Improved Successive Cancellation Decoding of Polar Codes

As improved versions of successive cancellation (SC) decoding algorithm, successive cancellation list (SCL) decoding and successive cancellation stack (SCS) decoding are used to improve the finite-length performance of polar codes. Unified descriptions of SC, SCL and SCS decoding algorithms are given as path searching procedures on the code tree of polar codes. Combining the ideas of SCL and SCS, a new decoding algorithm named successive cancellation hybrid (SCH) is proposed, which can achieve a better trade-off between computational complexity and space complexity. Further, to reduce the complexity, a pruning technique is proposed to avoid unnecessary path searching operations. Performance and complexity analysis based on simulations show that, with proper configurations, all the three improved successive cancellation (ISC) decoding algorithms can have a performance very close to that of maximum-likelihood (ML) decoding with acceptable complexity. Moreover, with the help of the proposed pruning technique, the complexities of ISC decoders can be very close to that of SC decoder in the moderate and high signal-to-noise ratio (SNR) regime.Comment: This paper is modified and submitted to IEEE Transactions on Communication

Low Complexity Belief Propagation Polar Code Decoders

Since its invention, polar code has received a lot of attention because of its capacity-achieving performance and low encoding and decoding complexity. Successive cancellation decoding (SCD) and belief propagation decoding (BPD) are two of the most popular approaches for decoding polar codes. SCD is able to achieve good error-correcting performance and is less computationally expensive as compared to BPD. However SCDs suffer from long latency and low throughput due to the serial nature of the successive cancellation algorithm. BPD is parallel in nature and hence is more attractive for high throughput applications. However since it is iterative in nature, the required latency and energy dissipation increases linearly with the number of iterations. In this work, we borrow the idea of SCD and propose a novel scheme based on sub-factor-graph freezing to reduce the average number of computations as well as the average number of iterations required by BPD, which directly translates into lower latency and energy dissipation. Simulation results show that the proposed scheme has no performance degradation and achieves significant reduction in computation complexity over the existing methods.Comment: 6 page

A Split-Reduced Successive Cancellation List Decoder for Polar Codes

This paper focuses on low complexity successive cancellation list (SCL) decoding of polar codes. In particular, using the fact that splitting may be unnecessary when the reliability of decoding the unfrozen bit is sufficiently high, a novel splitting rule is proposed. Based on this rule, it is conjectured that, if the correct path survives at some stage, it tends to survive till termination without splitting with high probability. On the other hand, the incorrect paths are more likely to split at the following stages. Motivated by these observations, a simple counter that counts the successive number of stages without splitting is introduced for each decoding path to facilitate the identification of correct and incorrect path. Specifically, any path with counter value larger than a predefined threshold \omega is deemed to be the correct path, which will survive at the decoding stage, while other paths with counter value smaller than the threshold will be pruned, thereby reducing the decoding complexity. Furthermore, it is proved that there exists a unique unfrozen bit u_{N-K_1+1}, after which the successive cancellation decoder achieves the same error performance as the maximum likelihood decoder if all the prior unfrozen bits are correctly decoded, which enables further complexity reduction. Simulation results demonstrate that the proposed low complexity SCL decoder attains performance similar to that of the conventional SCL decoder, while achieving substantial complexity reduction.Comment: Accepted for publication in IEEE Journal on Selected Areas in Communications - Special Issue on Recent Advances In Capacity Approaching Code