论文标题
A通道的有限块长度：未包含随机访问和组测试的应用
Finite-Blocklength Results for the A-channel: Applications to Unsourced Random Access and Group Testing
论文作者
论文摘要
我们为未包含的A通道提供了有限的可实现性界限。在此多次访问频道中，用户无噪音传输从普通代码簿中选出的代码字，并从$ q $ -ary Alphabet生成的条目。在每个通道使用时，接收器观察不同的传输符号的集合，而不是它们的多重性。我们表明，A通道可以在未包含的随机访问（URA）和组测试中找到应用。利用有限块长度边界提供的见解以及URA和非自适应组测试之间通过A通道进行的连接，我们提出了改进的A-ART A通道代码的解码方法，我们展示了A-inchannel代码如何提供新的结构性组测试矩阵。开发的界限允许评估基于随机A通道代码的组测试矩阵的可实现的错误概率，以进行任意数量的测试，项目和缺陷。我们表明，这种渐近结构可以实现最佳测试数量。此外，每个有效解释的A通道代码都可以用于构建具有子线性恢复时间的组测试矩阵。
We present finite-blocklength achievability bounds for the unsourced A-channel. In this multiple-access channel, users noiselessly transmit codewords picked from a common codebook with entries generated from a $q$-ary alphabet. At each channel use, the receiver observes the set of different transmitted symbols but not their multiplicity. We show that the A-channel finds applications in unsourced random-access (URA) and group testing. Leveraging the insights provided by the finite-blocklength bounds and the connection between URA and non-adaptive group testing through the A-channel, we propose improved decoding methods for state-of-the-art A-channel codes and we showcase how A-channel codes provide a new class of structured group testing matrices. The developed bounds allow to evaluate the achievable error probabilities of group testing matrices based on random A-channel codes for arbitrary numbers of tests, items and defectives. We show that such a construction asymptotically achieves the optimal number of tests. In addition, every efficiently decodable A-channel code can be used to construct a group testing matrix with sub-linear recovery time.
