In this paper non-group permutation modulated sequences for the Gaussian channel are considered. Without the restriction to group codes rather than subsets of group codes, arbitrary rates are achievable. The code construction utilizes the known optimal group constellations to ensure at least the same performance but exploit the Gray code ordering structure of multiset permutations as a selection criterion at the decoder. The decoder achieves near maximum likelihood performance at low computational cost and low additional memory requirements at the receiver.

A new class of space time codes with high performance is presented. The code design utilizes tailor-made permutation codes, which are known to have large minimal distances as spherical codes. A geometric connection between spherical and space time codes has been used to translate them into the final space time codes. Simulations demonstrate that the performance increases with the block lengths, a result that has been conjectured already in previous work. Further, the connection to permutation codes allows for moderate complex en-/decoding algorithms.

In this work, the geometric relation between space- time block code design for the coherent channel and its noncoherent counterpart is exploited to get an analog of the information-theoretic inequality I(X;S)lesI((X,H);S) in terms of diversity. It provides a lower bound on the performance of noncoherent codes when used in coherent scenarios. This leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced subtasks. Moreover, a geometrical criterion for high-performance space-time code design is derived

In this work, the natural geometric relation between the space time block code design if the channel is unknown at the receiver and its counterpart design if the receiver knows the channel is exploited, to establish an estimate on the corresponding diversities. This leads to a decomposition of code designs and splits the design problem into two complexity reduced sub tasks.

A new design method for high rate, fully diverse ('spherical') space frequency codes for MIMO-OFDM systems is proposed, which works for arbitrary numbers of antennas and subcarriers. The construction exploits a differential geometric connection between spherical codes and space time codes. The former are well studied e.g. in the context of optimal sequence design in CDMA systems, while the latter serve as basic building blocks for space frequency codes. In addition a decoding algorithm with moderate complexity is presented. This is achieved by a lattice based construction of spherical codes, which permits lattice decoding algorithms and thus offers a substantial reduction of complexity

Applying the Riemann geometric machinery of volume estimates in terms of curvature, bounds for the minimal distance of packings/codes in the Grassmann and Stiefel manifolds will be derived and analyzed. In the context of space-time block codes this leads to a monotonically increasing minimal distance lower bound as a function of the block length. This advocates large block lengths for the code design