Deep learning has been recently applied to physical layer processing in digital communication systems in order to improve end-to-end performance. In this work, we introduce a novel deep learning solution for soft bit quantization across wideband channels. Our method is trained end-to-end with quantization-and entropy-aware augmentations to the loss function and is used at inference in conjunction with source coding to achieve near-optimal compression gains over wideband channels. We prove and verify that a proper weight initialization scheme leads to a reduced feature variance, which allows us to use a fixed latent feature quantization scheme. When tested on channel distributions never seen during training, the proposed method achieves a compression gain of up to 10% in the high SNR regime versus previous state-of-the-art methods.