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This paper addresses the optimization problem of minimizing the distortion subject to a rate constraint for an MPEG-4 Advanced Audio Coding (AAC) encoder. We first develop a mathematical model of the AAC encoding process. In previous work, the joint optimization problem is modeled as a Viterbi search for a cheapest path through a trellis. This method involves an iteration over a Lagrangian multiplier. We improve on this method by deriving a very accurate guess for the value of the final Lagrangian multiplier of the iteration as a function of the Perceptual Entropy of the signal and the given rate constraint. This reduces the complexity of the Trellis Search significantly. Whereas previous methods including the Trellis Search did not provide optimal solutions to the problem of minimizing the distortion subject to a rate constraint, we establish two methods that for the first time solve this problem optimally. Our first method is based on the formulation and solution of a Mixed Integer Linear Program, whereas our second method uses a Dynamic Programming solution that does not rely on the iteration over a Lagrangian multiplier. Based on our optimal methods, we evaluate the performance of the heuristic Two Loop Search (TLS), which is used in most commercial AAC implementations to solve the problem under consideration, and the performance of the Trellis Search.
Date of Publication: Jan. 2006