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

TL;DR

This paper introduces a tensor-based modulation scheme that leverages algebraic coding theory for robust multi-user communication, demonstrating strong performance in noisy and fading channels.

Contribution

It explicitly links tensor-based modulation to non-binary linear block codes over Z_M, providing a new algebraic framework and practical insights for multi-user communication systems.

Findings

Robust performance in AWGN and fading channels

Strong interference resilience demonstrated through simulations

Explicit generator matrix derivation and code characterization

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.