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Partially Polarized Polar Codes: A New Design for 6G Control Channels

Arman Fazeli, Mohammad M. Mansour, Ziyuan Zhu, Louay Jalloul

TL;DR

This work tackles the high decoding burden of blind downlink control information (DCI) detection in 5G/6G by introducing Partially Polarized Polar (PPP) codes, which inter-segment interdependencies are created via a partial polarization layer. PPP codes partition the payload into segments, encode each with a conventional polar code, and apply a partial polarization ratio $\tau$ to balance segment capacities, enabling early termination in a two-stage decoding process. The authors prove that fixed $\tau$ PPP constructions are capacity-achieving under SC decoding and present multiple construction methods (Bhattacharyya tracking, $\alpha\beta$-expansion, and a GNN-based approach) to optimize the reliability sequence. Numerical results show PPP codes surpass standard segmentation and aggregation while leveraging existing polar-decoder hardware, approaching the performance of longer polar codes and offering practical benefits for low-latency, energy-efficient blind-detection in future PDCCH implementations. This approach effectively decouples blind detection from full DCI decoding and suggests concrete paths for design and hardware-friendly deployment in 6G control channels.

Abstract

We introduce a new family of polar-like codes, called Partially Polarized Polar (PPP) codes. PPP codes are constructed from conventional polar codes by selectively pruning polarization kernels, thereby modifying the synthesized bit-channel capacities to ensure a guaranteed number of non-frozen bits available early in decoding. These early-access information bits enable more effective early termination, which is particularly valuable for blind decoding in downlink control channels, where user equipment (UE) must process multiple candidates, many of which carry no valid control information. Our results show that PPP codes offer substantial performance gains over conventional polar codes, particularly at larger block lengths where hardware limitations restrict straightforward scaling. Compared with existing methods such as aggregation or segmentation, PPP codes achieve higher efficiency without the need for additional hardware support. Finally, we propose several frozen-bitmap design strategies tailored to PPP codes.

Partially Polarized Polar Codes: A New Design for 6G Control Channels

TL;DR

This work tackles the high decoding burden of blind downlink control information (DCI) detection in 5G/6G by introducing Partially Polarized Polar (PPP) codes, which inter-segment interdependencies are created via a partial polarization layer. PPP codes partition the payload into segments, encode each with a conventional polar code, and apply a partial polarization ratio to balance segment capacities, enabling early termination in a two-stage decoding process. The authors prove that fixed PPP constructions are capacity-achieving under SC decoding and present multiple construction methods (Bhattacharyya tracking, -expansion, and a GNN-based approach) to optimize the reliability sequence. Numerical results show PPP codes surpass standard segmentation and aggregation while leveraging existing polar-decoder hardware, approaching the performance of longer polar codes and offering practical benefits for low-latency, energy-efficient blind-detection in future PDCCH implementations. This approach effectively decouples blind detection from full DCI decoding and suggests concrete paths for design and hardware-friendly deployment in 6G control channels.

Abstract

We introduce a new family of polar-like codes, called Partially Polarized Polar (PPP) codes. PPP codes are constructed from conventional polar codes by selectively pruning polarization kernels, thereby modifying the synthesized bit-channel capacities to ensure a guaranteed number of non-frozen bits available early in decoding. These early-access information bits enable more effective early termination, which is particularly valuable for blind decoding in downlink control channels, where user equipment (UE) must process multiple candidates, many of which carry no valid control information. Our results show that PPP codes offer substantial performance gains over conventional polar codes, particularly at larger block lengths where hardware limitations restrict straightforward scaling. Compared with existing methods such as aggregation or segmentation, PPP codes achieve higher efficiency without the need for additional hardware support. Finally, we propose several frozen-bitmap design strategies tailored to PPP codes.
Paper Structure (5 sections, 1 theorem, 15 equations, 7 figures, 1 table)

This paper contains 5 sections, 1 theorem, 15 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Capacity Re-balancing and Two-Stage Decoding
  3. Partially Polarized Polar Codes
  4. Numerical Results
  5. Concluding Remarks

Key Result

Theorem 1

For any fixed $\tau = \tfrac{\lambda}{\Lambda}$, where $\Lambda = 2^m$ for some integer $m$ and $\lambda \in [0,\Lambda]$, PPP codes achieve the symmetric channel capacity under successive cancellation (SC) decoding.

Figures (7)

  • Figure 1: Illustration of inter-segment dependencies in PPP codes. The PPP ratio specifies the fraction of XOR operations retained in the final polarization layer: a ratio of $0$ removes all inter-segment dependencies, while a ratio of $1$ corresponds to a full polar transform, yielding maximum capacity imbalance.
  • Figure 2: Two-stage decoding with partially polarized inter-segment coding. Channel LLRs are first pre-processed using $F$ operations to generate the input for the first decoder. After the first decoding stage, $G$ operations combine the results to construct the synthesized LLRs for the second decoder.
  • Figure 3: Example of a PPP code with partial ratio $\tau = 1/2$.
  • Figure 4: Synthesized erasure channels obtained by combining two non-identical erasure channels. The Bhattacharyya parameters of the erasure channels are equal to their erasure probabilities.
  • Figure 5: Performance comparison for $(N,K,L)=(64,32,16)$. PPP significantly outperforms segmentation and approaches the performance of the larger polar code.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof