Recent research in ultra-reliable and low latency communications (URLLC) for future wireless systems has spurred interest in short block-length codes. In this context, we analyze arbitrary harmonic bandwidth (BW) expansions for a class of high-dimension constant curvature curve codes for analog error correction of independent continuous-alphabet uniform sources. In particular, we employ the circumradius function from knot theory to prescribe insulating tubes about the centerline of constant curvature curves. We then use tube packing density within a hypersphere to optimize the curve parameters. The resulting constant curvature curve tube (C3T) codes possess the smallest possible latency, i.e., block-length is unity under BW expansion mapping. Further, the codes perform within 5 dB signal-to-distortion ratio of the optimal performance theoretically achievable at a signal-to-noise ratio (SNR)$ < -5$dB for BW expansion factor$n \leq 10$. Furthermore, we propose a neural-network-based method to decode C3T codes. We show that, at low SNR, the neural-network-based C3T decoder outperforms the maximum likelihood and minimum mean-squared error decoders for all$n$. The best possible digital codes require two to three orders of magnitude higher latency compared to C3T codes, thereby demonstrating the latter’s utility for URLLC.

This work describes a practical implementation of a theoretically optimal distributed source quantization algorithm applied to the problem of encoding correlated images with separate encoders and a common decoder. We develop multi-dimensional codebooks based on a distributed form of the generalized Lloyd algorithm. We model image patches as elements of a Gaussian mixture model and show how a two-dimensional codebook of image patch codevectors can be used to significantly compress one image by using the reconstructed second image as partial side information. To test the approach we experiment with multimodal images of highly correlated electro-optical and infrared images and show the performance advantage of distributed source quantization over conventional non-distributed lossy compression.

We introduce a new geometric construction of cyclic group codes in odd-dimensional spaces formed by intersecting even-dimensional constant curvature curves with hyperplanes of one less dimension. This allows us to recast the cyclic group code as a uniform sampling of a constant curvature curve whereby the design of the constant curvature curve controls code performance. Using a tool from knot theory known as the circumradius function, we derive properties of cyclic group codes from properties of the constant curvature curve passing through every point of the spherical code. By relating the distribution of the squared circumradius function of the connecting curve to the distribution of the pairwise distances of the cyclic group code, we show that the distance spectrum of cyclic group codes achieves optimality in the sense of matching the random spherical code distance distribution bound as the block length grows large.

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.