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# f33-book-depend-pres-pt4 - Oct 2009 Part IV Errors...

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Oct. 2009 Part IV – Errors: Informational Distortions Slide 1

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Oct. 2009 Part IV – Errors: Informational Distortions Slide 2 About This Presentation This presentation is intended to support the use of the textbook Dependable Computing: A Multilevel Approach (traditional print or on-line open publication, TBD). It is updated regularly by the author as part of his teaching of the graduate course ECE 257A, Fault-Tolerant Computing, at Univ. of California, Santa Barbara. Instructors can use these slides freely in classroom teaching or for other educational purposes. Unauthorized uses, including distribution for profit, are strictly prohibited. © Behrooz Parhami Edition Released Revised Revised Revised Revised First Sep. 2006 Oct. 2007 Oct. 2009
Oct. 2009 Part IV – Errors: Informational Distortions Slide 3 Error Detection

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Oct. 2009 Part IV – Errors: Informational Distortions Slide 4
Oct. 2009 Part IV – Errors: Informational Distortions Slide 5

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Oct. 2009 Part IV – Errors: Informational Distortions Slide 6 13.1 Basics of Error Detection High-redundancy codes Duplication is a form of error coding: x represented as xx (100% redundancy) Detects any error in one version Two-rail logic elements AND: ( a 0 , a 1 ) ( b 0 , b 1 ) = ( a 0 b 0 , a 1 b 1 ) OR: ( a 0 , a 1 ) ( b 0 , b 1 ) = ( a 0 b 0 , a 1 b 1 ) NOT: ( a 0 , a 1 ) = ( a 1 , a 0 ) XOR: ( a 0 , a 1 ) ( b 0 , b 1 ) = ( a 0 b 1 a 1 b 0 , a 0 b 0 a 1 b 1 ) Encoding Decoding XOR f ( x ) f ( x ) Error signal x y Error checking Encoding Decoding XNOR f ( x ) f ( x ) Error signal x y Error checking Two-rail encoding x represented as xx (100% redundancy) e.g., 0 represented as 01; 1 as 10 Detects any error in one version Detects all unidirectional errors X X
Oct. 2009 Part IV – Errors: Informational Distortions Slide 7 Hamming Distance Definition: Hamming distance between two bit-vectors is the number of positions in which they differ Min H-dist Code capability 2 d = 1; SED 3 c = 1; SEC or ( d = 2; DED) 4 c = 1 and d = 2; SEC/DED 5 c = 2 or ( c = 1 and d = 3; SEC/3ED) h c EC/ d ED such that h = c + d + 1 A distance-2 code: 00011 00101 001 1 0 01001 01010 01100 10001 10010 10100 11000 4 3 2 1 Codeword Correctable error Detectable error Code- word Noncode- word 0011 1 (0 1 error) 001 0 0 (1 0 error) d c , so that d c represents the add’l detection capability

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Oct. 2009 Part IV – Errors: Informational Distortions Slide 8 Error Classification and Models Goal of error tolerance methods: Allow uninterrupted operation despite presence of certain errors Error model – Relationship between errors and faults (or other causes) Errors are detected/corrected through: Encoded (redundant) data, plus code checkers Reasonableness checks, activity monitoring, retry Errors are classified as: Single or Multiple (according to the number of bits affected) Inversion or Erasure (symbol or bit changed or lost)* Random or Correlated (correlation in the form of byte or burst error) Symmetric or Asymmetric (regarding 0 1 and 1 0 inversions) * Nonbinary codes have substitution rather than inversion errors Also of interest for nonelectronic systems are transposition errors Errors are permanent by nature; transient faults, not transient errors
Oct. 2009 Part IV – Errors: Informational

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f33-book-depend-pres-pt4 - Oct 2009 Part IV Errors...

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