Decoding method and device and systems implementing them

摘要

In order to decode a sequence alpha=(alpha₁, . . . , alpha_i, . . . , alpha_n) where alpha_i is the received electrical signal corresponding to a transmitted signal a_i representing the i^th binary element v_i of a word v=(v₁, . . . , v_n) chosen in a code C of words satisfying v.h^T=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 rho_ext[A(i,h)]=P[a_i=-1|A(i,h)]/P[a_i=+1|A(i,h)] is determined on each of the elements v_i covered by h, A(i,h) being the set of the received values alpha_j covered by h, with the exception of alpha_i, and P[a_i|A(i,h)] being the probability that the i^th signal transmitted was a_i. This gives rho_ext[A(i,h)]=[S₁(i)+S₃(i)+ . . . ]/[1+S₂(i)+S₄(i)+ . . . ] where the numbers S_r(i) are calculated by applying the recurrence $r^{-1}\sum _{i=1}^w{z}^{{\mathrm{alpha}}_i}{S}_{r-1}\left(i\right)-z^{{\mathrm{alpha}}_j}{S}_{r-1}\left(j\right)=S_r\left(j\right)$ to the numbers S₀(i) initialised to 1, with z=exp(-4 E/N), where E is the energy of the transmitted signals a_i and N is the spectral power density of the noise on the transmission channel.