This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given for mismatched, and then particularised to matched and universal decoding metrics. Two regimes are studied: for fixed list size, we derive an ensemble-tight random-coding error exponent, and show that, for the matched metric, it does not improve the error exponent of ordinary decoding. For list sizes growing exponentially with the block-length, we provide a non-trivial lower bound to the error exponent that is tight at high rates under the matched metric.

翻译：本文研究随机列表解码的随机编码误差指数，其中解码器以与码字解码度量成比例的概率随机选择$L$条消息。首先给出失配解码度量的指数（或界），随后特化到匹配解码度量与通用解码度量。研究两种机制：对于固定列表大小，我们推导出集系紧致的随机编码误差指数，并证明在匹配度量下该指数不会改进普通解码的误差指数。对于列表大小随分组长度呈指数增长的情形，我们给出了误差指数的非平凡下界，该下界在匹配度量下的高码率区域是紧致的。