A Low-Complexity Improved Successive Cancellation Decoder for Polar Codes (1412.5501v1)

Abstract: Under successive cancellation (SC) decoding, polar codes are inferior to other codes of similar blocklength in terms of frame error rate. While more sophisticated decoding algorithms such as list- or stack-decoding partially mitigate this performance loss, they suffer from an increase in complexity. In this paper, we describe a new flavor of the SC decoder, called the SC flip decoder. Our algorithm preserves the low memory requirements of the basic SC decoder and adjusts the required decoding effort to the signal quality. In the waterfall region, its average computational complexity is almost as low as that of the SC decoder.

• The paper presents a novel SC flip decoding method that mitigates error propagation by dynamically flipping low-confidence bit decisions.
• It combines CRC-based verification with iterative decoding to achieve error performance competitive with SC list decoders at reduced complexity.
• The approach maintains O(N) memory efficiency and adapts to signal conditions, highlighting its practical potential for hardware implementations.

An Insightful Overview of an Improved Successive Cancellation Decoder for Polar Codes

The paper "A Low-Complexity Improved Successive Cancellation Decoder for Polar Codes" by Orion Afisiadis, Alexios Balatsoukas-Stimming, and Andreas Burg puts forth a novel approach to overcoming inherent limitations in the conventional Successive Cancellation (SC) decoding of polar codes. Polar codes, introduced by Arikan, are capacity-achieving error-correcting codes with notable theoretical attractiveness due to their structured construction proving optimality for a variety of applications. Despite SC decoding's elegant structure and computational efficiency at $O(N \log N)$, its error-correcting performance at finite blocklengths is suboptimal compared to other modern codes like LDPC codes.

To address this issue, more complex algorithms such as SC list decoding and SC stack decoding have been suggested. These methods improve error performance by considering multiple decoding paths but at the expense of higher computational and memory complexities, scaling as $O(LN \log N)$ for SC list decoding and $O(DN \log N)$ for SC stack decoding. The proposed technique, termed the SC flip decoder, seeks to enhance error performance while retaining the low complexity of the traditional SC algorithm.

Concept of SC Flip Decoding

The SC flip decoder maintains the memory complexity of $O(N)$, akin to SC, and achieves physical layer performance gains by dynamically adjusting its computational demands based on instantaneous signal conditions. Unlike approaches requiring large memory footprints for worst-case scenarios, the SC flip decoder capitalizes on the insight that most errors stem from a single erroneous bit decision propagating through the decoding process. By introducing controlled "flips"—retrospective corrections in these error-prone decisions—the SC flip achieves error performance improvements significant enough to rival those of more exhaustive decoding methods.

Technical Essence and Complexity

SC flip decoding leverages the concept of flipping the least reliable bit decisions during an initial SC decoding attempt. This method involves determining an unreliable set of decisions, guided by a CRC (cyclic redundancy check) to ensure valid codewords. The algorithm then permits $T$ additional decoding attempts focused on rectifying bits deemed unreliable. A primary advantage is its average computational complexity, described as $O(N \log N(1 + T \cdot P_e(R, \text{SNR})))$, where $P_e(R, \text{SNR})$ denotes the FER, suggesting energy-proportional behavior because complexity naturally reduces at higher signal-to-noise ratios.

Performance Evaluation

Graphical analysis indicates the tangible error performance benefits of SC flip decoding. With $T = 32$, the decoder approximates the performance of an oracle-assisted SC, which theoretically corrects the first error imperatively. Notably, SC flip shows comparable error rates to SC list decoding but demands lower resource allocation, achieving the practical balance between performance and complexity.

Implications and Future Developments

The introduction of SC flip decoding stands as a pragmatic enhancement for scenarios where reduced complexity and resource efficiency are paramount. Beyond the plain improvement of FER, SC flip's lightweight complexity profile suits hardware implementations where traditional SC lists are impractical. Further investigation may explore adaptive strategies for dynamically tuning $T$ or integrating machine learning models to predict unreliable decisions better.

Moreover, understanding and mitigating the negative bias introduced by increasing potential erroneous positions as blocklength expands will be critical for extending this approach's scalability. As communication systems advance toward more challenging environments and massive data demands, the refinement and adoption of algorithms like SC flip are anticipated to play a vital role in next-generation error correction methodologies.