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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.
A parity bit is a bit that is added to a group of source bits to ensure that the number of set bits (i.e., bits with value 1) in the outcome is even or odd. It is a very simple scheme that can be used to detect single or any other odd number (i.e., three, five, etc.) of errors in the output.
Shown are only 20 encoded bits (5 parity, 15 data) but the pattern continues indefinitely. The key thing about Hamming codes that can be seen from visual inspection is that any given bit is included in a unique set of parity bits. To check for errors, check all of the parity bits.
For example, p 2 provides an even parity for bits 2, 3, 6, and 7. It also details which transmitted bit is covered by which parity bit by reading the column. For example, d 1 is covered by p 1 and p 2 but not p 3 This table will have a striking resemblance to the parity-check matrix (H) in the next section.
The two-dimensional parity-check code, usually called the optimal rectangular code, is the most popular form of multidimensional parity-check code. Assume that the goal is to transmit the four-digit message "1234", using a two-dimensional parity scheme. First the digits of the message are arranged in a rectangular pattern: 12 34
The simplest checksum algorithm is the so-called longitudinal parity check, which breaks the data into "words" with a fixed number n of bits, and then computes the bitwise exclusive or (XOR) of all those words. The result is appended to the message as an extra word.
A CRC is called an n-bit CRC when its check value is n-bits. For a given n, multiple CRCs are possible, each with a different polynomial. Such a polynomial has highest degree n, and hence n + 1 terms (the polynomial has a length of n + 1). The remainder has length n. The CRC has a name of the form CRC-n-XXX.
Hamming(7,4): a Hamming code that encodes 4 bits of data into 7 bits by adding 3 parity bits; Hamming distance: sum number of positions which are different; Hamming weight (population count): find the number of 1 bits in a binary word; Redundancy checks. Adler-32; Cyclic redundancy check; Damm algorithm; Fletcher's checksum; Longitudinal ...