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The JS++ programming language is able to analyze if an array index or map key is out-of-bounds at compile time using existent types, which is a nominal type describing whether the index or key is within-bounds or out-of-bounds and guides code generation. Existent types have been shown to add only 1ms overhead to compile times.
This LDPC code fragment represents a three-bit message encoded as six bits. Redundancy is used, here, to increase the chance of recovering from channel errors. This is a (6, 3) linear code, with n = 6 and k = 3. Again ignoring lines going out of the picture, the parity-check matrix representing this graph fragment is
A commonly used code encodes = eight-bit data symbols plus 32 eight-bit parity symbols in an =-symbol block; this is denoted as a (,) = (,) code, and is capable of correcting up to 16 symbol errors per block. The Reed–Solomon code properties discussed above make them especially well-suited to applications where errors occur in bursts. This is ...
Long code; Low-density parity-check code, also known as Gallager code, as the archetype for sparse graph codes; LT code, which is a near-optimal rateless erasure correcting code (Fountain code) m of n codes; Nordstrom-Robinson code, used in Geometry and Group Theory [31] Online code, a near-optimal rateless erasure correcting code; Polar code ...
A code with this ability to reconstruct the original message in the presence of errors is known as an error-correcting code. This triple repetition code is a Hamming code with m = 2, since there are two parity bits, and 2 2 − 2 − 1 = 1 data bit.
IF-MAP provides a common interface between the Metadata Access Point (MAP), a database server acting as a clearinghouse for information about security events and objects, and other elements of the TNC architecture. The IF-MAP protocol defines a publish/subscribe/search mechanism with a set of identifiers and data types.
The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, contains chapters on elementary error-correcting codes; on the theoretical limits of error-correction; and on the latest state-of-the-art error-correcting codes, including low-density parity-check codes, turbo codes, and fountain codes.
A bilinear map is a function: such that for all , the map (,) is a linear map from to , and for all , the map (,) is a linear map from to . In other words, when we hold the first entry of the bilinear map fixed while letting the second entry vary, the result is a linear operator, and similarly for when we hold the second entry fixed.