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 $κβ$ lower bounds on the maximal code sizes of each user using dirty paper coding.

翻译：本文研究了高斯广播信道中脏纸编码在有限码长下的可达性能，并针对该问题提出了两种不同的可达界。我们提出了Polyanskiy等人2010年提出的依赖测试界的广播信道适配形式，该界给出了固定输入下依赖于各错误事件信道色散项的平均错误概率上界。此外，我们利用脏纸编码推导了各用户最大码本尺寸的$κβ$下界。