Thesis

Generation and decoding of error correcting codes

The purpose of this project is to present error-correcting procedures and their encoding-decoding techniques. All codes are based on the mathematical concept of error-correcting codes. The codes described in this project are a single-error-correcting Hamming (7, 4) code, a burst-error-correcting Hamming (8, 4) code with a burst of error of length 2, and a double-error-correcting Bose- Chaudhuri-Hocguenghem (15, 7) code. The meggitt decoding (error-trapping decoding) is used to demonstrate practical application of the Hamming (7, 4) and (8, 4) codes. Also, one-step majority-logic decoding is used to demonstrate practical application of the Bose-Chaudhuri-Hocquenghem (15, 7) code. These decodings are simple applications of a variety of mathematical proofs and relations.

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