In the emerging field of goal-oriented communications, the focus has shifted from reconstructing data to directly performing specific learning tasks, such as classification, segmentation, or pattern recognition, on the received coded data. In the commonly studied scenario of classification from compressed images, a key objective is to enable learning directly on entropy-coded data, thereby bypassing the computationally intensive step of data reconstruction. Conventional entropy-coding methods, such as Huffman and Arithmetic coding, are effective for compression but disrupt the data structure, making them less suitable for direct learning without decoding. This paper investigates the use of low-density parity-check (LDPC) codes -- originally designed for channel coding -- as an alternative entropy-coding approach. It is hypothesized that the structured nature of LDPC codes can be leveraged more effectively by deep learning models for tasks like classification. At the receiver side, gated recurrent unit (GRU) models are trained to perform image classification directly on LDPC-coded data. Experiments on datasets like MNIST, Fashion-MNIST, and CIFAR show that LDPC codes outperform Huffman and Arithmetic coding in classification tasks, while requiring significantly smaller learning models. Furthermore, the paper analyzes why LDPC codes preserve data structure more effectively than traditional entropy-coding techniques and explores the impact of key code parameters on classification performance. These results suggest that LDPC-based entropy coding offers an optimal balance between learning efficiency and model complexity, eliminating the need for prior decoding.

We consider the use of look-up tables (LUT) to speed up and simplify the hardware implementation of a deep learning network for inferencing after weights have been successfully trained. The use of LUT replaces the matrix multiply and add operations with a small number of LUTs and addition operations resulting in a multiplier-less implementation. We compare the different tradeoffs of this approach in terms of accuracy versus LUT size and the number of operations.

Learning the distribution of natural images is one of the hardest and most important problems in machine learning. The problem remains open, because the enormous complexity of the structures in natural images spans all length scales. We break down the complexity of the problem and show that the hierarchy of structures in natural images fuels a new class of learning algorithms based on the theory of critical phenomena and stochastic processes. We approach this problem from the perspective of the theory of critical phenomena, which was developed in condensed matter physics to address problems with infinite length-scale fluctuations, and build a framework to integrate the criticality of natural images into a learning algorithm. The problem is broken down by mapping images into a hierarchy of binary images, called bitplanes. In this representation, the top bitplane is critical, having fluctuations in structures over a vast range of scales. The bitplanes below go through a gradual stochastic heating process to disorder. We turn this representation into a directed probabilistic graphical model, transforming the learning problem into the unsupervised learning of the distribution of the critical bitplane and the supervised learning of the conditional distributions for the remaining bitplanes. We learnt the conditional distributions by logistic regression in a convolutional architecture. Conditioned on the critical binary image, this simple architecture can generate large, natural-looking images, with many shades of gray, without the use of hidden units, unprecedented in the studies of natural images. The framework presented here is a major step in bringing criticality and stochastic processes to machine learning and in studying natural image statistics.