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arXiv · 2608.05692

Wireless Linear Computation Broadcast

Shuo Tan·Syed A. Jafar
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Abstract

A linear computation broadcast (LCBC) problem comprises $K$ users (receivers) and a transmitter. The users wish to compute various (vector) linear functions of a common dataset, and possess in advance heterogeneous side information corresponding to various other linear computations. The goal for the broadcast transmitter, who knows the dataset and all desired and side-information functions, is to satisfy all demands as efficiently as possible. Prior work has explored the information-theoretic capacity of LCBC for zero-error finite-field computation over an ideal (noiseless) broadcast channel (BC). This paper develops a wireless LCBC (WLCBC) framework for the Gaussian MIMO BC with noisy receiver-side information under a transmit power constraint and arbitrary antenna configurations. In the WLCBC setting, a Gaussian source is linearly precoded for broadcast; each user requests a linear function of the source and forms an estimate by linearly combining its channel observation with its noisy side information. Assuming perfect channel state information, we cast the centralized joint linear transceiver design as a weighted sum-MSE minimization problem and propose an efficient alternating optimization algorithm. For a fixed precoder, the optimal decoders are the linear minimum mean-square error (LMMSE) estimators. For fixed decoders, the precoder update reduces to a convex quadratically constrained quadratic program which leads to a semi-closed-form solution parameterized by a single dual variable. The resulting algorithm guarantees a monotonic decrease in the objective and convergence of the weighted sum-MSE (WSMSE) objective sequence. Simulations demonstrate pronounced robustness gains over natural baselines obtained from prior works.

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Shuo Tan, Syed A. Jafar. 2026-08-06. Wireless Linear Computation Broadcast. https://arxiv.org/abs/2608.05692

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