多址网络信息流与纠错码
Multiple-access Network Information-flow and Correction Codes
摘要：
这项工作认为，多址多播纠错的情况下，在一个分组化的网络与$z$恶意边缘对手。该网络具有最小切割$m$和长度为$\ell$的分组，并且每个宿需要来自源集合$\sources$的所有信息。容量区域的特点是一个“侧信道”模型（其中源和汇共享一些随机位，是秘密的对手）和一个“无所不知”的对抗模型（假设对手的知识没有限制）。在“侧信道”对抗模型中，与“全知”对抗模型相比，秘密信道的使用允许实现更高的速率，并且提供了多项式复杂度容量实现码。对于“全知”对抗模型，给出了两种实现容量的构造：第一种基于随机子空间码设计，在$\ell m$中具有指数复杂度;第二种使用了一种新的多域扩展技术，具有$O(\ell m^{|\sources|})$复杂度，在网络规模上是多项式的.我们的代码结构是“端到端”的，因为除了源和汇之外的所有节点都不知道对手，并且可以简单地实现预先设计的线性网络代码（随机或其他）。此外，这些来源独立行事，不了解来自其他来源的数据。
英文摘要：
This work considers the multiple-access multicast error-correction scenario over a packetized network with $z$ malicious edge adversaries. The network has min-cut $m$ and packets of length $\ell$, and each sink demands all information from the set of sources $\sources$. The capacity region is characterized for both a "side-channel" model (where sources and sinks share some random bits that are secret from the adversary) and an "omniscient" adversarial model (where no limitations on the adversary's knowledge are assumed). In the "side-channel" adversarial model, the use of a secret channel allows higher rates to be achieved compared to the "omniscient" adversarial model, and a polynomial-complexity capacity-achieving code is provided. For the "omniscient" adversarial model, two capacity-achieving constructions are given: the first is based on random subspace code design and has complexity exponential in $\ell m$, while the second uses a novel multiple-field-extension technique and has $O(\ell m^{|\sources|})$ complexity, which is polynomial in the network size. Our code constructions are "end-to-end" in that all nodes except the sources and sinks are oblivious to the adversaries and may simply implement predesigned linear network codes (random or otherwise). Also, the sources act independently without knowledge of the data from other sources.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
