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:

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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