Fast Polar Decoders: Algorithm and Implementation (1307.7154v2)

Abstract: Polar codes provably achieve the symmetric capacity of a memoryless channel while having an explicit construction. This work aims to increase the throughput of polar decoder hardware by an order of magnitude relative to the state of the art successive-cancellation decoder. We present an algorithm, architecture, and FPGA implementation of a gigabit-per-second polar decoder.

• The paper presents a fast polar decoder that reduces latency and boosts throughput by up to 40x over traditional SC decoders.
• It introduces algorithmic enhancements including systematic encoding and specialized node mergers to optimize the decoding process.
• Experimental FPGA results demonstrate gigabit-per-second performance, enabling practical high-speed polar code applications.

Overview of "Fast Polar Decoders: Algorithm and Implementation"

The paper "Fast Polar Decoders: Algorithm and Implementation" authored by Sarkis et al., addresses a significant barrier to the adoption of polar codes: the low throughput of their traditional successive-cancellation (SC) decoding algorithm. Polar codes, introduced by Arikan, are celebrated for achieving the symmetric capacity of memoryless channels with an explicit, structured construction. However, their low throughput and inferior performance at short to moderate lengths compared to other codes like low-density parity-check (LDPC) codes hinder their application, particularly in high-speed data storage systems.

The authors present a fast polar decoder offering flexible, gigabit-per-second performance. By refining the Simplified Successive-Cancellation (SSC) and Simplified Successive-Cancellation with Maximum-Likelihood (ML-SSC) approaches, the paper introduces an architecture capable of outperforming current state-of-the-art implementations by a considerable margin. Their proposal notably achieves throughput improvements by a factor of up to 40 in some cases compared to the best existing SC decoders when implemented via Field-Programmable Gate Arrays (FPGAs).

Key Contributions

1. Algorithmic Enhancements:
   • Improved Decoding Algorithms: The paper proposes new techniques and decoder structures, such as employing a single-parity-check-code node, repetition-code node, and specialized node mergers to exploit more classes of directly decodable constituent codes without recursion.
   • Utilization of Systematic Encoding: The use of systematic encoding combined with bit-reversed indexing reduces complexity by allowing direct ordering of output bits without the need for additional interleavers.
2. Architectural Innovations:
   • A hierarchical memory structure is utilized to manage both channel and internal LLR values efficiently, minimizing the resource footprint while maximizing throughput.
   • The optimized implementation of the f and g combining functions, leveraging two's complement arithmetic for simplicity in hardware, allows for faster processing speeds.
3. Implementation Results:
   • The implementation achieves significant reductions in decoding latency; experimental results show 54% of the latency of previous methods.
   • The authors demonstrate an information throughput capability that scales significantly with increased code rate and hardware parallelism, peaking at gigabit rates on an FPGA.

Implications

The research redefines practical polar code applications by making them feasible for high-throughput use cases such as broadband communication systems and high-density data storage. The effective reduction in decoder latency without sacrificing error-correction capability marks a potential inflection point in the preference for polar codes over LDPC codes in specific scenarios.

Future Directions

Given the robust performance characteristics and scalability of the presented decoder, future work might focus on adapting this architecture for ASIC implementations to further increase clock speed and reduce power consumption. Additionally, exploring the integration of the proposed decoder into real-world systems with dynamic code-rate adjustments could provide a field-oriented validation of its flexibility and throughput benefits. The fusion of polar codes with emerging machine learning techniques for adaptive error correction also presents an intriguing intersection for academic pursuit.

In conclusion, the paper by Sarkis et al. significantly advances the field of polar coding, providing a decoder architecture that effectively combines theoretical innovation with practical viability. By addressing both algorithmic and implementation challenges, this work contributes a notable increment to the corpus of high-throughput error-correcting solutions, potentially guiding the future trajectory of coding technologies in data-centric domains.