Hardware architectures for Successive Cancellation Decoding of Polar Codes (1011.2919v1)

Abstract: The recently-discovered polar codes are widely seen as a major breakthrough in coding theory. These codes achieve the capacity of many important channels under successive cancellation decoding. Motivated by the rapid progress in the theory of polar codes, we propose a family of architectures for efficient hardware implementation of successive cancellation decoders. We show that such decoders can be implemented with O(n) processing elements and O(n) memory elements, while providing constant throughput. We also propose a technique for overlapping the decoding of several consecutive codewords, thereby achieving a significant speed-up factor. We furthermore show that successive cancellation decoding can be implemented in the logarithmic domain, thereby eliminating the multiplication and division operations and greatly reducing the complexity of each processing element.

• The paper presents novel hardware architectures for SC decoding of polar codes, achieving O(n) complexity and constant throughput for efficient hardware implementation.
• The authors reduce computational burden by transitioning SC decoding to the logarithmic domain, approximating functions with a minimum operation to eliminate multiplication and division.
• Detailed architectures like the Pipelined Tree and Line SC reduce complexity, enabling practical VLSI implementation for polar codes in efficient future communication systems.

Hardware Architectures for Successive Cancellation Decoding of Polar Codes

The paper explores novel hardware architectures for implementing successive cancellation (SC) decoding of polar codes, emphasizing efficiency in terms of both hardware complexity and throughput. The authors, motivated by the significant advancement in polar codes, focus particularly on reducing the complexity of SC decoders and propose architectures that can be effectively implemented in hardware systems.

Key Contributions

The primary contribution of the paper is the presentation of several hardware architectures for SC decoding that achieve O(n) complexity in both processing and memory elements, while maintaining constant throughput. This stands in contrast to the conventional O(n log n) complexity initially suggested for SC decoding by Arıkan. The researchers introduce techniques to overlap the decoding of multiple codewords, thereby improving the throughput significantly.

Another crucial innovation is the transition of SC decoding to the logarithmic domain. By approximating the necessary transcendental functions with a simple minimum function, the authors markedly reduce the computational burden. This transformation eliminates multiplication and division operations, streamlining the processing elements significantly.

Detailed Analysis of Architectures

1. FFT-like SC Decoder: Initially rooted in the Fast Fourier Transform (FFT) structure proposed by Arıkan, this architecture consists of n log n node processors and registers. The scheduling is either left-to-right or right-to-left, introducing data dependencies and recursive calls for nodes, which complicates hardware implementation.
2. Pipelined Tree Architecture: This configuration utilizes resource sharing within the stages, allowing a sub-linear number of processing elements (PEs) to perform necessary operations. By leveraging the sequential nature of SC decoding, the pipelined tree architecture reduces complexity compared to the FFT-like decoder while maintaining the same throughput.
3. Line SC Architecture: Further reducing complexity, this architecture minimizes the number of PEs to a linear arrangement, utilizing multiplexers to emulate the tree structure efficiently. This design manages resource use more effectively, albeit at a minimal decrease in throughput.
4. Vector-overlapping SC Architecture: By using idle cycles in the pipelined architecture, the authors propose an approach to overlap the decoding of multiple vectors, enhancing throughput without duplicating the entirety of decoder resources. This approach scales well with additional vector parallelism through minimal duplication of specific stages.

Numerical Results and Implications

The architectures proposed in the paper show significant reductions in complexity while achieving constant throughput, positioning them as viable solutions for implementing SC decoders in hardware. The proposed line and pipelined architectures offer substantial improvements over traditional FFT-like decoders, particularly in reducing complexity and enhancing throughput when dealing with large codeword lengths.

Implications and Future Developments

The research provides a practical pathway to implementing polar codes using SC decoders in hardware, potentially influencing the design of error-correcting systems in communications technology where polar codes are relevant. With the potential for implementing these architectures on VLSI, this paper opens doors to scalable and efficient incorporation of polar codes into commercial applications.

Future advancements might include exploring semi-parallel architectures where components from these presented architectures are integrated with partial parallelism to further balance complexity and operational scalability—particularly necessary for handling massive data streams in future communication networks.

The advancement of these hardware implementations could significantly impact both theoretical developments in polar codes and their practical application in various cutting-edge communication systems, paving the way for their integration into emerging technologies demanding high-efficiency error correction.