Quantization effects in PDMM

Abstract

Nowadays, large-scale networks of computing units, often characterized by the absence of central control, have become more 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 the limited energy, computational power, and bandwidth, limitations imposed by such networks, place tight constraints on the transmission capacities of the individual nodes. For this reason quantization in distributed algorithms has become an interesting and popular topic. Already considerable research has been performed into quantization effects for various distributed algorithms, such as alternating-direction method of multipliers (ADMM). However, for the primal-dual method of multipliers (PDMM), a recently proposed promising distributed algorithm, no research into the effects of quantization exists. In this thesis the effects of subtractively dithered uniform quantization in PDMM are investigated for the synchronous distributed averaging problem. This specific averaging problem, which is often considered as the canonical distributed problem, was selected to start the research from a natural point. As such, the theory developed in this thesis can form a foundation for further research into quantization effects in PDMM in general. The quantization effects are discussed by considering the convergence rate of the algorithm. This is done by deriving expressions for the mean squared error (MSE) that include quantization noise. Also the required bitrate for quantized PDMM is considered. It was concluded that for practical applications quantization in PDMM can be applied with a near-fixed-rate quantizer, such that significant bitrate reduction can be achieved, without compromising the rate of convergence.