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Chapter 10 Error Detection and Correction

Chapter 10 Error Detection and The McGraw-Hill Companies, Inc. Permission required for reproduction or can be corrupted Notepduring applications require that errors be detected and correctederrors be detected and 1 INTRODUCTIONINTRODUCTIONLetLetusus firstfirstdiscussdiscusssomesome issuesissues related,related, directlydirectlyororindirectly,indirectl y, toto errorerror detectiondetection andand discussed in this section:Topics discussed in this section:Type s of E r ror sRedundancyD t tiVCtiDetection Versus CorrectionForward Error Correction Versus RetransmissionCodingCodingModular a single-bit Error , only 1 bit in the data it hhdunit has Single-bit burst Error means that 2 or more bits ithdtithhdin the data unit have Burst Error of length detect or correct errors, we need to dt( ddt) bitith d tsend extra (redundant) bits with The structure of encoder and this book, we concentrate on block dlltidcodes; we leave convolution codes to advanced modulo-N arithmetic, we use only the iti th0tN1iliintegers in the range 0 to N 1, XORing of two single bits or two 2 BLOCK CODINGBLOCK CODI

The Hamming distance between two word i th b f diffds is the number of differences between corresponding bits. 10.25. Example 10.4 Let us find the Hamming distance between two pairs of words. 1. The Hamming distance d(000, 011) is2because 2. The HiHamming distance d(10101, 11110) is 3 because

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Hamming distance • Measures the number of bit flipsto change one codeword into another • Hamming distance between two messages m 1, m 2: The number of bit flips needed to change m 1into m 2 • Example: Two bit flips needed to change codeword 00 to codeword 11, so they are Hamming distance of twoapart: 17 00 01 11

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