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"Don't repeat yourself" (DRY), also known as "duplication is evil", is a principle of software development aimed at reducing repetition of information which is likely to change, replacing it with abstractions that are less likely to change, or using data normalization which avoids redundancy in the first place.
[4] [5] The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors. Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth.
A cyclic redundancy check (CRC) is a non-secure hash function designed to detect accidental changes to digital data in computer networks. It is not suitable for detecting maliciously introduced errors.
Shannon–Fano–Elias coding produces a binary prefix code, allowing for direct decoding.. Let bcode(x) be the rational number formed by adding a decimal point before a binary code.
Here, () = = is the entropy, and Shannon's source coding theorem says that any code must have an average length of at least (). Hence we see that the Shannon–Fano code is always within one bit of the optimal expected word length.
A two-out-of-five code is an encoding scheme which uses five bits consisting of exactly three 0s and two 1s. This provides () = possible combinations, enough to represent the digits 0–9.
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 method was the first of its type, the technique was used to prove Shannon's noiseless coding theorem in his 1948 article "A Mathematical Theory of Communication", [1] and is therefore a centerpiece of the information age.