ECE 442 COMMUNICATION SYSTEM DESIGN LECTURE 10. LINEAR BLOCK CODES Husheng Li Dept. of EECS The University of Tennessee

SOME BASIC CONCEPTS Vector Sum Weight and Hamming Distance Linear Codes Systematic code Generator matrix G

HAMMING CODES A Hamming code is an (n,k) linear block code with n=2^q-1 and k=n-q. Hamming codes can be used to correct one error or detect two errors.

SYNDROME DECODING Parity check matrix H satisfies The decoding can be carried out by computing the syndrome The decoder looks up the error pattern from the syndrome and corrects the errors.

TABLE-LOOKUP DECODER

CYCLIC CODES In cyclic codes, the cyclic shift of a codeword is still a codeword. A cyclic code can be represented by a polynomial in the Galois fields: Why the cyclic codes are linear?

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