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We study the uplink of Wyner-type cellular models featuring short range inter-cell interference. We assume that the decoding of the message sent by a given transmitter is done locally, that is using only the signals received at the antennas in its vicinity. We derive upper and lower bounds on the achievable rate for a two-dimensional model and for a one-dimensional model with an attenuation parameter. The analysis of our cellular models will rely on rate splitting and genie-aided bounds, originally employed in the framework of the interference channel.