Reliably transmitting messages despite information loss due to a noisy channel is a core problem of information theory. One of the most important aspects of real world communication is that it may happen at varying levels of information transfer. The bandwidth-limited channel models this phenomenon. In this study we consider learning joint coding with the bandwidth-limited channel. Although, classical results suggest that it is asymptotically optimal to separate the sub-tasks of compression (source coding) and error correction (channel coding), it is well known that for finite block-length problems, and when there are restrictions to the computational complexity of coding, this optimality may not be achieved. Thus, we empirically compare the performance of joint and separate systems, and conclude that joint systems outperform their separate counterparts when coding is performed by flexible learnable function approximators such as neural networks. Specifically, we cast the joint communication problem as a variational learning problem. To facilitate this, we introduce a differentiable and computationally efficient version of the bandwidth-limited channel. We show that our design compensates for the loss of information by two mechanisms: (i) missing information is modelled by a prior model incorporated in the channel model, and (ii) sampling from the joint model is improved by auxiliary latent variables in the decoder. Experimental results justify the validity of our design decisions through improved distortion and FID scores.
to it's ubiquity as a fundamental component in the real world communication systems. The main contributions of this work include:
1. We cast the problem of learning joint communication as a variational learning problem, parallel to other work (Choi et al., 2019). 2. We justify the importance of jointly learned systems by empirically evaluating the gap between neural systems for joint and separate communication. 3. We design standard channels such as the Gaussian and Binary channel as differentiable probabilistic nodes, which serve as base for our design of the bandwidth-limited channel. 4. We investigate two core design choices of our neural joint model and bandwidth-limited channel:
(i) how transmission rate can be improved through learned prior models (ii) how we may improve image reconstructions in the low bandwidth regime through the introduction of auxiliary latent variables in the decoding process.
Paper Summary:
The paper proposes to use ML methods, specifically neural networks, to learn source and/or channel coding systems, either jointly or separately. Specifically, they investigate these systems under the bandwidth-limited channel.  They investigate their models applied to the task of transferring images across the channel.
Pros:
- The paper is in a difficult area, and needs to communicate ideas about communications and information as well as various deep learning models. The initial exposition does this well.
- The paper discusses ML-based communications models applied to the bandwidth limited channel and performs experiments to investigate joint vs. separate coding. 
Two main things of concern:
- This area (communications, compression, coding) is highly developed, yet there are no comparisons to practical, state of the art techniques in this paper. The experiments investigate using the authors' models to send images across a noisy channel. So shouldn't we see a comparison to an equivalent non-ML-based system that currently accomplishes this task, if only for perspective? 
- The paper contains too much exposition and the structure makes it difficult to read.  The authors' work seems to mostly be focused in sections 4 and 6, but prior work is summarized in section 5.  The authors want to communicate a lot of ideas which the audience might not be familiar with, and this is a difficult task. However, the paper could be reorganized such that the ideas are clearer. Rate distortion is delegated to an appendix, but two pages are spent on basic communications. Overall it could be much more focused. 
Some smaller concerns:
- Pg. 3 "hypothesis spaces can be searched increasingly quickly in an automated fashion, allowing researchers to search..." 
I think this statement may be over-reaching. The authors also frequently use the term "flexible function approximation". Neural networks do have interesting approximation properties. But this is not a complete picture of deep learning, and the situation is much more nuanced than this. Where is the role of optimization and data? In order to transmit data with the author's algorithms, do we need to go out and collect a large body of examples in the specific domain, like CelebA? Because you don't need to do that to e.g. compress any image with JPEG, code the data using LDPC to send across a channel. Is this comparing apples and oranges?
- Pg. 6 "Note, that a simple additive white Gaussian noise.... LDPC. However, in more general scenarios they do not perform as well and can be beaten by neural network architectures....."
I think the claims in this paragraph need to be toned down a bit. LDPC does not perform well in regards to what? Can be beaten under what conditions? Decode efficiently with regard to what block length? I don't think the picture is as clear as painted here.
- Pg. 4 The statements here regarding the bandwidth-limited channel appear to be the focus of the author's work. This section should be expanded and explained. Reading the first paragraph then going to the second paragraph ("To summarize..."), there's sort of a disconnect. How do we know these two things are equivalent? What exactly is novel that was introduced?
Small typos:
- Pg. 2 final paragraph, some  norm is used for the distortion, but this is not defined (either on pg. 2 or in App. B)
- Pg. 6 white is misspelled "withe"