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Accordingly, there are two variants of parity bits: even parity bit and odd parity bit. In the case of even parity, for a given set of bits, the bits whose value is 1 are counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number.
The bit following the 8 data bits in these bytes is an even parity bit, that is such that there's an even number of '1' bits (H or L according to the direct or inverse convention defined by TS) among the 8 data bits and the parity bit. TS also allows the card reader to confirm or determine the ETU, as one third of the delay between the first ...
Since the source is only 4 bits then there are only 16 possible transmitted words. Included is the eight-bit value if an extra parity bit is used (see Hamming(7,4) code with an additional parity bit). (The data bits are shown in blue; the parity bits are shown in red; and the extra parity bit shown in green.)
Logic parity RAM recalculates an always-valid parity bit each time a byte is read from memory, instead of storing the parity bit when the memory is written to; the calculated parity bit, which will not reveal if the data has been corrupted (hence the name "fake parity"), is presented to the parity-checking logic.
Add the digits (up to but not including the check digit) in the even-numbered positions (second, fourth, sixth, etc.) to the result. Take the remainder of the result divided by 10 (i.e. the modulo 10 operation). If the remainder is equal to 0 then use 0 as the check digit, and if not 0 subtract the remainder from 10 to derive the check digit.
The parity bit may be used within another constituent code. In an example using the DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits.
Parity bit 2 covers all bit positions which have the second least significant bit set: bits 2–3, 6–7, 10–11, etc. Parity bit 4 covers all bit positions which have the third least significant bit set: bits 4–7, 12–15, 20–23, etc.
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]