Information transmission over discrete-time channels with memoryless additive noise obeying a Cauchy, rather than Gaussian, distribution, are studied. The channel input satisfies an average power constraint. Upper and lower bounds to such additive white Cauchy noise (AWCN) channel capacity are established. In the high input power regime, the gap between upper and lower bounds is within 0.5 nats per channel use, and the lower bound can be achieved with Gaussian input. In the lower input power regime, the capacity can be asymptotically approached by employing antipodal input. It is shown that the AWCN decoder can be applied to additive white Gaussian noise (AWGN) channels with negligible rate loss, while the AWGN decoder when applied to AWCN channels cannot ensure reliable decoding. For the vector receiver case, it is shown that a linear combining receiver front end loses the channel combining gain, a phenomenon drastically different from AWGN vector channels.

翻译：本文研究了离散时间信道在加性噪声服从柯西分布（而非高斯分布）且无记忆条件下的信息传输问题。信道输入满足平均功率约束。针对此类加性白柯西噪声信道容量，本文建立了上界与下界。在高输入功率区域，上下界之间的差距在每信道使用0.5奈特以内，且下界可通过高斯输入实现。在低输入功率区域，采用反极性输入可渐近逼近信道容量。研究表明，AWCN解码器应用于加性白高斯噪声信道时速率损失可忽略不计，而AWGN解码器应用于AWCN信道时则无法保证可靠解码。对于矢量接收机情形，研究显示线性合并接收机前端会丧失信道合并增益，这一现象与AWGN矢量信道存在显著差异。