Lecture 37

Lecture 37 - 1 ECE52 Spring 11 Lecture 37 4/15/11 2 Beyond...

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Unformatted text preview: 1 ECE52 Spring 11 Lecture 37 4/15/11 2 Beyond SED greater distance How about error correcting codes , not just error detecting codes! Need greater distance to both detect and isolate the error. Consider a simple case: a 3-bit code with minimum distance 3, where 000 represents 0 111 represents 1 Any single error is certainly detected! for 0: 001 010 100 for 1: 110 101 011 Moreover, we can associate any single error with the code word closest to it to recover what was intended under the assumption of single errors only! 2 errors, were toast. Overhead here is 200% - rather high..! A SEDSEC code Single error detecting, single error correcting or can be DED Double error detecting, if we forego correction! 3 Error Correcting Codes Any distance 3 code can either correct any single error or detect any double error with no correction A distance 4 code can be used for single error correction AND double error detection (SECDED), or it can be used for triple error detection with no correction. Key to error correction is to be able to detect and locate faulty bits flip the faulty bit to fix! 4 Hamming Codes for error correction For each group of m information bits (the original message), k parity bits are added, call them p 1 , p 2 , , p k , forming an (m+k)- bit code. k separate parity checks will be performed, whose results will form a k-bit number which will identify which bit (if any) has been corrupted! Thus k must satisfy 2 k >= m+k+1 the +1 is for the no error case 5 Example: 4 information bits Suitable for transmitting BCD digits for example....
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This note was uploaded on 07/05/2011 for the course ECE 52 taught by Professor Dr.jonathanboard during the Spring '11 term at Duke.

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Lecture 37 - 1 ECE52 Spring 11 Lecture 37 4/15/11 2 Beyond...

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