An Adaptive Successive Cancellation List Decoder for Polar Codes with Cyclic Redundancy Check (1208.3091v1)

Abstract: In this letter, we propose an adaptive SC (Successive Cancellation)-List decoder for polar codes with CRC. This adaptive SC-List decoder iteratively increases the list size until the decoder outputs contain at least one survival path which can pass CRC. Simulation shows that the adaptive SC-List decoder provides significant complexity reduction. We also demonstrate that polar code (2048, 1024) with 24-bit CRC decoded by our proposed adaptive SC-List decoder with very large list size can achieve a frame error rate FER=0.001 at Eb/No=1.1dB, which is about 0.2dB from the information theoretic limit at this block length.

• The paper introduces an adaptive SCL decoder that dynamically adjusts the list size until a valid CRC path is identified.
• It achieves near-optimal error performance (FER ≤ 10^-3 at E_b/N_0 = 1.1 dB) while significantly reducing computational complexity.
• Simulation results demonstrate a substantial reduction in average complexity, enhancing the practical deployment of polar codes in energy-constrained systems.

Adaptive Successive Cancellation List Decoder for Polar Codes with CRC

This paper presents a novel approach to decoding polar codes by introducing an adaptive Successive Cancellation List (SCL) decoder, which significantly enhances the complexity management in decoding processes, especially when concatenated with Cyclic Redundancy Check (CRC). The authors propose an adaptive mechanism that determines the required list size dynamically, thus optimizing the decoding complexity without sacrificing performance.

Overview

Polar codes, introduced by Arıkan, represent a significant theoretical breakthrough in coding, capable of achieving Shannon capacity with low-complexity encoding and decoding mechanisms. However, the performance of simple successive cancellation (SC) decoders is suboptimal for short and moderate block lengths. An SC-List decoder improves the performance but increases complexity, especially when combined with CRC for error detection and correction.

The paper's primary contribution is an adaptive SC-List decoder, which operates by dynamically adjusting the list size during the decoding process until a valid path that passes the CRC is identified. This method aims to reduce the computational burden associated with large fixed list sizes while maintaining high error correction performance.

Main Contributions

1. Adaptive List Size: The adaptive SC-List decoder revises the list size iteratively, beginning with a small list size and enlarging it only if no valid path passes CRC checks. This adaptive approach significantly reduces computational complexity on average compared to the non-adaptive SC-List decoder with a fixed large list size.
2. Performance and Complexity: The adaptive decoder achieves a frame error rate (FER) close to the maximum-likelihood performance with significantly reduced average complexity. The paper reports a substantial gain, achieving FER ≤ 10^-3 at E_b/N_0 = 1.1 dB for the polar code (2048, 1024) with a 24-bit CRC, only 0.2 dB away from the theoretical limit.
3. Simulation Results: Simulation results substantiate the claim that the adaptive algorithm achieves comparable performance to the more complex fixed list size decoder, but with up to several thousand-fold reduction in average complexity in practical E_b/N_0 ranges. The report provides detailed numerical results on the average list size utilized in different scenarios to demonstrate efficiency.

Theoretical Implications

The paper enriches the understanding of polar codes' performance when augmented with adaptive decoding mechanisms. It suggests a concrete path for enhancing the practical deployability of polar codes by minimizing the energy consumption associated with decoding, which is paramount in power-constrained environments such as mobile handsets or base stations with multiple users.

Practical Implications and Future Work

By demonstrating that adaptive SC-List decoders can achieve high performance with lower average complexity, this work opens avenues for practical deployments of polar codes in modern communication systems. The integration of CRC with polar codes has shown potential in achieving robust error performance without excessively complicating the decoding process. Future studies could explore the adaptation of this methodology in conjunction with other coding paradigms or leverage this approach within more complex system architectures to further exploit its benefits.

This paper serves as a basis for future explorations of adaptive decoding methodologies in polar codes and other advanced coding techniques. The successful implementation of such techniques could significantly influence the efficiency of future communication systems, pushing closer to theoretical limits with practical low-resource utilization.