论文标题
未包含的多源稀疏回归代码达到了对称的MAC容量
Unsourced Multiuser Sparse Regression Codes achieve the Symmetric MAC Capacity
论文作者
论文摘要
未包含的随机访问（U-RA）是一种免费的随机访问，几乎无限的用户，其中只有一定数量的$ k_a $在同一时间插槽中处于活动状态。用户使用完全相同的代码簿，而接收方的任务是解码传输消息列表。最近，提出了AWGN通道上U-RA的串联编码结构，其中稀疏回归代码（SPARC）用作内部代码，以创建有效的外部或渠道。然后，使用外部代码来解决OR-MAC中的多访问干扰。在这项工作中，我们表明，这种串联结构可以在大块长度的极限和以对称的香农容量为单位的限制和大量的活跃用户中实现消失的每个用户误差概率，即只要$ k_ar <0.5 \ log_2（1+k_a \ snr）$。这将有关SPARCS的先前点对点最优性结果扩展到了未包含的多源场景。此外，我们计算算法阈值，该算法阈值与低复杂性AMP算法可靠地进行内部解码的总和率结合。
Unsourced random-access (U-RA) is a type of grant-free random access with a virtually unlimited number of users, of which only a certain number $K_a$ are active on the same time slot. Users employ exactly the same codebook, and the task of the receiver is to decode the list of transmitted messages. Recently a concatenated coding construction for U-RA on the AWGN channel was presented, in which a sparse regression code (SPARC) is used as an inner code to create an effective outer OR-channel. Then an outer code is used to resolve the multiple-access interference in the OR-MAC. In this work we show that this concatenated construction can achieve a vanishing per-user error probability in the limit of large blocklength and a large number of active users at sum-rates up to the symmetric Shannon capacity, i.e. as long as $K_aR < 0.5\log_2(1+K_a\SNR)$. This extends previous point-to-point optimality results about SPARCs to the unsourced multiuser scenario. Additionally, we calculate the algorithmic threshold, that is a bound on the sum-rate up to which the inner decoding can be done reliably with the low-complexity AMP algorithm.
