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In this paper a single-input-single-output wireless data transmission system with adaptive modulation and coding over correlated fading channel is considered, where run-time power adjustment is not available. Higher layer data packets are enqueued into a finite size buffer space before being released into the time-varying wireless channel. Without fixing the physical layer error probability, the objective is to minimize the average joint packet loss rate due to both erroneous transmission and buffer overflow. Two optimization techniques are incorporated to achieve the best solution. The first is policy domain optimization that formulates the data rate adaptation design as classical Markov decision problem. The second is channel domain optimization that appropriately partitions the channel variation based on particular fading environment and carried traffic pattern. The derived policy domain analytical model can precisely map any policy design into various QoS performance metrics with finite buffer setup. We then propose a tractable suboptimization framework to produce different two-dimensional suboptimal solutions with scalable complexity-optimality tradeoff for practical implementations.