Decoding method and device and systems implementing them
Abstract:
In order to decode a sequence α=(α1, . . . , αi, . . . , αn) where αi 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 v·hT=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 ρext[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 αj covered by h, with the exception of αi, and P[ai|A(i,h)] being the probability that the ith signal transmitted was ai. This gives ρext[A(i,h)]=[S1(i)+S3(i)+ . . . ]/[1+S2(i)+S4(i)+ . . . ] where the numbers Sr(i) are calculated by applying the recurrence r - 1 ⁢ ∑ i = 1 w ⁢ z α i ⁢ S r - 1 ⁢ ( i ) - z α j ⁢ S r - 1 ⁢ ( j ) = S r ⁢ ( j ) 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.
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