We consider the problem of reliable communication over a discrete memoryless channel (DMC) with the help of a relay, termed the information bottleneck (IB) channel. There is no direct link between the source and the destination, and the information flows in two hops. The first hop is a noisy channel from the source to the relay. The second hop is a noiseless but limited-capacity backhaul link from the relay to the decoder. We further assume that the relay is oblivious to the transmission codebook. We examine two mismatch scenarios. In the first setting, we assume the decoder is restricted to use some fixed decoding rule, which is mismatched to the actual channel. In the second setting, we assume that the relay is restricted to use some fixed compression metric, which is again mismatched to the statistics of the relay input. We establish bounds on the random- coding capacity of both settings, some of which are shown to be ensemble tight.

翻译：我们研究了在离散无记忆信道（DMC）上借助中继进行可靠通信的问题，该信道被称为信息瓶颈（IB）信道。信源与目的地之间无直接链路，信息经两跳传输：第一跳是从信源到中继的噪声信道，第二跳是从中继到解码器的无噪但容量受限的回程链路。我们进一步假设中继对传输码本无意识。本文考察两种失配场景：第一种场景假设解码器受限于使用某种固定的译码规则，该规则与实际信道失配；第二种场景假设中继受限于使用某种固定的压缩度量，该度量同样与中继输入的统计特性失配。我们为两种场景建立了随机编码容量的界，其中部分界被证明具有系综紧致性。