Interleaved Polar Encoding for Short-Code Spectrum Improvement
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Solution Overview
Problem
Polar codes with short code lengths suffer from poor code spectrum performance, and existing decoding algorithms like Fano decoding are complex and not suitable for hardware implementation.
Innovation Solution
An encoding method that determines information and fixed bits based on generator matrix reliability and row weights, incorporating interleaving at various stages to optimize code spectrum and improve decoding performance, applicable to polar and Reed-Muller codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If polar code with short code length is used, then encoding complexity is reduced, but code spectrum performance deteriorates
Solution Approach 1:
The encoding process is divided into multiple stages with interleaving operations between them. The to-be-encoded sequence undergoes first encoding to generate intermediate sequences, then interleaving reorders these sequences, followed by second encoding. This segmentation allows optimization of code spectrum performance without requiring a single complex encoding operation.
Solution Approach 2:
An interleaving operation is introduced as an intermediary step between the first encoding and second encoding. This interleaver reorders the intermediate encoded sequences before the final encoding stage, acting as a mediator that optimizes the code spectrum characteristics while maintaining the overall encoding structure.
2Reliability
If Fano decoding algorithm is used for PAC code, then decoding performance is improved, but hardware implementation complexity increases
Solution Approach 1:
The complex Fano decoding algorithm is extracted and replaced with a simpler successive cancellation decoding approach. The patent uses a decoding structure that processes the encoded sequence through multiple stages corresponding to the encoding stages, but with simplified decoding operations that are more suitable for hardware implementation while maintaining acceptable decoding performance.
3Reliability
If interleaving is added in encoding process, then code spectrum performance is optimized, but encoding process complexity increases
Solution Approach 1:
The interleaving operation introduces dynamic reordering of encoded sequences at specific stages of the encoding process. This dynamic manipulation of the sequence order optimizes the code spectrum by creating more favorable distance distributions, while the interleaving structure itself remains a relatively simple permutation operation that doesn't significantly increase overall complexity.
Data Source
AI summary
An encoding apparatus may obtain a to-be-encoded sequence, where the to-be-encoded sequence includes information bits and fixed bits, and the information bits and the fixed bits are determined based on reliability and/or row weights of generator matrices corresponding to the to-be-encoded bits; and perform a encoding process on the to-be-encoded sequence to obtain an encoded sequence, where the encoding process includes at least one interleaving process.