We present a new systematic approach to constructing spherical codes in dimensions 2k, based on Hopf foliations. Using the fact that a sphere S2n-1 is foliated by manifolds Scosηn-1 × Ssinηn-1, η ∈ [0, π/2], we distribute points in dimension 2k via a recursive algorithm from a basic construction in R4. Our procedure outperforms some current constructive methods in several small-distance regimes and constitutes a compromise between achieving a large number of codewords for a minimum given distance and effective constructiveness with low encoding computational cost. Bounds for the asymptotic density are derived and compared with other constructions. The encoding process has storage complexity O(n) and time complexity O(n log n). We also propose a sub-optimal decoding procedure, which does not require storing the codebook and has time complexity O(n log n).

We present a new approach to construct spherical codes in 2 ^k dimensions, based on Hopf foliations. Using the fact that a sphere S ²ⁿ⁻¹ is foliated by manifolds $S_{\cos \eta }^{n - 1} \times S_{\sin \eta }^{n - 1}$, η ∈ [0,π/2], we distribute points in dimension 2 ^k via a recursive algorithm from a basic construction in R ⁴ . Our procedure outperforms some current constructive methods in several smalldistance regimes and constitutes a compromise between optimality and computational effort.Detailed proofs of some results can be found in [1]

We propose novel compression algorithms for time-varying channel state information (CSI) in wireless communications. The proposed scheme combines (lossy) vector quantisation and (lossless) compression. First, the new vector quantisation technique is based on a class of parametrised companders applied on each component of the normalised CSI vector. Our algorithm chooses a suitable compander in an intuitively simple way whenever empirical data are available. Then, the sequences of quantisation indices are compressed using a context-tree-based approach. Essentially, we update the estimate of the conditional distribution of the source at each instant and encode the current symbol with the estimated distribution. The algorithms have low complexity, are linear-time in both the spatial dimension and time duration, and can be implemented in an online fashion. We run simulations to demonstrate the effectiveness of the proposed algorithms in such scenarios.