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Cooperative decoding at the base stations (or access points) of an infrastructure wireless network is currently well recognized as a promising approach for intercell interference mitigation, thus enabling high frequency reuse. Deployment of cooperative multicell decoding depends critically on the tolopology and quality of the available backhaul links connecting the base stations. This work studies a scenario where base stations are connected only if in adjacent cells, and via finite-capacity links. Relying on a linear Wyner-type cellular model with no fading, achievable rates are derived for the two scenarios where base stations are endowed only with the codebooks of local (in-cell) mobile stations, or also with the codebooks used in adjacent cells. Moreover, both uni- and bidirectional backhaul links are considered. The analysis sheds light on the impact of codebook information, decoding delay, and network planning (frequency reuse) on the performance of multicell decoding as enabled by local and finite-capacity backhaul links. Analysis in the high-signal-to-noise ratio (SNR) regime and numerical results validate the main conclusions.