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.

翻译：基于张量的调制（TBM）为无源随机接入中的盲多用户分离提供了一种多线性扩频框架。本文证明TBM本质上是一种建立在$\mathbb{Z}_M$上非二进制线性分组码的编码调制方案，其符号通过$M$-PSK调制映射，构成几何均匀的信号空间编码。我们显式推导了该码的生成矩阵，刻画其秩缺陷特性，并证明张量可辨识性所需的参考符号对应于码缩短操作——根据TBM所采用的参考符号数量，可生成准系统码或系统码。在单用户AWGN信道与非相干多用户多天线衰落信道中的仿真表明，该方案具有强鲁棒性与抗干扰能力，从而确立TBM作为一种可扩展的、具有代数结构的调制-编码方案，有效连接了张量表示与现代编码理论。