Map decoding method using augmented lattices

MAP decoding method of a signal received through a noisy channel, said signal being composed of symbols belonging to a predetermined alphabet, affected by an additional Gaussian white noise, the probability distribution of symbols within this alphabet being non-uniform, the symbols being represented by points in a lattice Λ={x|x=Ma, aεZN} generated by a matrix M with dimension N×N, characterised in that:

• a vector y with dimension N representative of the received signal is determined (310);
• an augmented vector
• y
• exp
• =
• [
• y
• 0
• N
• ]
• is created (320) in which 0N is a null vector with dimension N;
• an augmented lattice Λexp={x|x=Mexpa, aεZN} (330) with generator matrix
• M
• exp
• =
• [
• M
• β
• 
• 
• M
• ]
• is formed in which
• β
• =
• σ
• 2
• σ
• v
• 2
• is the ratio between variance of the noise and variance of a Gaussian probability distribution modelling the non-uniform probability distribution of the symbols in the alphabet;
• a search is made (340) among points in the augmented lattice to find the point closest to the vector representative of the received signal, â;
• the received symbol is estimated (350) from the generating matrix M and the closest neighbour, {circumflex over (v)}MAP*=Mâ.