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arXiv · 2603.07729

Tensor-Based Modulation on the Unit Circle: A Coding Perspective

Sweta Suresh·Charly Poulliat·Claire Goursaud·Maxime Guillaud
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Abstract

Tensor-based modulation (TBM) provides a multi-linear spreading framework for blind multi-user separation in unsourced random access. In this paper, we show that TBM is a coded modulation built on a non-binary linear block code over $\mathbb{Z}_M$, whose symbols are mapped to $M$-PSK modulation, defining a geometrically uniform signal space code. We explicitly derive this generator matrix, characterize its rank deficiency, and show that reference symbols for tensor identifiability correspond to code shortening, producing a quasi-systematic or a systematic code, depending on the number of considered reference symbols for the TBM. Simulations in single-user AWGN and multi-user non-coherent multi-antenna fading channels demonstrate strong robustness and interference resilience, establishing TBM as a scalable, algebraically structured modulation-coding scheme bridging tensor representations and modern coding theory.

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Sweta Suresh, Charly Poulliat, Claire Goursaud, Maxime Guillaud. 2026-03-08. Tensor-Based Modulation on the Unit Circle: A Coding Perspective. https://arxiv.org/abs/2603.07729

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