基于LDGM的MSE Quantization码的设计与分析
Design and Analysis of LDGM-Based Codes for MSE Quantization
摘要：
在R^n的均方误差（MSE）量化中接近1.5329 dB整形（粒度）增益限制在许多问题中是重要的，特别是脏纸编码。为此，我们从一个二进制低密度生成矩阵（LDGM）码开始，并通过周期性地重复其二进制码字的集合来构造量化码书，或者通过Gray映射将其映射到m元码字。量化算法基于置信度传播，并且它使用抽取过程来进行收敛所需的猜测。利用一个真正的典型抽取器（TTD）的结果作为参考，它表明，所提出的量化器的渐近性能可以表征一定的单调性条件的代码的不动点属性，可以分析与密度演化，并进行度分布优化。当迭代次数有限时，通过引入从"坏“猜测中恢复的算法来分析所产生的损失，并且这种分析的结果使得能够进一步优化抽取的速度和度分布。仿真结果表明，在计算复杂性相近的情况下，基于LDGM的量化器的整形增益为1.4906 dB，比极限增益低0.0423 dB，明显优于网格编码量化（TCQ）.
英文摘要：
Approaching the 1.5329-dB shaping (granular) gain limit in mean-squared error (MSE) quantization of R^n is important in a number of problems, notably dirty-paper coding. For this purpose, we start with a binary low-density generator-matrix (LDGM) code, and construct the quantization codebook by periodically repeating its set of binary codewords, or them mapped to m-ary ones with Gray mapping. The quantization algorithm is based on belief propagation, and it uses a decimation procedure to do the guessing necessary for convergence. Using the results of a true typical decimator (TTD) as reference, it is shown that the asymptotic performance of the proposed quantizer can be characterized by certain monotonicity conditions on the code's fixed point properties, which can be analyzed with density evolution, and degree distribution optimization can be carried out accordingly. When the number of iterations is finite, the resulting loss is made amenable to analysis through the introduction of a recovery algorithm from ``bad'' guesses, and the results of such analysis enable further optimization of the pace of decimation and the degree distribution. Simulation results show that the proposed LDGM-based quantizer can achieve a shaping gain of 1.4906 dB, or 0.0423 dB from the limit, and significantly outperforms trellis-coded quantization (TCQ) at a similar computational complexity.
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