  This paper introduces the notion of soft bits to address the rate-distortion
optimization for learning-based image compression. Recent methods for such
compression train an autoencoder end-to-end with an objective to strike a
balance between distortion and rate. They are faced with the zero gradient
issue due to quantization and the difficulty of estimating the rate accurately.
Inspired by soft quantization, we represent quantization indices of feature
maps with differentiable soft bits. This allows us to couple tightly the rate
estimation with context-adaptive binary arithmetic coding. It also provides a
differentiable distortion objective function. Experimental results show that
our approach achieves the state-of-the-art compression performance among the
learning-based schemes in terms of MS-SSIM and PSNR.
