多播不匹配容量的单字母上界
A Single-Letter Upper Bound on the Mismatch Capacity via Multicast Transmission
摘要：
我们引入了一种新的分析技术，推导出一个固定的，单用户，无记忆信道的解码度量$q$的失配容量的单字母上界。我们的界限是通过考虑在两个用户的广播信道与解码度量$q$和$ρ$在接收器，称为$(q,ρ)$ -肯定退化的多播传输。该信道具有这样的特性，即接收机$1$的正确$q$解码和接收机$2$的错误$ρ$解码的交叉事件对于特定组成$P$的任何固定组成码本具有零概率。我们的界限持有在强烈的相反意义上的指数衰减的概率正确解码率以上的界限。此外，我们完善的证明，并提出了一个界限，至少是紧的$ρ$的任何选择。几个例子表明，严格的改进，我们的界限相比，以前的结果进行了分析。最后，我们检测等价类的同构通道度量对$(W,q)$共享相同的失配容量。我们证明，如果类包含一个匹配的对，那么我们的界是紧的，整个类的失配能力是充分的特点，等于LM率，这是可以实现的随机编码，并可能严格低于匹配的能力。
英文摘要：
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.
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。
