Search results
Results from the WOW.Com Content Network
Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: = + ′ ′, where is any Boolean function, is a variable, ′ is the complement of , and and ′ are with the argument set equal to and to respectively.
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...
For another, both Shannon’s and Fano’s coding schemes are similar in the sense that they both are efficient, but suboptimal prefix-free coding schemes with a similar performance. Shannon's (1948) method, using predefined word lengths, is called Shannon–Fano coding by Cover and Thomas, [ 4 ] Goldie and Pinch, [ 5 ] Jones and Jones, [ 6 ...
More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies [(())] [ (())], where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol. An entropy coding attempts to ...
Although "bit" is more frequently used in place of "shannon", its name is not distinguished from the bit as used in data-processing to refer to a binary value or stream regardless of its entropy (information content) Other units include the nat, based on the natural logarithm, and the hartley, based on the base 10 or common logarithm.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
For example, David Ellerman's analysis of a "logic of partitions" defines a competing measure in structures dual to that of subsets of a universal set. [14] Information is quantified as "dits" (distinctions), a measure on partitions. "Dits" can be converted into Shannon's bits, to get the formulas for conditional entropy, and so on.
Karyn Hascal, The Healing Place’s president and CEO, said she would never allow Suboxone in her treatment program because her 12-step curriculum is “a drug-free model. There’s kind of a conflict between drug-free and Suboxone.” For policymakers, denying addicts the best scientifically proven treatment carries no political cost.