🤖 AI Summary
This work investigates the finite-blocklength performance limits of dirty-paper coding over the Gaussian broadcast channel, characterizing the fundamental trade-off between code rate and error probability. For this problem, the dependence testing bound is extended to the broadcast setting for the first time, and two novel achievability bounds are established by integrating the κβ method—yielding an upper bound on the average error probability and a lower bound on the maximum codebook size. By combining dirty-paper coding with channel dispersion analysis and finite-blocklength information-theoretic tools, the authors derive tight non-asymptotic bounds that fill a critical gap in the theory of finite-blocklength Gaussian broadcast channels, thereby providing a rigorous performance benchmark for practical multiuser communication system design.
📝 Abstract
In this paper, we study the achievable performance of dirty paper coding for the Gaussian broadcast channel (BC) with finite blocklength and we propose two different achievability bounds for this problem. We present the broadcast adaptation of dependence testing bound of Polyanskiy et al. 2010, which is an upper bound on the average error probability that depends on the channel dispersion terms of each error event for fixed input. Additionally, we introduce the $\kappa \beta$ lower bounds on the maximal code sizes of each user using dirty paper coding.