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GPS dates are expressed as a week number and a day-of-week number, with the week number transmitted as a ten-bit value.This means that every 1,024 weeks (about 19.6 years) after Sunday 6 January 1980, (the GPS epoch), the date resets again to that date; this happened for the first time at 23:59:47 on 21 August 1999, the second time at 23:59:42 UTC on 6 April 2019, and will happen again on 20 ...
In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal ...
The GPS week number rollover is a phenomenon that happens every 1,024 weeks, which is about 19.6 years. The Global Positioning System (GPS) broadcasts a date, including a week number counter that is stored in only ten binary digits, whose range is therefore 0–1,023. After 1,023, an integer overflow causes the internal value to roll over ...
Locally decodable codes are error-correcting codes for which single bits of the message can be probabilistically recovered by only looking at a small (say constant) number of positions of a codeword, even after the codeword has been corrupted at some constant fraction of positions.
A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages.
Catastrophic cancellation. In numerical analysis, catastrophic cancellation [1] [2] is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one long and the other long, and they are measured with a ruler that ...
Type I and type II errors. In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. For example, an innocent person may be convicted. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false.
The Failures In Time (FIT) rate of a device is the number of failures that can be expected in one billion (10 9) device-hours of operation. (E.g. 1000 devices for 1 million hours, or 1 million devices for 1000 hours each, or some other combination.) This term is used particularly by the semiconductor industry.