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We consider the problem of gathering measurements in a wireless sensor network consisting of a large number of sensor nodes. A practical joint source-channel coding scheme is proposed and evaluated. The scheme uses lattices to extend a previously proposed scheme to higher dimensions. The key idea is to use conventional point-to-point communication for a subset of the sensor nodes and side-information aware transmission for the remaining sensor nodes. The selection of sensors is based on their instantaneous channel quality. It is shown that by expanding from one to eight dimensions, a gain of about 1 dB is achievable. The overall transmission delay of the scheme is still very low and it is therefore suitable to use in delay-sensitive applications.