Quantisation effects in PDMM: A first study for synchronous distributed averaging

Large-scale networks of computing units, often characterised by the absence of central control, have become commonplace in many applications. To facilitate data processing in these large-scale networks, distributed signal processing is required. The iterative behaviour of distributed processing algorithms combined with energy, computational power, and bandwidth limitations imposed by such networks, place tight constraints on the transmission capacities of the individual nodes. In this paper we investigate the effects of subtractive dithered uniform quantisation in PDMM for the synchronous distributed averaging problem. This is done by deriving expressions for the mean squared error (MSE) that include quantisation noise. Also, the required data rate for quantised PDMM is considered. It was found that for practical applications quantisation in PDMM can be applied with a fixed-rate quantiser, such that significant data rate reduction can be achieved, without compromising the rate of convergence.