Packing tubes on tori: An efficient method for low SNR analog error correction

In this study we introduce a new class of bandwidth-expansion source-channel codes for analog error correction that can work in any even dimensional space and show superior performance in the low SNR region. Our codes are constructed as geodesics on flat tori as previous studies have done, but we use a tube radius construct derived from the global circumradius function. We prove that geodesics on flat tori lead to constant generalized curvature curves and exploit that property to give a single-argument form for the circumradius function. We optimize encoder parameters by minimizing the global radius of curvature subject to harmonic frequency structure which leads to closed twisted tubes with maximal tube radius on the tori. We exploit the isometry of the flat torus with the hyperrectangle to derive simple closed-form decoders based on torus projections that come with 2 dB of the maximum likelihood decoder.