论文标题
使用精灵接收器的不匹配的可靠性函数和容量上的上限
Upper Bounds on the Mismatched Reliability Function and Capacity Using a Genie Receiver
论文作者
论文摘要
我们开发了一个新颖的框架，用于证明用于通道编码的相反定理，该框架基于多播传输的分析技术，并具有额外的辅助接收器，该技术是原始接收器的精灵。精灵提供了原始的接收器一定的狭窄代码字列表，可供选择，其中包括传输的代码字。该技术用于在离散无内存通道的不匹配能力以及具有不匹配的解码度量的可靠性函数上得出上限。与以前的作品不同，我们的边界技术还利用了代码字的固有对称要求，从而导致了这些新的上限。由于对不匹配能力的大多数已知界限的计算非常复杂，因此我们进一步提出了一种获得易于计算的轻松界限的方法。例如，我们分析了二进制输入通道案例中获得的边界。最后，我们通过在可靠性函数上提出更简单的界限，并为它们在某些速率范围内的紧密程度提供足够的条件。
We develop a novel framework for proving converse theorems for channel coding, which is based on the analysis technique of multicast transmission with an additional auxiliary receiver, which serves as a genie to the original receiver. The genie provides the original receiver a certain narrowed list of codewords to choose from that includes the transmitted one. This technique is used to derive upper bounds on the mismatch capacity of discrete memoryless channels as well as the reliability function with a mismatched decoding metric. Unlike previous works, our bounding technique exploits also the inherent symmetric requirement from the codewords, leading to these new upper bounds. Since the computations of most of the known bounds on the mismatch capacity are rather complicated, we further present a method to obtain relaxed bounds that are easier to compute. As an example, we analyze the obtained bounds in the binary-input channels case. We conclude by presenting simpler bounds on the reliability function, and provide sufficient conditions for their tightness in certain ranges of rates.
