Polar Code Decoding with Local Feedback and Convolutional Precoding
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Solution Overview
Problem
Polar codes used in error correction face challenges in reducing communication receiver complexity while maintaining performance, particularly in systems that cannot afford complex decoding algorithms like CRC-aided list decoding.
Innovation Solution
The implementation of local feedback mechanisms in polar code decoding, combined with convolutional codes, to improve error correction capabilities without significantly increasing computational complexity, using techniques such as successive-cancellation decoding and Viterbi-aided SC decoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If CRC-aided list decoding is used to improve error correction performance, then reliability is improved, but device complexity increases significantly
Solution Approach 1:
The decoder is segmented into multiple independent components: a successive-cancellation decoder for initial decoding, a separate CRC check module for error detection, and a list extension module that only activates when CRC fails. This segmentation allows the system to achieve high reliability through CRC-aided list decoding while maintaining low average complexity by avoiding full list decoding in all cases.
Solution Approach 2:
The system applies partial list decoding by extending the list only when necessary (when CRC check fails on the first decoded candidate). Instead of performing exhaustive list decoding for all codewords, the system uses a selective approach where list extension is applied partially only to cases that require it, thereby improving error correction performance while controlling complexity.
2Ease of operation
If successive-cancellation decoding is used to reduce computational complexity, then ease of operation is improved, but error correction performance deteriorates
Solution Approach 1:
The system implements feedback through bidirectional communication between the successive-cancellation decoder and the CRC check module. When the CRC check detects errors in the decoded codeword, this feedback triggers list extension and re-decoding attempts. This feedback mechanism allows the simple successive-cancellation decoder to achieve improved error correction performance by combining it with adaptive list extension based on CRC feedback.
3Reliability
If convolutional codes are concatenated with polar codes to improve error correction, then reliability is improved, but device complexity increases
Solution Approach 1:
The system merges convolutional coding and polar coding into a concatenated encoding scheme where convolutional codes provide outer code protection and polar codes provide inner code protection. This merging of two different coding approaches creates a hybrid system that leverages the strengths of both: convolutional codes' robust error correction and polar codes' capacity-achieving properties, thereby improving overall reliability while distributing complexity across two specialized components.
Data Source
AI summary
Disclosed are devices, systems and methods for precoding and decoding polar codes using local feedback are described. One example method for improving an error correction capability of a decoder includes receiving a noisy codeword vector of length n, the codeword having been generated based on a concatenation of a convolutional encoding operation and a polar encoding operation and provided to a communication channel prior to reception by the decoder, performing a successive-cancellation decoding operation on the noisy codeword vector to generate a plurality of polar decoded symbols (n), generating a plurality of information symbols (k) by performing a convolutional decoding operation on the plurality of polar decoded symbols, wherein k/n is a rate of the concatenation of the convolutional encoding operation and the polar encoding operation, and performing a bidirectional communication between the successive-cancellation decoding operation and the convolutional decoding operation.