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Singleparitycheck codę

A single-parity-check codę uses a single-parity bit to generate codeword with an even or odd parity, i.e. an evcn or odd number of nonzero bits respectively. Then.

n = k + 1: w = [/| ■•■i_kp]

and for an even-parity codę. parity-check sum:

>=i

Parity-check matrix and generator matrix are trivial:

H = [I* * *JJ1

G =

I ---01 0 - - 1 1

Decoder calculates the overall parity-check syndrome:

>=i

Such codę has = 2. It detects not only occurrence of all single errors but also all other odd numbcrs of errors (error pattems of an odd weight). Then. probability of erroneous decoding: