where is the conditional mathematical expectation over and . The channel likelihood is written in its classical form

(7) |

Expression (6) assumes that the precoder does space-time spreading within the same fading block . Its main role is to collect transmit diversity. Time diversity is collected by the convolutional code whereas receive diversity is naturally collected by the detector. The information rate transmitted by the space-time BICM is bits per time periods. An outage occurs if the instantaneous capacity, i.e. in our case, is less than . The outage probability associated to the rotation at a given signal-to-noise ratio is

The new design, called IOM (Information Outage Minimization), selects a matrix within the ensemble of random unitary matrices such that

(9) |

As an example, choosing the best rotation within an ensemble limited to 2000 matrices yields the matrix written below, for QPSK alphabet with and coding rate

(10) |

As an example, choosing the best rotation within an ensemble limited to 2000 matrices yields the matrix written below, for QPSK alphabet with and coding rate

In a similar fashion, a DNA-IOM precoder minimizes the information outage and satisfies DNA constraints [10]. The matrix given below corresponds to and . The DNA-IOM precoder is obtained by combining with . Also, the DNA cyclotomic precoder is constructed by combining to given previously in (3).