A unified view on nearest-neighbor decoding rates for noncoherent and semicoherent fading channels

For fast-fading memoryless single-user channels, we present new rate expressions that are achievable with i.i.d. Gaussian codes and successive nearest-neighbor decoders based on a Euclidian distance metric. The use of successive decoding is motivated by two factors: firstly, it was recently discovered that successive decoding potentially enhances achievable rates on single-user channels with imperfect channel-state information at the receiver (semicoherent channels); secondly, in the limit as the number of decoding steps tends to infinity, some of these rate expressions become tractable and expressible as integrals. To offer a unified view, we choose to put all rate expressions-old and new-into this integral representation inspired by the infinitesimal successive-decoding approach, in order to unveal their similarities.