Classical Error-Correcting Codes

Publication year: 2012
Source: Classical and Quantum Information, 2012, Pages 345-454

Dan C., Marinescu , Gabriela M., Marinescu

 Summary: This chapter covers topics from the theory of classical error detection and error correction. After an informal introduction we cover block codes and introduce algebraic structures used for coding. Linear codes are analyzed next; we discuss the Hamming, Singleton, Gilbert-Varshamov, and Plotkin bounds, Hamming codes and Reed-Muller codes. The next sections cover cyclic codes and the BSH bound. Then we discuss burst error correcting codes, Reed-Solomon codes, convolutional codes, product codes, and turbo codesKey Wordsblock codes; linear codes; Hamming distance; maximum likelihood decoding; bounds; Hamming codes; Reed-Muller codes Reed-Solomon codes; convolutional codes; product codes; turbo codes;