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A binary symmetric channel (or BSCp) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver will receive a bit. The bit will be "flipped" with a "crossover probability " of p, and otherwise is received correctly.
As with other codes, the maximum likelihood decoding of an LDPC code on the binary symmetric channel is an NP-complete problem, [24] shown by reduction from 3-dimensional matching. So assuming P != NP, which is widely believed, then performing optimal decoding for an arbitrary code of any useful size is not practical.
The BCH code with and higher has the generator polynomial. This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. It is also denoted as: (15, 1) BCH code. In fact, this code has only two codewords: 000000000000000 and 111111111111111 (a trivial repetition code ).
A binary coderepresents text, computer processor instructions, or any other datausing a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary stringof eight bits (which is ...
Bacon's cipher or the Baconian cipher is a method of steganographic message encoding devised by Francis Bacon in 1605. [1] [2] [3] A message is concealed in the presentation of text, rather than its content. Baconian ciphers are categorized as both a substitution cipher (in plain code) and a concealment cipher (using the two typefaces).
The Reed–Solomon code is actually a family of codes, where every code is characterised by three parameters: an alphabet size , a block length, and a message length, with <. The set of alphabet symbols is interpreted as the finite field F {\displaystyle F} of order q {\displaystyle q} , and thus, q {\displaystyle q} must be a prime power .
Cyclic redundancy check. A cyclic redundancy check ( CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. [1] [2] Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents.
e. In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit ), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.