We study error exponents for the problem of relaying a message over a tandem of two channels sharing the same transition law, in particular moving beyond the 1-bit setting studied in recent related works. Our main results show that the 1-hop and 2-hop exponents coincide in both of the following settings: (i) the number of messages is fixed, and the channel law satisfies a condition called pairwise reversibility, or (ii) the channel is arbitrary, and a zero-rate limit is taken from above. In addition, we provide various extensions of our results that relax the assumptions of pairwise reversibility and/or the two channels having identical transition laws, and we provide an example for which the 2-hop exponent is strictly below the 1-hop exponent.

翻译：本文研究了在两个共享相同转移律的串联信道上进行消息中继的误差指数问题，特别地，我们超越了近期相关工作所研究的1比特设定。主要结果表明，在以下两种情况下，1跳和2跳指数是一致的：(i) 消息数量固定，且信道律满足称为成对可逆性的条件；或 (ii) 信道是任意的，且从上方取零速率极限。此外，我们提供了多种扩展结果，放宽了成对可逆性和/或两个信道具有相同转移律的假设，并给出了一个2跳指数严格低于1跳指数的实例。