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The quantity is called the relative redundancy and gives the maximum possible data compression ratio, when expressed as the percentage by which a file size can be decreased. (When expressed as a ratio of original file size to compressed file size, the quantity R : r {\displaystyle R:r} gives the maximum compression ratio that can be achieved.)
In computer science and information theory, set redundancy compression are methods of data compression that exploits redundancy between individual data groups of a set, usually a set of similar images. It is wide used on medical and satellital images.
The BSC has a capacity of 1 − H b (p) bits per channel use, where H b is the binary entropy function to the base-2 logarithm: A binary erasure channel (BEC) with erasure probability p is a binary input, ternary output channel. The possible channel outputs are 0, 1, and a third symbol 'e' called an erasure.
According to the redundancy theory of truth (also known as the disquotational theory of truth), asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence " 'Snow is white' is true" is equivalent to asserting the sentence "Snow is white".
There are many names for interaction information, including amount of information, [1] information correlation, [2] co-information, [3] and simply mutual information. [4] Interaction information expresses the amount of information (redundancy or synergy) bound up in a set of variables, beyond that which is present in any subset of those variables.
Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
Theorems are those logical formulas where is the conclusion of a valid proof, [4] while the equivalent semantic consequence indicates a tautology. The tautology rule may be expressed as a sequent :
In general, a quantum code for a quantum channel is a subspace , where is the state Hilbert space, such that there exists another quantum channel with () = =, where is the orthogonal projection onto .