We address the problem of coding for classical multiple-access channels (MACs) with the assistance of non-signaling correlations between parties. It is well-known that non-signaling assistance does not change the capacity of classical point-to-point channels. However, it was recently observed that one can construct MACs from two-player non-local games while relating the winning probability of the game to the capacity of the MAC. By considering games for which entanglement increases the winning probability, this shows that for some specific kinds of channels, entanglement between the senders can increase the capacity. We make several contributions towards understanding the capacity region for MACs with the assistance of non-signaling correlations. We develop a linear program computing the optimal success probability for coding over $n$ copies of a MAC $W$ with size growing polynomially in $n$. Solving this linear program allows us to achieve inner bounds for MACs. Applying this method to the binary adder channel, we show that using non-signaling assistance, the sum-rate $1.5425$ can be reached even with zero error, which beats the maximum sum-rate capacity of $1.5$ in the unassisted case. For noisy channels, where the zero-error non-signaling assisted capacity region is trivial, we can use concatenated codes to obtain achievable points in the capacity region. Applied to a noisy version of the binary adder channel, we show that non-signaling assistance still improves the sum-rate capacity. Complementing these achievability results, we give an outer bound on the non-signaling assisted capacity region that has the same expression as the unassisted region except that the channel inputs are not required to be independent. Finally, we show that the capacity region with non-signaling assistance shared only between each sender and the receiver independently is the same as without assistance.

翻译：我们研究了在各方之间借助非信令关联进行经典多址信道（MAC）编码的问题。众所周知，非信令辅助不会改变经典点对点信道的容量。然而，近期研究发现，可以通过将两方非局域博弈与MAC容量相关联来构造MAC，其中博弈获胜概率与MAC容量存在关联。通过考虑纠缠可提升获胜概率的博弈，这表明对于某些特定类型的信道，发送方之间的纠缠能够增加信道容量。我们为理解非信令关联辅助下MAC的容量区域做出了多项贡献。我们开发了一种线性规划方法，用于计算在规模随n多项式增长的n个MAC副本W上进行编码的最优成功概率。求解该线性规划使我们能够获得MAC的内界。将此方法应用于二进制加法信道，我们发现即使以零错误率，借助非信令辅助也能达到和速率1.5425，这超过了无辅助情况下1.5的最大和速率容量。对于噪声信道（其零错误非信令辅助容量区域是平凡的），我们可采用级联码在容量区域内获得可达点。将此法应用于二进制加法信道的含噪版本，结果表明非信令辅助仍能提升和速率容量。作为这些可达性结果的补充，我们给出了非信令辅助容量区域的外界，其表达式与无辅助情形相同，但信道输入无需满足独立性假设。最后，我们证明当非信令关联仅独立存在于每个发送方-接收方对之间时，其容量区域与无辅助情形相同。