Polar-BCH Code Design for Finite-Length Error Correction

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Solution Overview

Problem

Polar codes exhibit subpar finite length performance compared to LDPC and turbo codes, and existing methods for improving error correction, such as list successive cancellation and code concatenation, fail to account for channel characteristics and algebraic properties effectively.

Innovation Solution

A method for designing a polar code that incorporates algebraic codes by transforming the parity matrix to include additional parity, ensuring simultaneous hard and soft decision decoding capabilities, and optimizing the minimum distance through analysis of the zero spectrum of the BCH code.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If polar codes are used for error correction, then the code structure is simple and encoding is efficient, but the finite length performance lags behind LDPC and turbo codes

Engineering Contradiction:

Improveencoding efficiencyVSAvoidfinite length performance

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

The patent combines polar codes with algebraic codes (specifically BCH codes) to create a hybrid code structure. The polar code provides efficient encoding and good asymptotic performance, while the algebraic code component adds structured parity bits that improve finite length performance and enable better error correction capabilities at practical code lengths.

Inventive Principle:

Principle #5Merging (Combining)

Solution Approach 2:

The patent creates a composite code by integrating two different code types (polar code and algebraic code) into a single hybrid structure. This composite approach leverages the strengths of both code types: the channel-characteristic-adaptive nature of polar codes and the algebraic structure of BCH codes that provides improved minimum distance and finite length performance.

Inventive Principle:

Principle #40Composite materials

2Reliability

If CRC codes are concatenated with polar codes to improve error correction, then error correction ability improves dramatically, but algebraic properties become difficult to analyze

Engineering Contradiction:

Improveerror correction abilityVSAvoidanalysis complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent segments the code structure into distinct functional components: the polar code portion handles channel adaptation and basic error correction, while the algebraic code portion provides structured redundancy with analyzable properties. This segmentation allows each component to be analyzed independently using its own mathematical framework, maintaining analytical tractability while achieving improved error correction.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The algebraic code acts as an intermediary layer between the polar code and the channel, providing a mathematically tractable structure that bridges the gap between the polar code's channel adaptation and the need for analyzable algebraic properties. This intermediary structure enables both improved error correction and mathematical analysis.

Inventive Principle:

Principle #24Intermediary (Mediator)

3Difficulty of detecting and measuring

If algebraic codes are used, then algebraic properties such as minimum distance are easy to analyze, but efficient soft decoding methods are not known

Engineering Contradiction:

Improvealgebraic property analysisVSAvoidsoft decoding efficiency

Core Design Contradiction:

Difficulty of detecting and measuringVSEase of operation

Solution Approach 1:

The hybrid code structure serves multiple functions: it maintains the algebraic structure of BCH codes for easy analysis of minimum distance and error correction capabilities, while simultaneously enabling soft decoding through the polar code component's LSC (list successive cancellation) algorithm. This multi-functionality resolves the contradiction between analytical ease and decoding efficiency.

Inventive Principle:

Principle #6Universality (Multi-functionality)

4Device complexity

If polar codes are designed without considering channel characteristics, then code design is simpler, but performance in practical LSC decoders with list size 8-32 deteriorates

Engineering Contradiction:

Improvecode design complexityVSAvoidpractical decoder performance

Core Design Contradiction:

Device complexityVSReliability

Solution Approach 1:

The patent performs preliminary analysis of channel characteristics and algebraic properties during the code design phase. By pre-determining the optimal algebraic code parameters and their integration with the polar code structure based on channel conditions, the system achieves good practical performance without adding complexity to the actual decoding operation. The preliminary design phase captures the channel adaptation needs.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS12476658B2Apparatus and method for designing codes by using polar and algebraic codes

Publication Date: 2025.11.18 ELECTRONICS & TELECOMM RES INST

AI summary

Proposed are an apparatus and a method for designing codes by using polar and algebraic codes. The operating method of the apparatus for designing a code may include a step of identifying a polar code defined as at least one information set, a step of identifying a parity matrix of the polar code, a step of identifying a vector corresponding to the polar code, a step of identifying a row that is representable in a way by linearly combining each row of the parity matrix, a step of identifying a specific binarization matrix in which the representable row does not exist, a step of generating a transformed parity matrix by adding the specific binarization matrix to the parity matrix and a step of generating a pre-code corresponding to the transformed parity matrix.