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Over the last centuries, hearing aids have evolved from crude and bulky horn-shaped instruments to lightweight and almost invisible digital signal processing devices. While most of the research has focused on the design of monaural apparatus, the use of a wireless link has been recently advocated to enable data transfer between hearing aids such as to obtain a binaural system. The availability of a wireless link offers brand new perspectives but also poses great technical challenges. It requires the design of novel signal processing schemes that address the restricted communication bitrates, processing delays and power consumption limitations imposed by wireless hearing aids. The goal of this dissertation is to address these issues at both a theoretical and a practical level. We start by taking a distributed source coding view on the problem of binaural noise reduction. The proposed analysis allows deriving mean square optimal coding strategies, and to quantify the noise reduction enabled by a wireless link as a function of the communication bitrate. The problem of rate allocation between the hearing aids is also studied. In a more general setting, these findings are used to design algorithms for distributed estimation in sensor networks, under both a linear approximation and a compression constraint. The potential of our approach in this context is illustrated by means of a simple case study based on a first-order autoregressive model. Two important practical aspects of binaural noise reduction are then investigated. The first issue pertains to multichannel filtering in the transformed domain using a weighted overlap-add filter bank. We propose three subband filtering strategies together with recursive algorithms for the computation of the filter coefficients. Some numerical methods to reduce their computational complexity are also discussed. The second problem concerns the estimation of binaural characteristics using the wireless link. These characteristics are modeled in two different ways. The first approach is based on binaural cues. A source coding method to estimate these cues in a distributed fashion is proposed. It takes advantage of the particularities of the recording setup to reduce the transmission bitrate. The second approach involves a filter that is sparse in the time domain. This sparsity allows for the design of a novel distributed scheme based on annihilating filters. Finally, application of these methods to the distributed coding of spatial audio is presented.