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Linear filtering methods for fixed rate quantisation with noisy symmetric error channels

机译：带有噪声对称误差通道的固定速率量化的线性滤波方法

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摘要

This study considers linear filtering methods for minimising the end-to-end average distortion of a fixed-rate source quantisation system. For the source encoder, both scalar and vector quantisation are considered. The codebook index output by the encoder is sent over a noisy discrete memoryless channel whose statistics could be unknown at the transmitter. At the receiver, the code vector corresponding to the received index is passed through a linear receive filter, whose output is an estimate of the source instantiation. Under this setup, an approximate expression for the average weighted mean-square error (WMSE) between the source instantiation and the reconstructed vector at the receiver is derived using high-resolution quantisation theory. Also, a closed-form expression for the linear receive filter that minimises the approximate average WMSE is derived. The generality of framework developed is further demonstrated by theoretically analysing the performance of other adaptation techniques that can be employed when the channel statistics are available at the transmitter also, such as joint transmit-receive linear filtering and codebook scaling. Monte Carlo simulation results validate the theoretical expressions, and illustrate the improvement in the average distortion that can be obtained using linear filtering techniques.
机译：这项研究考虑了线性滤波方法，以最小化固定速率源量化系统的端到端平均失真。对于源编码器，要同时考虑标量和矢量量化。编码器输出的码本索引通过一个嘈杂的，无记忆的离散信道发送，该信道的统计信息可能在发送器处未知。在接收器处，与接收到的索引相对应的代码向量通过线性接收滤波器，其输出是源实例的估计。在这种设置下，使用高分辨率量化理论推导了源实例化和接收器重构向量之间的平均加权均方误差（WMSE）的近似表达式。此外，推导了线性接收滤波器的最小化近似平均WMSE的闭式表达式。通过理论上分析在发射机也可获得信道统计信息时可以采用的其他自适应技术的性能，进一步证明了所开发框架的通用性，例如联合发射-接收线性滤波和码本缩放。蒙特卡洛仿真结果验证了理论表达式，并说明了使用线性滤波技术可以获得的平均失真的改善。

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    《Signal Processing, IET》 |2013年第9期|888-896|共9页
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