While product code VQ is an effective paradigm for reducing the encoding search and memory requirements of vector quantization, a significant limitation of this approach is the heuristic nature of bit allocation among the product code features. We propose an optimal bit allocation strategy for PCVQ through the explicit incorporation of an entropy constraint within the product code framework. Unrestricted entropy-constrained PCVQs require joint entropy codes over all features and concomitant encoding and memory storage complexity. To retain manageable complexity, we propose "product-based" entropy code structures, including independent and conditional feature entropy codes. We also propose an iterative, locally optimal encoding strategy to improve performance over greedy encoding at a small cost in complexity. This approach is applicable to a large class of product code schemes, allowing joint entropy coding of feature indices without exhaustive encoding. Simulations demonstrate performance gains for image coding based on the mean-gain-shape product code structure.
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