删减误差指数并非普遍可实现
The Expurgated Error Exponent is Not Universally Achievable
AI总结：
该研究证明了离散无记忆信道中删减误差指数无法普遍实现，且MMI解码方法在该情况下也失效。
摘要：
我们研究了离散无记忆信道（DMCs）中删减误差指数的普遍可实现性。虽然随机编码指数已知可以通过最大互信息（MMI）解码在DMCs中普遍可实现，但删减指数是否普遍可实现仍是一个开放问题。我们证明在一般情况下并非如此。具体来说，我们构造了一个信道家族，其中不存在单一的码序列能同时在该家族中的所有信道上实现删减指数，即使在零速率下也是如此。此外，对于同一信道家族，我们还证明MMI解码在任何信道上都无法实现删减指数。
英文摘要：
We study the universal attainability of the expurgated error exponent for discrete memoryless channels (DMCs). While the random-coding exponent is known to be universally attainable for every fixed input distribution via maximum mutual information (MMI) decoding for DMCs, it remains open whether the expurgated exponent can be attained universally. We show that this is not the case in general. Specifically, we construct a family of DMCs for which no single sequence of codes can attain the expurgated exponent simultaneously for all channels in the family, even at rate zero. In addition, for the same channel family, we show that MMI decoding fails to achieve the expurgated exponent for any channel in the family.
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。
