Tensor Decomposition Bounds for TBM-Based Massive Access

TL;DR

This paper analyzes the theoretical limits of tensor decomposition in tensor-based modulation for massive access, providing bounds on estimation accuracy and demonstrating improved decoding performance with classical coding schemes.

Contribution

It introduces Cramér-Rao bounds for tensor decomposition in TBM, an approximate perturbation model for LLR computation, and shows performance gains with coding schemes.

Findings

Cramér-Rao bounds are tight at high SNR.

The approximate LLR improves decoding performance at low SNR.

Tensor decomposition limits are characterized for TBM-based massive access.

Abstract

Tensor-based modulation (TBM) has been proposed in the context of unsourced random access for massive uplink communication. In this modulation, transmitters encode data as rank-1 tensors, with factors from a discrete vector constellation. This construction allows to split the multi-user receiver into a user separation step based on a low-rank tensor decomposition, and independent single-user demappers. In this paper, we analyze the limits of the tensor decomposition using Cram\'er-Rao bounds, providing bounds on the accuracy of the estimated factors. These bounds are shown by simulation to be tight at high SNR. We introduce an approximate perturbation model for the output of the tensor decomposition, which facilitates the computation of the log-likelihood ratios (LLR) of the transmitted bits, and provides an approximate achievable bound for the finite-length error probability. Combining TBM with classical forward error correction coding schemes such as polar codes, we use the approximate LLR to derive soft-decision decoder showing a gain over hard-decision decoders at low SNR.