This paper presents finite-blocklength achievability bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a sphere and a maximum likelihood decoder, the derived MAC bound on each transmitter's rate matches the MolavianJazi-Laneman bound (2015) in its first- and second-order terms, improving the remaining terms to $\frac12\frac{\log n}{n}+O \left(\frac 1 n \right)$ bits per channel use. The result then extends to a RAC model in which neither the encoders nor the decoder knows which of $K$ possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time $n_t$ that depends on the decoder's estimate $t$ of the number of active transmitters $k$. Single-bit feedback from the decoder to all encoders at each potential decoding time $n_i$, $i \leq t$, informs the encoders when to stop transmitting. For this RAC model, the proposed code achieves the same first-, second-, and third-order performance as the best known result for the Gaussian MAC in operation.
翻译:本文展示了高斯多访问频道(MAC)和随机访问频道(RAC)在平均和最大强度限制下,在平均和最大强度限制下,对高斯多访问频道(MAC)和随机访问频道(RAC)的有限区块长可获取性约束值。使用随机代码词统一分布在一个球体和最大可能性解码器上,根据每个发报机的速率,衍生出的MAC值与摩拉维亚贾齐-拉内曼(2015年)第一和第二级约束值相符(2015年),将剩余条件提高到每频道使用平均和最大强度限制下1 nn\n\ O\left(frac 1 n\right) 美元。结果随后延伸到RAC模型模式模式模式中,编码人或解码人既不知道哪个是$K,也不知道哪个是可能的发射机。 在拟议的无价调战略中,解码在某个时候发生,但取决于解码机的估计数$t$(美元)。 解码器向每个潜在解码者提供单位反馈,在第一个解码时间里, 美元,将运行到R_i。