منابع مشابه
Theory of Error - Correcting Codes
The field of channel coding started with Claude Shannon’s 1948 landmark paper. Fifty years of efforts and invention have finally produced coding schemes that closely approach Shannon’s channel capacity limit on AWGN channels, both power-limited and band-limited. Similar gains are being achieved in other important applications, such as wireless channels. This course is divided in two parts. In t...
متن کاملA Theory of Quantum Error-Correcting Codes
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after...
متن کاملTheory of Error Correcting Codes Mt461/mt5461
These notes cover the part of the syllabus for MT461/MT5461 that is not part of MT361. Further installments will be issued as they are ready. All handouts and problem sheets will be put on the MT361 Moodle page, marked MSc/MSci. I would very much appreciate being told of any corrections or possible improvements to these notes. You are warmly encouraged to ask questions in lectures, and to talk ...
متن کاملError Correcting Codes in Quantum Theory.
A new type of uncertainty relation is presented, concerning the information-bearing properties of a discrete quantum system. A natural link is then revealed between basic quantum theory and the linear error correcting codes of classical information theory. A subset of the known codes is described, having properties which are important for error correction in quantum communication. It is shown t...
متن کاملHamming codes and some theory of linear error correcting codes
The topic is how to reduce the error of communication in the presence of noise. Block encoding is an expansion function from a block of plaintext alphabet symbols to a block of communication alphabet symbols where the block lengths are k and n respectively, and k ≤ n. Without loss of generality we consider both alphabets to be bit strings. The notation for an i length bit string is σ ∈ { 0, 1 }...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1979
ISSN: 0001-8708
DOI: 10.1016/0001-8708(79)90034-3