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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.
Error-free message: aaaabbbbccccddddeeeeffffgggg Transmission with a burst error: aaaabbbbccc____deeeeffffgggg Here, each group of the same letter represents a 4-bit one-bit error-correcting codeword.
Propagation of uncertainty. In statistics, propagation of uncertainty (or propagation of error) is the effect of variables ' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement ...
Errorless learning was an instructional design introduced by psychologist Charles Ferster in the 1950s as part of his studies on what would make the most effective learning environment. B. F. Skinner was also influential in developing the technique, noting that, ...errors are not necessary for learning to occur.
A repetition code is a coding scheme that repeats the bits across a channel to achieve error-free communication. Given a stream of data to be transmitted, the data are divided into blocks of bits. Each block is transmitted some predetermined number of times.
The first element of a CIRC decoder is a relatively weak inner (32,28) Reed–Solomon code, shortened from a (255,251) code with 8-bit symbols. This code can correct up to 2 byte errors per 32-byte block. More importantly, it flags as erasures any uncorrectable blocks, i.e., blocks with more than 2 byte errors.
DNA damage, due to environmental factors and normal metabolic processes inside the cell, occurs at a rate of 10,000 to 1,000,000 molecular lesions per cell per day. While this constitutes at most only 0.0003125% of the human genome's approximately 3.2 billion bases, unrepaired lesions in critical genes (such as tumor suppressor genes) can impede a cell's ability to carry out its function and ...
This expression is valid only for positive values of x, but it can be used in conjunction with erfc x = 2 − erfc(−x) to obtain erfc(x) for negative values. This form is advantageous in that the range of integration is fixed and finite.