Algebraic Constructions for PSK Space-Time Coded Modulation

We consider the design of phase shift keyed space-time coded modulation for two antenna systems based on linear codes over rings. Design rules for constructing full diversity systematic space-time codes based on underlying existing algebraic codes were rst presented by Ham-mons and El Gamal in 2000. We reformulate and simplify these design rules, resulting in the condition that the characteristic polynomial of the parity generation matrix must be irreducible. We further extend the results to non-systematic codes. These results yield a recursive construction based on the Schur determinant formula. The resulting block codes are guranteed to provide full diversity advantage. In addition, the code construction is such that the corresponding parity check matrix is sparse, enabling the use of the powerful Sum-Product algorithm for decoding.