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 the generation of frozen sets, leading to suboptimal performance in decoding and error correction.
Innovation Solution
The apparatus and method generate a frozen set associated with a polar code that efficiently admits automorphisms belonging to a block lower triangular affine (BLTA) group, incorporating elements of the upper triangular linear (UTL) group, enabling automorphism ensemble decoding with lower latency and improved block error rate (BLER) performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If conventional successive cancellation decoding is used, then the decoding process is simple to implement, but the decoding efficiency is low and latency is high
Solution Approach 1:
The patent divides the code into multiple segments and processes them in parallel using multiple decoding units. Each decoding unit handles a specific segment of the code, allowing simultaneous processing of different parts of the encoded data, thereby improving overall decoding efficiency while maintaining implementation simplicity
Solution Approach 2:
The patent introduces a new dimension of parallelism by organizing decoding operations across multiple processing units working simultaneously. This transforms the traditionally sequential single-threaded decoding process into a multi-dimensional parallel processing architecture, significantly reducing latency without complicating the fundamental decoding algorithm
2Productivity
If conventional automorphism ensemble decoding is used, then multiple decoders run in parallel, but the permutations may not be chosen carefully resulting in identical decoding results
Solution Approach 1:
The patent implements a feedback mechanism where the selection of permutations is guided by information from previous decoding attempts and performance metrics. The system learns from decoding outcomes and adjusts permutation selections to ensure diversity and effectiveness, preventing identical results from repeated permutations
Solution Approach 2:
The patent dynamically changes permutation parameters based on code characteristics and decoding performance. By adjusting permutation parameters adaptively rather than using fixed permutations, the system ensures that each parallel decoder operates with distinct transformations, improving both reliability and effectiveness of ensemble decoding
3Ease of manufacture
If the frozen set is generated using conventional methods, then the generation process is straightforward, but the performance in decoding and error correction is suboptimal
Solution Approach 1:
The patent performs preliminary optimization of the frozen set generation process by pre-calculating and storing optimal frozen set configurations for different code lengths and rates. This preliminary action ensures that when decoding is performed, the system uses pre-optimized frozen sets that maximize error correction performance without adding complexity to the real-time decoding operation
Data Source
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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 x 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 so that the associated polar code admits all affine automorphisms belonging to the BLTA group.