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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.)
The second pattern of potentially globally redundant proofs appearing in global redundancy definition is related to the well-known [further explanation needed] notion of regularity [further explanation needed]. Informally, a proof is irregular if there is a path from a node to the root of the proof such that a literal is used more than once as ...
Turbo coding is an iterated soft-decoding scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
The Source coding theorem states that for any ε > 0, i.e. for any rate H(X) + ε larger than the entropy of the source, there is large enough n and an encoder that takes n i.i.d. repetition of the source, X 1:n, and maps it to n(H(X) + ε) binary bits such that the source symbols X 1:n are recoverable from the binary bits with probability of ...
In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured).
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 :
Redundancy, by definition, requires extra parts (in this case: logical terms) which raises the cost of implementation (either actual cost of physical parts or CPU time to process). Logic redundancy can be removed by several well-known techniques, such as Karnaugh maps , the Quine–McCluskey algorithm , and the heuristic computer method .
Naive attempts to work around this often either enable a chosen-ciphertext attack to recover the secret key or, by encoding redundancy in the plaintext space, invalidate the proof of security relative to factoring. [1] Public-key encryption schemes based on the Rabin trapdoor function are used mainly for examples in textbooks.