Error exponents for multi-source multi-relay parallel relay networks with limited backhaul capacity

In this paper, we assess the random coding error exponents (EEs) corresponding to decode-and-forward (DF), compress-and-forward (CF) and quantize-and-forward (QF) relaying strategies for a parallel relay network (PRN), consisting of two sources, two relay stations (RSs) and single destination where the RSs access to the destination via orthogonal, error-free, limited-capacity backhaul links. Among these relaying strategies, the DF and QF studied in this paper differ from their well-known conventional versions in certain aspects. In the DF relaying, each RS applies maximum-likelihood (ML) detection and sends the message corresponding to the detected signal along with a reliability information to the destination which finalize the decision on the transmitted message. In QF relaying, as opposed to the Gaussian codebook and vector quantization (VQ) theoretical model used for deriving bounds, we consider a simple and practical relaying strategy consisting of finite-alphabet constellations (i.e., M-QAM) at the sources and symbol-by-symbol uniform scalar quantizers (uSQs) at the RSs. We also show, through numerical analysis, that the proposed QF relaying can provide better EEs than the others when the modulation constellation sizes selected by the sources match to the network conditions, i.e., operating signal-to-noise ratio (SNR), and the backhaul capacity is sufficient. This behavior is due to the structure inherent in the considered modulation alphabets, which Gaussian signaling lacks.