Summary
This manuscript proposes two classes of deep-learning assisted encoder and decoders for a broadcast channel. The first is an extension of the RNN-based architecture, and the second is a lighter MLP-based architecture. The authors compare them with conventional concatenated codes in various settings, indicating that the proposed architectures outperform conventional codes. In addition, they consider the federated learning scheme for the models and examine the performance when the gradient of trainable weights is transmitted over noisy channels.
Strengths
* The proposed models are the first fully-learnable architectures for an AWGN-broadcast channel (AWGN-BC). They show excellent performance compared with a conventional concatenated linear code.
* The authors investigate a federated learning strategy for training weights in the models. In particular, they examine the effect of noise in transmitting gradients in the training process.
* These issues are of importance in terms of future wireless communications.
Weaknesses
Although the reviewer agrees with the importance of the issues, there are several flaws in this manuscript.
1. **Poor technical contributions**
The contributions of this manuscript are twofold: the proposal of deep-learning architectures for AWGN-BC and the proposal of federated learning for these models. However, the proposed architectures are simple extensions of existing models for single-user cases. In short, the modifications are only learning multiple decoders and changing the loss function. As for federated learning, the concept is familiar and the modifications of the learning process are straightforward. Including not providing any theoretical analyses, the reviewer cannot avoid judging that the contributions of this manuscript are poor.
2. **Lack of comparison between proposed models**
The authors proposed two models for AWGN-BC. It is claimed that LightBC is lighter than RPC-BC, but the authors do not explicitly compare the number of trainable weights and/or training costs of these models. This will be important because the comparison of model size is a performance metric other than an error rate. In addition, it will be related to the analysis of the numerical results, e.g., Fig. 3.
3. **Lack of comparison with other models**
Another issue is that the numerical results do not contain those of other learning-based AWGN-BC codes such as [Li et al. 2022] in the manuscript. Even if Li's model is not fully learnable, as stated in Sec. 1.1, there is no reason to omit the model from comparison in this manuscript.
4. **Possibly insufficient numerical experiments on federated learning**
The authors state, "We choose to explore the uncoded downlink versus a quantized method as it has been shown that there is better convergence behavior in federated learning with noisy downlinks Amiri et al. (2021)." in Line 126-129. However, Fig. 3 only contains the results of uncoded transmission (Line 490). The manuscript seems to be flawed.
5. **No theoretical analysis nor interpretation of numerical results**
The manuscript contains no theoretical analysis of the proposed models or federated learning process. At the very least, I believe that the interpretation of the numerical results should be described in the manuscript. However, the manuscript only describes the facts from numerical results. See the "Question" section for more details.
Questions
Questions:
1. In some numerical results, RPC-BC shows an error floor in the high SNR region but LightBC does not, which is described by "LightBC behaves somewhat like a linear feedback code" (Line448). The reviewer wonders the reason of the fact because RPC-BC must be more flexible than LightBC. A possible reason is the hardness of learning RPC-BC. Is there any explanation of the fact?
Another question: why LightBC can behaves like linear codes? Does learned LightBC really have some linearlity like a linear code? How to examine it?
2. Is there any possible reason that LightBC outperforms RPC-BC in some settings? Is it related to the hardness of learning models?
3. In Fig.3, why LightBC by federated learning performs close to LightBC by global learning?
4. What is the benefit of fully-learnanable AWGN-BC code?
5. Are the training parameters in Tab. 1 optimized for AWGN-BC? The reviewer is concerned that the use of parameters "consistent with the training parameters proposed in the single user versions" (Line 408) may be unsuitable for the AWGN-BC case, resulting in poor performance of RPC-BC.
Suggestions:
1. The size of trainable parameters should be described. It will be helpful to show how much LightBC is lighter than RPC-BC.
2. In Line 232, $\mathbb{R}^{N_s,2}$ should be $\mathbb{R}^{N_{s,2}}$.
3. In Line 394, "The decoder sends the length $|W_\ell|$−length vector..." is somewhat confusing.
4. In Fig. 2(a), the term "SU" is confusing because it is denoted by "TDD" in the main text.