This book serves as an introductory text to algebraic coding theory. The contents are suitable for final year undergraduate and first year graduate courses in electrical and computer engineering, and will give the reader knowledge of coding fundamentals that is essential for a d…
by GUY, Richard K., Brown, Ezra
fromThe Carus mathematical monographs
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of…
The research that led to this thesis was inspired by Sudan's breakthrough that demonstrated that Reed-Solomon codes can correct more errors than previously thought. This breakthrough can render the current state-of-the-art Reed-Solomon decoders obsolete. Much of the importance o…
This dissertation is concerned with algebraic list-decoding of error-correcting codes. During the past decade, significant advances in this are were achieved. The breakthrough papers of Sudan, Guruswami & Sudan, and Koetter & Vardy showed that the well-known Reed-Solomon (and ot…
Low-density parity-check (LDPC) codes have made it possible to communicate at information rates very close to the Shannon capacity by combining sparsity with quasi-randomness, which enables the use of low-complexity iterative message-passing (IMP) decoders. So far, most systemat…
This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS), Hermitian, and Steane enlargement constructions to certain classes of classical codes…
