The Aladdin-Pythagoras space-time code

Our motivation is the design of space-time coding which is optimal under both maximum likelihood and iterative decoding. We describe the construction of new full-rate space-time codes with non-vanishing determinant that satisfy the genie conditions for iterative probabilistic decoding. The problem combining the genie conditions and the rank criterion is rewritten in terms of a quadratic form. The construction over ¿[i] (the cubic lattice) yields a family of codes defined by Pythagorean triples. The space-time code built over ¿[i] and involving the quaternion algebra (i,5/¿(i)) is referred to as the Aladdin-Pythagoras code. The construction over ¿[j] (the hexagonal lattice) also yields a full-rate non-vanishing determinant code that is suitable for iterative decoding on multiple antenna channels.