We study list-decoding over adversarial channels governed by oblivious adversaries (a.k.a. oblivious Arbitrarily Varying Channels (AVCs)). This type of adversaries aims to maliciously corrupt the communication without knowing the actual transmission from the sender. For any oblivious AVCs potentially with constraints on the sender's transmitted sequence and the adversary's noise sequence, we determine the exact value of the minimum list-size that can support a reliable communication at positive rate. This generalizes a classical result by Hughes (IEEE Transactions on Information Theory, 1997) and answers an open question posed by Sarwate and Gastpar (IEEE Transactions on Information Theory, 2012). A lower bound on the list-decoding capacity (whenever positive) is presented. Under a certain combinatorial conjecture, we also prove a matching upper bound. En route to a tight characterization of the list-decoding capacity, we propose a method for subcode construction towards the resolution of the combinatorial conjecture.

中文翻译：

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受约束的 Oblivious AVC 的严格列表大小

我们研究了由不经意的对手（又名不经意的任意变化频道（AVC））控制的对抗性频道的列表解码。这种类型的攻击者旨在在不知道来自发送者的实际传输的情况下恶意破坏通信。对于可能对发送方的传输序列和对手的噪声序列有约束的任何不经意的 AVC，我们确定可以支持以正速率进行可靠通信的最小列表大小的确切值。这概括了 Hughes 的经典结果（IEEE Transactions on Information Theory，1997）并回答了 Sarwate 和 Gastpar 提出的一个悬而未决的问题（IEEE Transactions on Information Theory，2012）。给出了列表解码容量的下限（当为正时）。在某种组合猜想下，我们还证明了匹配的上限。在对列表解码能力进行严格表征的过程中，我们提出了一种用于解决组合猜想的子码构造方法。