Polar Code Frozen Set Generation for BLTA Automorphism Decoding
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Solution Overview
Problem
Conventional methods for generating polar codes suffer from inefficiency and unreliability, particularly in terms of automorphism ensemble decoding, leading to suboptimal performance in bit-channel polarization and error correction.
Innovation Solution
The apparatus and method generate a frozen set associated with a polar code that efficiently and reliably admits automorphisms belonging to a block lower triangular affine (BLTA) group, incorporating elements of the upper triangular linear (UTL) group, enabling improved automorphism ensemble decoding with lower latency and better block error rate (BLER) performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional successive cancellation decoding is used, then the decoding process can be implemented, but the latency is high and block error rate performance is suboptimal
Solution Approach 1:
The invention segments the code word processing into multiple parallel paths by dividing the set of permutations into multiple subsets, where each subset is processed by a separate decoder instance. This parallel processing structure reduces the sequential dependency that causes high latency in conventional SC decoding while maintaining accurate bit-channel reliability estimation.
Solution Approach 2:
The invention performs preliminary action by pre-calculating and storing the frozen set based on the BLTA group structure before decoding begins. This pre-computed frozen set enables the decoders to efficiently process permuted code words without requiring complex real-time calculations, thereby reducing decoding latency while improving block error rate performance.
2Productivity
If conventional automorphism ensemble decoding is used with improperly chosen permutations, then multiple decoders run in parallel, but the result is identical to un-permuted code word decoding, causing inefficiency
Solution Approach 1:
The invention applies local quality by carefully selecting specific permutations from the BLTA group that target particular bit-channel positions with different reliability characteristics. Instead of using arbitrary permutations, the method chooses transformations that specifically address local reliability variations in the code word, ensuring each parallel decoder provides unique and valuable decoding information.
Solution Approach 2:
The invention changes parameters by transforming the code word using specific BLTA group permutations that alter the reliability distribution across bit channels. These parameter changes in the form of structured permutations ensure that each parallel decoder processes a genuinely different version of the code word, improving both decoding efficiency and reliability compared to conventional approaches.
Data Source
AI summary
An apparatus for generating a frozen set associated with a polar code of length ‘N’ and dimension ‘K’ comprises a processing unit configured to take in input the polar code length ‘N’, the dimension ‘K’, and a profile of a structure of a block lower triangular affine (BLTA) group. The BLTA group structure is associated with an affine transformation matrix of size ‘n×n’ and the profile is an ordered set of a plurality of values corresponding to block sizes of blocks. The blocks are sub-matrices of the affine transformation matrix with all the diagonals of blocks in the same order as the ordered block sizes, forming the diagonal of the affine transformation matrix, each of the block sizes is such that ‘n’ is equal to the sum of block sizes and ‘n’ is equal to log2(N). The processing unit generates the frozen set.