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Redundancy of compressed data refers to the difference between the expected compressed data length of messages () (or expected data rate () /) and the entropy (or entropy rate ). (Here we assume the data is ergodic and stationary , e.g., a memoryless source.)
the information entropy and redundancy of a source, and its relevance through the source coding theorem; the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem;
Redundancy theorists infer from this premise that truth is a redundant concept—in other words, that "truth" is merely a word that it is conventional to use in certain contexts but not one that points to anything in reality.
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.
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:
Every request received by a non-failing node in the system must result in a response. This is the definition of availability in CAP theorem as defined by Gilbert and Lynch. [1] Note that availability as defined in CAP theorem is different from high availability in software architecture. [5] Partition tolerance
the information entropy and redundancy of a source, and its relevance through the source coding theorem; the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem;
This result is known as the Shannon–Hartley theorem. [11] When the SNR is large (SNR ≫ 0 dB), the capacity ... Redundancy; Sender, Data compression, Receiver;