Sample-adaptive product quantization: Asymptotic analysis and examples

Vector quantization (VQ) is an efficient data compression technique for low bit rate applications. However, the major disadvantage of VQ is that its e ncoding complexity increases dramatically with I,it rate and vector dimensi on. Even though one can use a modified VQ, such as the tree-structured VQ, to reduce the encoding complexity, it is practically infeasible to implemen t such a VQ at a high bit rate or for large vector dimensions because of th e huge memory requirement for its codebook and for the very large training sequence requirement. To overcome this difficulty, a. structurally constrai ned VQ called the sample-adaptive product quantizer (SAPQ) has recently bee n proposed. In this paper, we extensively study the SAPQ that is based on s calar quantizers in order to exploit the simplicity of scalar quantization, Through an asymptotic distortion result, me discuss the achievable perform ance and the relationship between distortion and encoding complexity, We il lustrate that even when SAPQ is based on scalar quantizers, it can provide VQ-level performance, We also provide numerical results that show a 2-3 dB improvement over the Lloyd-Max quantizers for data rates above 4 b/point.