Source-linked AI summary
DeepJSCC-Q: Constellation Constrained Deep Joint Source-Channel Coding
Tze-Yang Tung, David Burth Kurka, Mikolaj Jankowski, Deniz Gunduz
TL;DR
Commercial hardware and standardized protocols can constrain JSCC to fixed channel input constellations. DeepJSCC-Q is an end-to-end optimized scheme designed for such constraints, and it can perform nearly as well as unquantized DeepJSCC while using a fixed constellation.
Problem
Commercial hardware and standardized protocols impose fixed channel input constraints that limit JSCC applicability.
Method
DeepJSCC-Q is an end-to-end optimized joint source-channel coding scheme for wireless image transmission that uses a fixed channel input constellation.
Results
DeepJSCC-Q can perform nearly as well as DeepJSCC and achieve similar performance to unquantized DeepJSCC despite its constrained constellation.
Takeaways & Limitations
A fixed channel input constellation can support wireless image transmission with performance approaching that of unconstrained DeepJSCC.
Abstract
from arXiv · showhide
Recent works have shown that modern machine learning techniques can provide an alternative approach to the long-standing joint source-channel coding (JSCC) problem. Very promising initial results, superior to popular digital schemes that utilize separate source and channel codes, have been demonstrated for wireless image and video transmission using deep neural networks (DNNs). However, end-to-end training of such schemes requires a differentiable channel input representation; hence, prior works have assumed that any complex value can be transmitted over the channel. This can prevent the application of these codes in scenarios where the hardware or protocol can only admit certain sets of channel inputs, prescribed by a digital constellation. Herein, we propose DeepJSCC-Q, an end-to-end optimized JSCC solution for wireless image transmission using a finite channel input alphabet. We show that DeepJSCC-Q can achieve similar performance to prior works that allow any complex valued channel input, especially when high modulation orders are available, and that the performance asymptotically approaches that of unconstrained channel input as the modulation order increases. Importantly, DeepJSCC-Q preserves the graceful degradation of image quality in unpredictable channel conditions, a desirable property for deployment in mobile systems with rapidly changing channel conditions.
I. Introduction
DeepJSCC jointly maps images to channel inputs and can outperform separate digital schemes, but its arbitrary complex-valued symbols conflict with hardware and protocol constellations. DeepJSCC-Q addresses this constraint with quantization and fixed or learned finite constellations while retaining graceful quality degradation.
- Finite-blocklength JSCC can achieve lower distortion than separate source and channel coding.
- DeepJSCC directly maps source signals to modulated channel inputs without converting them to bits.
- DeepJSCC has shown lower end-to-end distortion, channel adaptation, feedback exploitation, and adaptive-bandwidth transmission.
- Graceful image-quality degradation as channel quality decreases avoids the cliff-effect of separation-based schemes.
- Unlike digital schemes using finite constellations, DeepJSCC transmits arbitrary complex-valued symbols under a power constraint.
- DeepJSCC-Q introduces quantization for fixed or learned finite constellations and targets performance close to unconstrained DeepJSCC and superior to BPG plus LDPC.
II. Related Works
Prior JSCC research spans cross-layer, unequal-error-protection, analog, and DNN-based designs. DeepJSCC improved image transmission performance and avoided cliff effects, but generally assumed arbitrary complex channel inputs; this work studies finite alphabets for natural images.
- Earlier cross-layer and unequal-error-protection schemes jointly optimized coding parameters but introduced complexity through multiple codes and successive decoding.
- DNN-based DeepJSCC learned encoder-decoder mappings through an autoencoder and surpassed JPEG2000 followed by LDPC coding.
- DeepJSCC and its extensions demonstrated cliff-effect avoidance, channel-feedback exploitation, bandwidth adaptation, OFDM operation, multi-user use, and video transmission.
- Most prior DNN-based schemes implicitly assumed communication hardware could transmit arbitrary complex-valued channel inputs.
- Related discrete-input work studied learned representations for MNIST over binary erasure channels, whereas this paper considers natural images over a differentiable finite-input channel.
- Constellation-learning research optimized input distributions or constellation points, while this work targets end-to-end distortion for natural-image sources and channel codes.
III. Problem Statement
The problem is wireless image transmission over noisy static or fading channels with finite bandwidth, power, and constellation constraints. The goal is to learn encoder and decoder functions that maximize reconstructed image quality under these conditions.
- Wireless image transmission is modeled over a noisy channel, with reconstruction produced by a decoder from the channel output.
- Communication transmits one symbol from a finite set at each channel use, with static and fading scenarios considered.
- In the static scenario, the channel gain is constant and known to transmitter and receiver, corresponding to AWGN transmission.
- In the fading scenario, the channel gain changes independently per image and is known only to the receiver, which performs equalization.
- The design objective is to maximize average reconstructed image quality under bandwidth ratio ρ, average power P, and constellation C constraints.
IV. Proposed Solution
DeepJSCC-Q inserts a constellation quantizer between convolutional encoder and decoder networks, supporting fixed or jointly learned finite constellations. The method trains the end-to-end system while allowing constellation geometry optimization.
- DeepJSCC-Q is a DNN-based JSCC scheme trained end to end for finite channel input alphabets.
- Two strategies use either a fixed constellation or a constellation trained as parameters for a given order.
- The encoder first maps an image to a complex latent vector and then quantizes it to constellation symbols.
- A fully convolutional encoder and decoder are jointly trained in an autoencoder architecture.
- The encoder output channel count controls the number of channel uses k.
