PAC List Decoding with Dynamic Frozen Bits for Short Blocks
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Solution Overview
Problem
Polar codes exhibit suboptimal performance at short block lengths under standard successive-cancellation decoding, particularly in low-SNR regimes, with high worst-case complexity and latency, limiting their effectiveness in certain communication scenarios.
Innovation Solution
Implementing polarization-adjusted convolutional (PAC) codes with dynamic freezing of bits and list decoding, utilizing convolutional precoding and list decoding algorithms to extend multiple paths independently, reducing complexity and latency by leveraging dynamically frozen bits and shift register circuits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard successive-cancellation decoding is used for polar codes, then decoding simplicity is maintained, but error correction performance deteriorates at short block lengths and low-SNR regimes
Solution Approach 1:
The decoding process is segmented into multiple independent paths in the list decoding framework. Each path represents a different candidate codeword, allowing the decoder to explore multiple possibilities simultaneously rather than following a single sequential path, thereby improving error correction performance while maintaining manageable complexity through parallel processing
Solution Approach 2:
The patent introduces dynamically frozen bits that can take different values (0 or 1) depending on the specific path being explored in the list decoding process. This dynamic adaptation allows the decoder to optimize its search strategy based on received signal conditions, improving reliability in low-SNR regimes without requiring excessive computational resources
2Loss of time
If sequential decoding is used, then decoding latency is reduced, but worst-case complexity increases significantly
Solution Approach 1:
The list decoding algorithm maintains a limited list of candidate paths (e.g., list size L=4 or L=8) rather than exploring all possible codewords. This partial exploration approach provides sufficient error correction performance for practical applications while bounding the worst-case complexity, avoiding the exponential complexity growth that would occur with exhaustive sequential decoding
Solution Approach 2:
The encoder prepares dynamically frozen bits in advance according to a predetermined pattern, allowing the decoder to efficiently evaluate multiple paths without requiring complex real-time computations. This preliminary structuring of the code enables the decoder to maintain low latency while achieving improved error correction through list-based parallel evaluation
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.