Efficient inference of Deep Neural Networks (DNNs) on resource-constrained edge devices is essential. Quantization and sparsity are key techniques that translate to repetition and sparsity within tensors at the hardware-software interface. This paper introduces the concept of repetition-sparsity trade-off that helps explain computational efficiency during inference. We propose PLUM, a unified co-design framework that integrates DNN inference systems and quantization (forward and backward pass) to leverage the repetition-sparsity trade-off to improve inference efficiency. Our results demonstrate that PLUM's quantization method is more accurate than binary quantization with the same number of non-zero weights. Detailed analysis indicates that signed binarization generates a smaller distribution of effectual (non-zero) parameters nested within a larger distribution of total parameters of latent full-precision weights for a DNN block. Finally, the proposed PLUM framework achieves a 26% speedup on real hardware, doubles energy efficiency, and reduces density by 2.8x compared to binary methods while retaining top-1 accuracy when compared to prior-art methods for ResNets on ImageNet (by achieving 66.2% top-1 accuracy), presenting an alternative solution for deploying efficient models in resource-limited environments.