- The architecture allocates channel bandwidth and power resources through attention focused on regions requiring higher bit rate.
A. Quantization
The encoder’s latent vector is quantized so its outputs become symbols from a finite constellation. The paper considers both a soft-to-hard quantizer and an extension that learns the constellation itself.
- The encoder output is quantized to produce channel symbols from a finite constellation.
- The method considers a soft-to-hard quantizer and a learned variant that also optimizes the constellation.
1) Soft-to-hard quantizer:
The soft-to-hard quantizer uses nearest-constellation hard assignments for transmission while retaining a differentiable soft assignment for training. The soft assignment weights constellation points according to their squared distances from each latent value.
- 1) Soft-to-hard quantizer:: Hard quantization maps each latent value to its nearest constellation symbol, producing the channel input.
- 1) Soft-to-hard quantizer:: For QPSK, the procedure illustrates the distinction between nearest-point hard quantization and distance-weighted soft quantization.
- 1) Soft-to-hard quantizer:: Soft quantization forms each output as a softmax-weighted sum of constellation symbols based on squared l2 distances.
- 1) Soft-to-hard quantizer:: The forward pass uses hard quantization, while the backward pass uses gradients from the soft quantized value.
- 1) Soft-to-hard quantizer:: The constellations are modeled as uniformly distributed square lattices in the complex plane, including M-QAM symbols.
2) Learned soft-to-hard quantizer:
The learned soft-to-hard quantizer treats the constellation as trainable alongside the quantization process. It estimates symbol usage from training batches and normalizes symbol power during optimization.
- 2) Learned soft-to-hard quantizer:: The learned quantizer makes the constellation C part of the trainable parameters.
- 2) Learned soft-to-hard quantizer:: The gradient of the soft quantized value with respect to the input supports optimization through quantization.
- 2) Learned soft-to-hard quantizer:: Constellation points are initialized and then updated during training, with symbol power normalized to maintain the power constraint.
- 2) Learned soft-to-hard quantizer:: Symbol-selection probabilities are estimated over batches using the convex weights from the soft assignment.
- 2) Learned soft-to-hard quantizer:: The empirical probability estimate is applied to each constellation point using its distance-based assignment weights.
B. Training Strategy
Training adds a KL-divergence regularizer between the empirical constellation distribution and a uniform distribution. This encourages exploration of available constellation points while retaining a distortion-based objective.
- B. Training Strategy: The training objective adds a KL-divergence regularizer between the constellation distribution P(C) and uniform distribution U(C).
- B. Training Strategy: KL divergence measures the difference between two distributions and equals zero exactly when they are equal.
- B. Training Strategy: The regularizer encourages the quantizer to explore available constellation points and may improve end-to-end performance.
- B. Training Strategy: The distortion term uses MSE for PSNR evaluation or 1-MS-SSIM for MS-SSIM evaluation.
- B. Training Strategy: The weighting parameter λ controls the amount of regularization in the final loss.
V. Experimental Results
Experiments evaluate DeepJSCC-Q on AWGN and slow-fading channels using finite constellations, comparing training choices, modulation orders, learned constellations, and separation-based coding. Results show graceful image-quality degradation, strong performance relative to separation, and convergence toward unconstrained DeepJSCC at high modulation orders.
- AWGN channel: DeepJSCC-Q preserves graceful degradation of image quality as channel quality decreases despite finite constellation constraints.This matches the behavior previously observed for unconstrained DeepJSCC.
- Modulation order: M = 4096 DeepJSCC-Q beats the separation-based schemes for SNRTrain = 7, 10dB, while lower-order models can underperform separation.Increasing modulation order improves performance at the relevant SNRs.
- Modulation order: Performance improves monotonically with modulation order and asymptotically approaches unconstrained DeepJSCC, with |C| = 4096 performing nearly the same.The comparison removes the quantizer for the non-quantized DeepJSCC reference.
- Learned constellations: Learned constellations substantially outperform QAM constellations in slow fading, with L-64 even exceeding 4096-QAM on PSNR.The results emphasize optimizing channel-input geometry and distribution for non-Gaussian channels.
- Constellation structure: Learned constellation geometry becomes increasingly non-square and power-asymmetric at higher orders, assigning greater power to first-quadrant points while compensating through usage frequency.For slow fading, L-16 forms two circles and uses a radially decreasing probability distribution to maintain average power.
- Comparison with separation: DeepJSCC-Q performs better than BPG-LDPC separation in all but one evaluated instance, demonstrating an advantage in the finite block length regime.The exception is 64-QAM at bandwidth compression ratio ρ = 1/6.
VI. Conclusions
DeepJSCC-Q is an end-to-end JSCC scheme for wireless image transmission that uses a fixed finite channel input constellation. It achieves performance similar to unquantized DeepJSCC, outperforms separation-based schemes, and approaches unconstrained DeepJSCC as modulation order increases.
- DeepJSCC-Q is an end-to-end optimized JSCC scheme that operates over a fixed channel input constellation.It is designed for wireless image transmission with finite channel inputs.
- DeepJSCC-Q achieves similar performance to unquantized DeepJSCC while using a constrained constellation.
- DeepJSCC-Q achieves superior performance to separation-based schemes using BPG source coding and LDPC channel coding.
- DeepJSCC-Q avoids the cliff-effect that affects separation-based schemes.
- With sufficiently high modulation order, DeepJSCC-Q approaches the performance of DeepJSCC without a fixed channel input constellation.
- A learned finite channel input alphabet can further improve DeepJSCC-Q performance, producing a constellation with highly non-trivial geometry and distribution.