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Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings. When r and m are integers with 0 ≤ r ≤ m, the Reed–Muller code with parameters r and m is denoted as RM ( r , m ). When asked to encode a message consisting of k bits, where holds, the RM ( r , m) code produces a codeword ...
A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events.
Today, Reed–Solomon codes are widely implemented in digital storage devices and digital communication standards, though they are being slowly replaced by Bose–Chaudhuri–Hocquenghem (BCH) codes. For example, Reed–Solomon codes are used in the Digital Video Broadcasting (DVB) standard DVB-S, in conjunction with a convolutional inner code ...
Convolutional code. In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'.
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix .This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.
Sample entropy. Sample entropy (SampEn) is a modification of approximate entropy (ApEn), used for assessing the complexity of physiological time-series signals, diagnosing diseased states. [1] SampEn has two advantages over ApEn: data length independence and a relatively trouble-free implementation. Also, there is a small computational ...
To do so technically would require a more sophisticated grammar, like a Chomsky Type 1 grammar, also termed a context-sensitive grammar. However, parser generators for context-free grammars often support the ability for user-written code to introduce limited amounts of context-sensitivity. (For example, upon encountering a variable declaration ...