从经典信道到量子信道：实现正隐蔽速率
From Classical to Quantum Channels: Achieving Positive Covert Rates
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中文总结 AI 辅助
本文研究经典、经典-量子及量子离散无记忆信道上正隐蔽速率通信的可行性条件，提出通过输入单纯形维数、无辜符号选择及混合无辜状态等机制实现正隐蔽速率，并证明多址信道约束更宽松。
中文摘要 AI 辅助
在本文中，我们研究了在离散无记忆经典信道、经典-量子信道和量子信道上，正隐蔽速率下隐蔽通信可行的条件。对于经典点对点信道，我们证明如果信道输入概率单纯形的维数超过信道输出概率单纯形的维数，等价地，如果输入字母表的基数大于输出字母表的基数，那么对于某些类别的离散无记忆信道（DMC），正隐蔽速率是可实现的。我们进一步证明，允许无辜符号（即在无通信模式下传输的符号）被适当选择，可以扩大可实现正隐蔽速率的DMC类别。我们还研究了经典多址信道（MAC）上的隐蔽通信，其中额外的发射机有效地扩大了可用的信道输入对集合，并且我们证明对于MAC，满足隐蔽性约束所需的条件比点对点信道更不严格。我们将这些结果扩展到经典-量子DMC，通过证明如果输入概率单纯形的维数超过可在信道输出处引起的输出状态集的仿射维数，那么对于某些类别的经典-量子DMC，正隐蔽速率是可实现的。最后，对于量子信道，我们证明如果无辜状态（即在无通信模式下传输的状态）是混合的，那么隐蔽性约束总是可以通过一个非平凡的输入系综来满足。因此，只要合法接收者能够在这样一个合适的系综中区分至少两个状态，正隐蔽速率就是可实现的。
英文摘要
In this paper, we study the conditions under which covert communication at positive rates is feasible over discrete memoryless classical, classical-quantum, and quantum channels. For classical point-to-point channels, we show that if the dimension of the channel input probability simplex exceeds that of the channel output probability simplex, equivalently, if the input alphabet has larger cardinality than the output alphabet, then positive covert rates are achievable for certain classes of Discrete Memoryless Channels (DMCs). We further show that allowing the innocent symbol (i.e., the symbol transmitted in the no-communication mode) to be chosen appropriately can enlarge the class of DMCs for which positive covert rates are achievable. We also study covert communication over classical Multiple-Access Channels (MACs), where the additional transmitter effectively enlarges the set of available channel input pairs, and we show that the conditions required to satisfy the covertness constraint are less restrictive for MACs than for point-to-point channels. We extend these results to classical-quantum DMCs by showing that if the dimension of the input probability simplex exceeds the affine dimension of the set of output states that can be induced at the channel output, then positive covert rates are achievable for certain classes of classical-quantum DMCs. Finally, for quantum channels, we show that if the innocent state (i.e., the state transmitted in the no-communication mode) is mixed, then the covertness constraint can always be satisfied by a non-trivial input ensemble. Consequently, positive covert rates are achievable whenever the legitimate receiver can distinguish at least two states in a suitable such ensemble.
发表机构
- Columbia University（哥伦比亚大学）
- Nokia Bell Labs（诺基亚贝尔实验室）
机构由 AI 辅助整理，请以论文原文为准。
