论文标题
标量量化器和M-PSK的最佳索引分配通过离散卷积重态不平等
Optimal Index Assignment for Scalar Quantizers and M-PSK via a Discrete Convolution-Rearrangement Inequality
论文作者
论文摘要
本文研究了从（M）最大熵标量量化的（M）量级量化的（M）-PSK符号（例如，在降低概率密度函数（例如AWGN）下降后，添加噪声）从（M）-PSK符号中找到最佳的非二进制指数分配的问题，以最大程度地减少通道均值扭曲。已知在最大似然（ML）下的所谓曲折映射是渐近的最佳选择，但是确定任何给定信噪比（SNR）的最佳索引分配的问题仍然开放。基于Hardy-Little Wood卷积重新制定不等式的广义版本，我们证明ML解码下的锯齿形映射对于所有SNR都是最佳的。进一步证明，相同的最优结果在最低均值率（MMSE）解码下也保持不变。给出了数值结果，以验证我们的最佳结果，并证明（M）ARY索引分配的性能增长在AWGN通道上（8）-PSK的情况下对最新的二进制二进制对应物的性能。
This paper investigates the problem of finding an optimal nonbinary index assignment from (M) quantization levels of a maximum entropy scalar quantizer to (M)-PSK symbols transmitted over a symmetric memoryless channel with additive noise following decreasing probability density function (such as the AWGN channel) so as to minimize the channel mean-squared distortion. The so-called zigzag mapping under maximum-likelihood (ML) decoding was known to be asymptotically optimal, but the problem of determining the optimal index assignment for any given signal-to-noise ratio (SNR) is still open. Based on a generalized version of the Hardy-Littlewood convolution-rearrangement inequality, we prove that the zigzag mapping under ML decoding is optimal for all SNRs. It is further proved that the same optimality results also hold under minimum mean-square-error (MMSE) decoding. Numerical results are presented to verify our optimality results and to demonstrate the performance gain of the optimal (M)-ary index assignment over the state-of-the-art binary counterpart for the case of (8)-PSK over the AWGN channel.
