The problem of learning a channel decoder is considered for two channel models. The first model is an additive noise channel whose noise distribution is unknown and nonparametric. The learner is provided with a fixed codebook and a dataset comprised of independent samples of the noise, and is required to select a precision matrix for a nearest neighbor decoder in terms of the Mahalanobis distance. The second model is a non-linear channel with additive white Gaussian noise and unknown channel transformation. The learner is provided with a fixed codebook and a dataset comprised of independent input-output samples of the channel, and is required to select a matrix for a nearest neighbor decoder with a linear kernel. For both models, the objective of maximizing the margin of the decoder is addressed. Accordingly, for each channel model, a regularized loss minimization problem with a codebook-related regularization term and hinge-like loss function is developed, which is inspired by the support vector machine paradigm for classification problems. Expected generalization error bounds for the error probability loss function are provided for both models, under optimal choice of the regularization parameter. For the additive noise channel, a theoretical guidance for choosing the training signal-to-noise ratio is proposed based on this bound. In addition, for the non-linear channel, a high probability uniform generalization error bound is provided for the hypothesis class. For each channel, a stochastic sub-gradient descent algorithm for solving the regularized loss minimization problem is proposed, and an optimization error bound is stated. The performance of the proposed algorithms is demonstrated through several examples.
翻译:学习频道解码器的问题被考虑用于两个频道模式。 第一个模式是添加噪音分布未知且不参数化的噪音添加频道。 向学习者提供固定代码和由独立噪音样本组成的数据集。 向学习者提供由噪音样本组成的固定代码和由独立声音样本组成的数据集, 并且需要为最近的邻居解码器选择精确矩阵, 并且需要从Mahalanobis 距离的角度为最近的代码器选择一个精确矩阵。 第二个模式是一个非线性通道, 配有添加白高尔西亚噪音和未知频道变换。 向学习者提供固定代码和由该频道独立输入输出样本组成的数据集。 需要为最近的邻居解码器选择一个带有线性内内内内内内内内内内内内核的解码器。 因此, 对于每个频道模式, 都开发一个固定化的损失最小化矩阵问题, 由支持矢量机机的分类问题模型模式来激励。 给两个模型的错误概率损失概率值的界限是, 在最优化的正规化参数参数参数中, 将一个基于升级的精度导路路段 。 向一般的精度 的精度 。 将显示的精度 的精度 的精度 的精度 度 度 的精度 的精度的精度 将精度 的精度的精度的精度的精度 的精度 的精度 的精度 的精度 的精度 的精度 的精度 的精度