[Paper Review] Enlarging Context with Low Cost: Efficient Arithmetic Coding with Trimmed Convolution

Mu Li, Shuhang Gu+2 more|arXiv (Cornell University)|Jan 15, 2018

Video Coding and Compression Technologies4 citations

TL;DR

This paper proposes Trimmed Convolutional Arithmetic Encoding (TCAE), a highly efficient method for arithmetic coding in image compression that uses trimmed convolutions to model large contexts with shared computation, enabling real-time encoding. It further introduces slope TCAE for parallel decoding, achieving over 60× speedup without significant compression loss.

ABSTRACT

Arithmetic coding is an essential class of coding techniques. One key issue of arithmetic encoding method is to predict the probability of the current coding symbol from its context, i.e., the preceding encoded symbols, which usually can be executed by building a look-up table (LUT). However, the complexity of LUT increases exponentially with the length of context. Thus, such solutions are limited to modeling large context, which inevitably restricts the compression performance. Several recent deep neural network-based solutions have been developed to account for large context, but are still costly in computation. The inefficiency of the existing methods are mainly attributed to that probability prediction is performed independently for the neighboring symbols, which actually can be efficiently conducted by shared computation. To this end, we propose a trimmed convolutional network for arithmetic encoding (TCAE) to model large context while maintaining computational efficiency. As for trimmed convolution, the convolutional kernels are specially trimmed to respect the compression order and context dependency of the input symbols. Benefited from trimmed convolution, the probability prediction of all symbols can be efficiently performed in one single forward pass via a fully convolutional network. Furthermore, to speed up the decoding process, a slope TCAE model is presented to divide the codes from a 3D code map into several blocks and remove the dependency between the codes inner one block for parallel decoding, which can 60x speed up the decoding process. Experiments show that our TCAE and slope TCAE attain better compression ratio in lossless gray image compression, and can be adopted in CNN-based lossy image compression to achieve state-of-the-art rate-distortion performance with real-time encoding speed.

Motivation & Objective

• Address the computational inefficiency of traditional look-up table (LUT)-based arithmetic coding when modeling large contexts.
• Overcome the limitation of sequential probability prediction in deep learning-based entropy coding, which hinders real-time performance.
• Enable efficient, fully convolutional probability prediction across all symbols in a single forward pass by respecting encoding order and context dependencies.
• Accelerate decoding by restructuring 3D code maps into independent blocks for parallel processing.
• Integrate the proposed method into CNN-based lossy image compression pipelines to improve rate-distortion performance with real-time encoding speed.

Proposed method

• Introduce trimmed convolution operations that apply binary masks to exclude non-encoded symbols from context during probability prediction, preserving encoding order constraints.
• Design a fully convolutional network architecture that performs joint probability prediction for all symbols in one forward pass, leveraging shared computation across neighboring symbols.
• Apply trimmed convolutions not only to input layers but also to hidden feature maps, where context information is already encoded and thus can be safely included.
• Propose a slope TCAE schedule that partitions 3D code maps into blocks based on the sum of coordinates (i+j+k=t), ensuring independence within each block.
• Enable parallel decoding by removing inter-block dependencies, allowing simultaneous processing of code blocks while maintaining correct decoding order.
• Utilize a 3D code map representation where each point (i,j,k) corresponds to a binary code, and define code blocks as sets of points with equal i+j+k values.

Experimental results

Research questions

• RQ1 Can a fully convolutional network with trimmed convolutions efficiently model large contexts for arithmetic coding while maintaining computational efficiency?
• RQ2 How does the use of trimmed convolutions improve the efficiency of probability prediction compared to independent predictions for each symbol?
• RQ3 To what extent can parallel decoding via block partitioning accelerate the decoding process without sacrificing compression ratio?
• RQ4 Can the proposed TCAE and slope TCAE methods be effectively integrated into CNN-based lossy image compression systems to improve rate-distortion performance?
• RQ5 What is the trade-off between compression efficiency and decoding speed when using slope TCAE compared to standard TCAE and prior entropy coding methods?

Key findings

• TCAE achieves a 7–20× speedup in encoding compared to the convolutional entropy encoder in Li et al. [4], with encoding times as low as 0.166 seconds for a 752×496×3 image.
• Slope TCAE reduces decoding time to 0.62 seconds for a 94×68×64 code map, achieving over 60× speedup compared to TCAE and 25× speedup compared to the baseline encoder.
• For lossless gray image compression, TCAE and slope TCAE outperform PNG and JPEG2000-LS in compression ratio, especially at higher bitrates.
• When integrated into CNN-based lossy compression (e.g., [4]), TCAE improves rate-distortion performance across all tested bitrates (bpp ≥ 0.4), outperforming competing methods.
• The slope TCAE model incurs only a minor drop in compression ratio (negligible in experiments) while enabling massive decoding speedup, validating the independence assumption within code blocks.
• The method achieves near real-time encoding (e.g., 25 fps) for standard image sizes, making it suitable for practical deployment in real-time systems.