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Majority Logic Decoding
In error detection and correction, majority logic decoding is a method to decode repetition codes, based on the assumption that the largest number of occurrences of a symbol was the transmitted symbol. Theory In a binary alphabet made of 0,1, if a (n,1) repetition code is used, then each input bit is mapped to the code word as a string of n-replicated input bits. Generally n=2t + 1, an odd number. The repetition codes can detect up to /2/math> transmission errors. Decoding errors occur when more than these transmission errors occur. Thus, assuming bit-transmission errors are independent, the probability of error for a repetition code is given by P_e = \sum_^ \epsilon^ (1-\epsilon)^{(n-k)}, where \epsilon is the error over the transmission channel. Algorithm Assumption: the code word is (n,1), where n=2t+1, an odd number. * Calculate the d_H Hamming weight of the repetition code. * if d_H \le t , decode code word to be all 0's * if d_H \ge t+1 , decode code word to be all 1's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Detection And Correction
In information theory and coding theory with applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repetition Code
In coding theory, the repetition code is one of the most basic linear error-correcting codes. In order to transmit a message over a noisy channel that may corrupt the transmission in a few places, the idea of the repetition code is to just repeat the message several times. The hope is that the channel corrupts only a minority of these repetitions. This way the receiver will notice that a transmission error occurred since the received data stream is not the repetition of a single message, and moreover, the receiver can recover the original message by looking at the received message in the data stream that occurs most often. Because of the bad error correcting performance coupled with the low code rate (ratio between useful information symbols and actual transmitted symbols), other error correction codes are preferred in most cases. The chief attraction of the repetition code is the ease of implementation. Code parameters In the case of a binary repetition code, there exist two co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Code Word (communication)
In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, clarity, brevity, or secrecy. See also * Code word (figure of speech) * Coded set * Commercial code (communications) * Compartmentalization (information security) * Duress code * Error correction and detection * Marine VHF radio * Password * Safeword * Spelling alphabet A spelling alphabet (#Terminology, also called by various other names) is a set of words used to represent the Letter (alphabet), letters of an alphabet in Speech, oral communication, especially over a two-way radio or telephone. The words chosen t ... References * * *UNHCR Procedure for Radio Communication External links UNHCR Procedure for Radio Communication Data transmission Cryptography {{crypto-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Weight
The Hamming weight of a string (computer science), string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a given set of bits, this is the number of bits set to 1, or the digit sum of the Binary numeral system, binary representation of a given number and the Taxicab geometry, ''ℓ''₁ norm of a bit vector. In this binary case, it is also called the population count, popcount, sideways sum, or bit summation. History and usage The Hamming weight is named after the American mathematician Richard Hamming, although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James Whitbread Lee Glaisher, James W. L. Glaisher to give a formula for Gould's sequence, the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Function
In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.e. the value of the function equals the value of the majority of the inputs. Boolean circuits A ''majority gate'' is a logical gate used in circuit complexity and other applications of Boolean circuits. A majority gate returns true if and only if more than 50% of its inputs are true. For instance, in a full adder, the carry output is found by applying a majority function to the three inputs, although frequently this part of the adder is broken down into several simpler logical gates. Many systems have triple modular redundancy; they use the majority function for majority logic decoding to implement error correction. A major result in circuit complexity asserts that the majority function cannot be computed by AC0 circuits of subexponential size. Properties For any ''x'', ''y'', and ''z'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
