In order to decode a sequence =(1, . . . , i,
. . . , n) where i is the received electrical
signal corresponding to a transmitted signal ai representing the ith
binary element vi of a word v=(v1, . . . , vn)
chosen in a code C of words satisfying vhT=0, where h is a row
n-tuplet on the set {0,1 }, whose number of 1 is denoted w, an item of extrinsic
information ext[A(i,h)]=P[ai=-;1|A(i,h)]/P[ai=+1|A(i,h)]
is determined on each of the elements vi covered by h, A(i,h) being
the set of the received values j covered by h, with the exception
of i, and P[ai|A(i,h)] being the probability that
the ith signal transmitted was ai. This gives ext[A(i,h)]=[S1(i)+S3(i)+
. . . ]/[1+S2(i)+S4(i)+ . . . ] where the numbers Sr(i)
are calculated by applying the recurrence
##EQU1##
to the numbers S0(i) initialised to 1, with z=exp(-;4 E/N), where E
is the energy of the transmitted signals ai and N is the spectral power
density of the noise on the transmission channel.
