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：针对两种信道模型研究了信道译码器的学习问题。第一种模型是加性噪声信道，其噪声分布未知且非参数化。学习器配备固定码本和包含独立噪声样本的数据集，需要为基于马氏距离的最近邻译码器选择精度矩阵。第二种模型是含加性高斯白噪声的非线性信道，其信道变换未知。学习器配备固定码本和包含信道独立输入-输出样本的数据集，需要为线性核的最近邻译码器选择矩阵。针对这两种模型，均以实现译码器间隔最大化为目标。据此，为每种信道模型建立了正则化损失最小化问题，其包含与码本相关的正则化项和类似合页损失的函数，该思路受分类问题中支持向量机范式的启发。在正则化参数最优选择条件下，给出了两种模型下错误概率损失函数的期望泛化误差界。针对加性噪声信道，基于该界限提出了训练信噪比选择的理论指导。此外，针对非线性信道，提供了假设类的高概率一致泛化误差界。对每种信道，提出了求解正则化损失最小化问题的随机次梯度下降算法，并给出了优化误差界。通过多个算例验证了所提算法的性能。