PAC List Decoding Using Dynamic Frozen Bits for Low-SNR Reliability
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Solution Overview
Problem
Polar codes at short block lengths under standard successive-cancellation decoding perform poorly, and sequential decoding is inefficient in low-SNR regimes and worst-case complexity and latency scenarios.
Innovation Solution
Polarization-adjusted convolutional (PAC) codes employ convolutional precoding and list decoding, with dynamically frozen bits to improve error correction, using a method that extends multiple paths independently during list decoding, reducing latency and complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If sequential decoding is used for polar codes at short block lengths, then decoding can be performed, but error correction performance is poor and latency varies in low-SNR regimes
Solution Approach 1:
The patent applies dynamics by making the frozen bits dynamic rather than static. The convolutional precoder generates frozen bits that change based on the information bits and channel conditions, allowing the decoder to adapt to varying SNR regimes. This dynamic approach enables consistent latency across different channel conditions while maintaining good error correction performance, resolving the contradiction between reliability and time loss.
Solution Approach 2:
The patent segments the decoding process into list-based parallel path exploration rather than sequential single-path decoding. By maintaining multiple candidate paths simultaneously and using dynamically generated frozen bits to guide path selection, the system achieves both good error correction (through multiple candidates) and consistent latency (through bounded list size), resolving the contradiction between reliability and time loss.
2Reliability
If sequential decoding is used, then decoding can proceed, but complexity increases in worst-case scenarios
Solution Approach 1:
The dynamic frozen bits generated by convolutional precoding provide structured guidance that reduces the effective search space for the decoder. By making frozen bits dependent on previous bits and channel conditions, the system dynamically prunes unlikely paths, maintaining low complexity even in worst-case scenarios while preserving error correction capability through list-based parallel exploration.
Solution Approach 2:
The patent incorporates feedback mechanisms where the convolutional precoder uses previously decoded bits to generate subsequent frozen bits. This feedback structure creates a deterministic relationship between information bits and frozen bits, allowing the decoder to efficiently eliminate invalid paths without exhaustive search, thus reducing complexity while maintaining reliability.
3Reliability
If standard polar encoding is used, then encoding is simple, but performance is insufficient at short block lengths
Solution Approach 1:
The patent creates a composite coding structure by combining convolutional codes with polar codes. The convolutional precoder layer adds structured redundancy and dynamic frozen bit generation, while the polar encoder provides capacity-achieving performance. This composite approach significantly improves error correction at short block lengths while adding only moderate encoding complexity through the convolutional precoding step.
Solution Approach 2:
The encoding process is segmented into two distinct stages: convolutional precoding that generates dynamic frozen bits and structures the information, followed by polar encoding that achieves reliable transmission. This segmentation allows each component to specialize - the convolutional part handles dynamic adaptation and the polar part handles capacity-achieving encoding - improving performance without excessive complexity.
Data Source
AI summary
Devices, systems and methods for list decoding of polarization-adjusted convolutional (PAC) codes are described. One example method for improving error correction in a decoder for data in a communication channel includes receiving a noisy codeword, the codeword having been generated using a polarization-adjusted convolutional (PAC) code and provided to the communication channel prior to reception by the decoder, and performing PAC list decoding on the noisy codeword, wherein an encoding operation of the PAC code comprises a convolutional precoding operation that generates one or more dynamically frozen bits, and wherein the PAC list decoding comprises extending, based on the one or more dynamically frozen bits, at least two paths of a plurality of paths in the PAC list decoding differently and independently.