Jointly optimized VQ index assignment and transmission energy allocation

In this work we address the problem of designing robust, vector quantizer (VQ) based communication systems for operation over time-varying Gaussian channels. Transmission energy allocation (TEA) to VQ codeword bits, according to their error sensitivities, is a powerful tool for improving robustness to channel noise. The power of this technique can be further enhanced by appropriately combining it with index assignment methods. We pose the corresponding joint optimization problem and suggest a simple iterative algorithm for finding a locally optimal solution. The susceptibility of the solution to poor local minima is significantly reduced by an enhanced version of the algorithm which invokes the the method of noisy channel relaxation, whereby, the VQ system is optimized while gradually decreasing the assumed level of channel noise. The resulting combined technique is shown to outperform standard pseudo-Gray coding by up to 3.5 dB, and to exhibit graceful degradation at mismatched channel conditions. We conclude with a brief discussion of the impact of TEA on the peak-to-average energy ratio of the transmitted modulated signals