Coding Error location not detection only through expansion of general parity scheme k=m x n n- columns and m rows Two-Dimensional Parity or Longitudinal Redundancy Check with Block Check Character

8 Checksum Checking A checksum is a fixed-size datum computed from an arbitrary block of digital data for the purpose of detecting accidental erros The integrity of the data can be checked at any later time by recomputing the checksum and comparing it with the stored one. The procedure that yields the checksum from the data is called a checksum function or checksum algorithm A good checksum algorithm will yield a different result with high probability when the data is accidentally corrupted; if the checksums match, the data is very likely to be free of accidental errors.

9 Cyclic Redundancy Check Error detection method used in computer networks Also know as polynomial codes Message sent must be sent with a calculated CRC code so that it may be verified by receiver CRC calculation realised by a division operation applied to binary number Polynomials arithmetic is done modulo 2

10 A k-bit frame is seen as the coefficient list for a polynomial with k terms, ranging from k 1 x to 0 x

11 XOR No addition or borrows for subtraction A division is said to go into the dividend, if they have an equal number of bits Subtraction is replaced by exclusive OR (XOR) operation

12 CRC division using polynomials

13 CRC encoder and decoder

14 Division in CRC encoder

15 Division in the CRC decoder for two cases

16 Widely Accepted Polynomials

17 Burst Errors Each CRC standard detects errors in bursts of less than (r+1) bits Even an error in bursts of more than or equal to (r+1) bits is detected with a probability of r (1 0.5 ) Odd bit errors are detect

18 Dankie! Be nice to geeks because one day you might be working for one!