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Low Complexity Successive Cancellation Decoding of Polar Codes based on Pruning Strategy in Deletion Error Channels

He Sun, Rongke Liu, Bin Dai

TL;DR

This work tackles the high complexity of SC decoding for polar codes over $$d$$-deletion channels by introducing a pruning-based approach that prunes low-probability scenarios under a per-node pruning-error bound. A PSPC framework assigns node-specific thresholds to avoid pathological pruning while maintaining performance, and a simplified SPSPC method leverages the hypergeometric structure of scenario probabilities to compute thresholds using only $$d+1$$ peak values, reducing complexity from $$O(d^2)$$ to $$O(d)$$ and storage to linear in the code length. The approach reduces the number of decodable scenarios from $$ rac{(d+1)(d+2)}{2}$$ to $$d+1$$ without sacrificing reliability, offering a practical path to low-complexity polar codes in deletion-prone channels. Overall, the method enhances decoding efficiency and makes polar codes more viable for synchronization-challenged communication and storage systems.

Abstract

A novel SC decoding method of polar codes is proposed in $d$-deletion channels, where a new pruning strategy is designed to reduce decoding complexity. Considering the difference of the scenario weight distributions, pruning thresholds for each node are designed separately according to a uniform constraint on the pruning error probability, which further reduce the number of scenarios that need to be calculated during the decoding procedure. In addition, by exploiting the properties of the joint weight distribution, a simplified calculation method of thresholds is proposed. Using this simplified calculation method, the number of scenarios that required to be calculated is reduced from $(d+1)(d+2)/2$ to $d+1$.

Low Complexity Successive Cancellation Decoding of Polar Codes based on Pruning Strategy in Deletion Error Channels

TL;DR

This work tackles the high complexity of SC decoding for polar codes over -deletion channels by introducing a pruning-based approach that prunes low-probability scenarios under a per-node pruning-error bound. A PSPC framework assigns node-specific thresholds to avoid pathological pruning while maintaining performance, and a simplified SPSPC method leverages the hypergeometric structure of scenario probabilities to compute thresholds using only peak values, reducing complexity from to and storage to linear in the code length. The approach reduces the number of decodable scenarios from to without sacrificing reliability, offering a practical path to low-complexity polar codes in deletion-prone channels. Overall, the method enhances decoding efficiency and makes polar codes more viable for synchronization-challenged communication and storage systems.

Abstract

A novel SC decoding method of polar codes is proposed in -deletion channels, where a new pruning strategy is designed to reduce decoding complexity. Considering the difference of the scenario weight distributions, pruning thresholds for each node are designed separately according to a uniform constraint on the pruning error probability, which further reduce the number of scenarios that need to be calculated during the decoding procedure. In addition, by exploiting the properties of the joint weight distribution, a simplified calculation method of thresholds is proposed. Using this simplified calculation method, the number of scenarios that required to be calculated is reduced from to .
Paper Structure (10 sections, 1 theorem, 14 equations, 4 figures, 3 tables)

This paper contains 10 sections, 1 theorem, 14 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Polar Codes
  4. Noisy D-Deletion Channel Model
  5. SC Decoding Method in D-Deletion Channel
  6. SC Decoding Based on Pruning Strategy
  7. Pruning Strategy Based on Pruning Error Bounds
  8. Simplified Calculation Method of Pruning Thresholds
  9. Storage Complexity Analysis
  10. Conclusion

Key Result

Proposition 1

The pruning threshold is defined as follows, Specifically, ${\eta _1} > Pe_{\text{bound}} \cdot {\eta _{d + 1}}$ denotes that all peak values are larger than $Pe_{\text{bound}} \cdot {\eta _{d + 1}}$, which means that the performance loss caused by pruning is small. Then the pruning threshold is set to

Figures (4)

  • Figure 1: Noisy $d$-deletion channel in cascade with the AWGN channel.
  • Figure 2: Factor graph of polar codes with $N=4$.
  • Figure 3: Pruning Error Probability of the SSSC pruning. ($d=5$.)
  • Figure 4: Probability Distribution of Scenarios in $v_{ < 1 ,1 ,2 > }$. ($N=16$, $d=3$)

Theorems & Definitions (2)

  • Remark 1
  • Proposition 1