论文标题
通过多播变速器在不匹配能力上的单个字母上限
A Single-Letter Upper Bound on the Mismatch Capacity via Multicast Transmission
论文作者
论文摘要
我们介绍了一种新的分析技术，以在固定，单用户，无内存的通道的不匹配能力上得出单个字母的上限，并带有解码度量$ Q $。我们的界限是通过考虑在两种用户广播频道上进行的多播变速箱，该频道在接收器上使用解码指标$ q $和$ρ$进行了解码，称为$（q，ρ）$ - 肯定会退化。该通道的属性是，$ q $ - 对接收器$ 1 $的交叉事件和错误的$ρ$ - 对接收器的编码为$ 2 $的错误概率为零概率，任何特定构图$ p $的固定复合代码簿。我们的界限具有强烈的匡威意义，即以高于界限的速率正确解码的概率指数衰减。此外，我们完善了证明，并提出了至少与$ρ$的任何选择一样紧的界限。分析了与先前结果相比，几个证明我们约束的严格改善的示例。最后，我们检测出具有相同不匹配能力的同构通道 - 金对（W，Q）的等效类别。我们证明，如果该类包含匹配对，那么我们的界限是紧密的，并且整个类的不匹配能力是完全表征的，并且等于LM速率，这是可以通过随机编码来实现的，并且可能严格降低了匹配能力。
We introduce a new analysis technique to derive a single-letter upper bound on the mismatch capacity of a stationary, single-user, memoryless channel with a decoding metric $q$. Our bound is obtained by considering a multicast transmission over a two-user broadcast channel with decoding metrics $q$ and $ρ$ at the receivers, referred to as $(q,ρ)$-surely degraded. This channel has the property that the intersection event of correct $q$-decoding of receiver $1$ and erroneous $ρ$-decoding of receiver $2$ has zero probability for any fixed-composition codebook of a certain composition $P$. Our bound holds in the strong converse sense of an exponential decay of the probability of correct decoding at rates above the bound. Further, we refine the proof and present a bound that is at least as tight as that of any choice of $ρ$. Several examples that demonstrate the strict improvement of our bound compared to previous results are analyzed. Finally, we detect equivalence classes of isomorphic channel-metric pairs $(W,q)$ that share the same mismatch capacity. We prove that if the class contains a matched pair, then our bound is tight and the mismatch capacity of the entire class is fully characterized and is equal to the LM rate, which is achievable by random coding, and may be strictly lower that the matched capacity.
