In this work, we investigate the construction of channel decoders based on machine learning solutions, and more specifically, Support Vector Machines (SVM). The channel decoding problem being a high-dimensional multiclass classification problem, previous attempts were made in the literature to construct SVM-based channel decoders. However, existing solutions suffer from a dimensionality curse, both in the number of SVMs involved –which are exponential in the block length– and in the training dataset size. In this work, we revisit SVM-based channel decoders by alleviating these limitations and prove that the suggested SVM construction can achieve optimal Bit Error Probability (BEP) by attaining the performance of the bit-Maximum A Posteriori (MAP) decoder in the Additive White Gaussian Noise (AWGN) channel.