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cyclic codes
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Error control coding EEE 470 (3+0) credits
Error control coding EEE 470 (3+0) creditsSpring 2015Instructor: Dr.Hafiz M.Asif
Cyclic shift:Cyclic codes:Definition A code C is cyclic if(i) C is a linear code; (ii) any cyclic shift of a codeword is also a codeword, i.e., whenever a0, an -1 C, then also an -1 a0 an 2 C.
CC representation:
Code polynomial of minimum degree:
Cyclic codes:
CC code construction:Example 5.2
CC Generator matrix:
CC Generator matrix:CC Generator matrix:Dual of CC:Dual of CC is also cyclic.Example 5.3
Encoding of cyclic codes:Three important steps of encoding
CC encoder:
15
16
Syndrome and error detection:Syndrome circuit:
Example 5.7:Example 5.7:
Example 5.7 solution:
Syndrome property:
Decoding cyclic codes:Syndrome decoding:Syndrome computationError pattern detectionError correction
Example 5.9:
(7,4) CC decoding circuit:
Suggested problems:All relevant examplesProblems: 5.1-5, 5.11