The channel reliability function is an important tool that characterizes the reliable transmission of messages over communication channels. For many channels, only upper and lower bounds of the function are known. We analyze the computability of the reliability function and its related functions. We show that the reliability function is not a Turing computable performance function. The same also applies to the functions related to the sphere packing bound and the expurgation bound. Furthermore, we consider the $R_\infty$ function and the zero-error feedback capacity, since they play an important role in the context of the reliability function. Both the $R_\infty$ function and the zero-error feedback capacity are not Banach Mazur computable.

翻译：信道可靠度函数是刻画信息在通信信道上可靠传输的重要工具。对于许多信道，仅已知该函数的上下界。我们分析了可靠度函数及其相关函数的可计算性。结果表明，可靠度函数并非图灵可计算的性能函数。同样，与球堆积界和剔除界相关的函数也不具有图灵可计算性。此外，我们进一步考虑了$R_\infty$函数和零错误反馈容量，因为它们在可靠度函数研究领域中扮演重要角色。$R_\infty$函数和零错误反馈容量均不是巴拿赫-马祖尔可计算的。