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We propose resource allocation algorithms based on the auction method for uplink OFDMA cellular networks. We consider cellular systems that employ the traditional static frequency reuse as well as the next-generation systems that aim to achieve a universal frequency reuse via base-station coordination. Our algorithms are designed for finite input alphabets and also account for non-ideal practical outer codes, and they can be implemented in a distributed manner, when applied for multi-cell resource allocation. The proposed algorithms have a complexity of O(N) per user per iteration, where N denotes the number of subcarriers in the system, and are also well suited for parallel implementations. We also address power and bandwidth constraints that are motivated by practical concerns. The proposed algorithms exhibit very low complexity and simulation results demonstrate that they offer near-optimal performance.