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Linear Block Codes

Linear Block Codes. The parity bits of linear block codes are linear combination of the message. Therefore, we can represent the encoder by a linear system described by matrices. . Basic Definitions. Linearity: where m is a k -bit information sequence c is an n -bit codeword.

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Lecture 16 Perfect Codes and the Sphere-Packing Condition (Section 4.5)

Lecture 16 Perfect Codes and the Sphere-Packing Condition (Section 4.5). Theory of Information. Spheres in Z n r. Definition Let x be a string of length n over an r- ary code, and let ? be a nonnegative

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Information and Coding Theory Hamming codes. Golay codes.

Information and Coding Theory Hamming codes. Golay codes. Juris Viksna, 2014. Hamming code [7,4]. G - generator matrix A (4 bit) message x is encoded as xG , i.e. if x = 0110 then c = xG = 0110011. Decoding? - there are 16 codewords, if there are no errors, we can just find

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1.32k views • 13 slides

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Perfect codes - PowerPoint PPT Presentation

Linear Block Codes

Lecture 16 Perfect Codes and the Sphere-Packing Condition (Section 4.5)

Information and Coding Theory Hamming codes. Golay codes.