PAC Code Construction Using Q-Learning for Short Blocklengths
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Solution Overview
Problem
Polar codes exhibit poor performance for short blocklengths due to inadequate distance properties and sub-optimal decoding methods, leading to a significant gap between their performance and the dispersion bound in noisy channels.
Innovation Solution
The development of Polarization Assisted Convolutional (PAC) codes using reinforcement learning (RL) methods, specifically Q-learning, to construct optimal rate profiles and improve the Hamming distance of polar codes, thereby enhancing their performance under noisy conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If polar codes are used for short blocklengths, then encoding and decoding complexity is low, but performance is insufficient and far from the dispersion bound
Solution Approach 1:
The patent combines polar codes with convolutional precoding to create PAC codes, merging two different coding approaches to achieve performance close to the dispersion bound while maintaining practical complexity. This composite structure allows the system to benefit from both polar code channel polarization properties and convolutional code distance properties.
Solution Approach 2:
The patent modifies the traditional polar code construction by introducing a convolutional precoding polynomial with specific parameters (degree, coefficients) to transform the code properties. By adjusting these parameters, the system achieves improved distance properties and performance without significantly increasing complexity.
2Device complexity
If conventional polar codes are used, then the structure is simple, but distance properties are poor leading to suboptimal performance
Solution Approach 1:
The patent applies convolutional precoding to the information bits before they are encoded by the polar code. This preliminary transformation improves the distance properties of the overall code by ensuring that information bits are distributed in a way that maximizes minimum distance, thereby improving error correction capability.
Solution Approach 2:
The convolutional precoding polynomial acts as an intermediary transformation between the information bits and the polar encoding process. This intermediate step modifies the input to the polar encoder to achieve better overall code properties without complicating the fundamental polar code structure.
3Device complexity
If standard polar decoding is used, then decoding complexity is low, but the gap to dispersion bound is significant
Solution Approach 1:
The patent employs successive cancellation list (SCL) decoding which maintains multiple candidate paths and uses feedback from partial decoding results to guide the decoding process. This feedback mechanism allows the decoder to correct errors more effectively by comparing multiple hypotheses against the received signal, reducing the gap to the dispersion bound.
Solution Approach 2:
The patent uses dynamic list management in SCL decoding where the number of candidate paths is adaptively controlled. The list size and pruning decisions are made dynamically based on the received signal quality and partial decoding outcomes, allowing the system to achieve better performance without linearly increasing complexity.
Data Source
AI summary
A method for constructing Polarization Assisted Convolutional (PAC) codes, the method including passing a codeword through a noisy channel to obtain a first bit and a noise value, determining whether the first bit is an information bit or a non-information bit based on the noise value by decoding the codeword to obtain a decoded codeword, selecting at least one of a reward or a penalty for the first bit based on the decoded codeword, the reward being set based on a probability of decoding, and the selecting selects the penalty for the first bit in response to determining the first bit is incorrectly decoded, and iterating the passing, the determining and the selecting according to Q-values for each state among a plurality of states, at least one of the Q-values corresponding to the first bit.