Scaling Deep Learning-based Decoding of Polar Codes via Partitioning (1702.06901v1)

Abstract: The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a high-level of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-the-art polar decoders such as successive cancellation list and belief propagation decoding.

• The paper introduces a partitioned neural network decoder that segments polar code encoding graphs, reducing computational complexity for deep learning models.
• It achieves competitive BER performance and low latency by training on smaller, independent sub-blocks rather than full codewords.
• Experimental results reveal trade-offs between partition-induced loss and neural network suboptimality, guiding future advances in scalable ECC decoding.

Scaling Deep Learning-based Decoding of Polar Codes via Partitioning

The paper entitled "Scaling Deep Learning-based Decoding of Polar Codes via Partitioning" introduces a novel approach for improving the scalability of neural network-based decoders for polar codes, a class of error-correcting codes (ECCs) gaining traction in modern communication standards such as 5G and IoT. The authors address the inherent limitations of neural network decoding (NND) due to computational complexity with increasing codeword lengths, termed as the 'curse of dimensionality.' They propose a partitioned neural network (PNN) decoding approach that divides the encoding graph into smaller sub-graphs for more manageable deep learning model training and inference.

Overview of the Approach

The key innovation in this paper lies in the partitioning strategy applied to the polar codes’ encoding graph. This strategy involves segmenting the encoding graph into independent sub-blocks. These sub-blocks, termed as partitions, allow the replacement of conventional iterative decoding components with neural network-based modules in a non-iterative, parallelizable decoding framework. The framework presents an alternative to the traditional Successive Cancelation List (SCL) decoding approach and aims for a solution that is both computationally efficient and close to maximum a posteriori (MAP) performance.

Key advantages of this partitioning approach are twofold: it simplifies the training process by reducing the block size that the NND needs to handle, and it enables a high degree of parallelism in decoding, thus addressing latency issues. Each partition is independently trained to approximate MAP performance, a significant departure from the fully integrated training of larger code lengths. This system is subsequently coupled with a belief propagation (BP) stage to complete the decoding process.

Performance and Benchmarking

The paper provides a detailed comparison between the proposed PNN approach and traditional decoding algorithms such as SCL and BP. With block lengths such as $N=128$ and various partition sizes, the paper highlights the potential trade-offs between the BER performance and decoding latency. The results indicate that while there is a performance gap (quantified as normalized error or NE) relative to optimal SCL decoding, the PNN approach achieves competitive BER performance with reduced latency.

The experimental analysis further discerns between the loss due to partitioning $(\lambda_{\text{part}})$ and the loss due to neural network suboptimality $(\lambda_{\text{NN}})$. The observations suggest that the partition-induced degradation is more significant, highlighting the need to balance partition size and computational efficiency.

Implications and Future Directions

The practical implications of this work are profound for applications where low-latency decoding is paramount. The method offers a scalable pathway leveraging recent advancements in machine learning frameworks to mitigate computational complexity at large block lengths, a critical need in high-throughput communication systems.

Looking forward, the paper sets the stage for potential improvements in neural network architectures to handle larger sub-blocks, thereby reducing dependence on partition sizes. Enhancements in deep learning models, possibly via more advanced structures or training techniques, could further bridge the BER performance gap and improve the robustness of the PNN approach.

The partitioning strategy suggests a broader applicability beyond polar codes, hinting at adaptations for other ECCs where similar challenges of complexity and latency exist. It also opens prospects for integrating more sophisticated machine learning models, potentially combining techniques such as reinforcement learning or transfer learning to refine the decoding process dynamically.

In summary, this paper contributes significantly to the ongoing discourse on scaling deep learning for practical error correction in communications, advancing towards efficient and scalable decoding protocols adaptable to evolving standards in wireless communications.