APM-LDPC Coding for Short-Cycle Reduction in Signal Transmission
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current structured LDPC codes in communication systems are limited by their cycle structure, which is affected by the parent matrix, restricting the upper limit of girth and leading to performance deterioration due to short-length cycles.
Innovation Solution
The use of Affine Permutation Matrix (APM)-LDPC codes, which generate codewords through a preset structured encoding scheme, maximizing girth while minimizing complexity by employing Affine permutation matrices and function chains to analyze and remove short-length cycles on the Tanner graph.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional structured LDPC codes are used, then device complexity is reduced through structured encoding, but girth is limited by the parent matrix structure causing performance deterioration
Solution Approach 1:
The patent transforms the conventional structured LDPC code by changing the parameter representation from standard permutation matrices to Affine Permutation Matrices defined by parameters (a, b) where the permutation is given by π(i) = (ai + b) mod L. This parameterization allows for greater flexibility in cycle structure control while maintaining the structured encoding benefits, thereby improving girth without significantly increasing device complexity.
2Productivity
If the parent matrix structure is used to define LDPC codes, then encoding efficiency is improved, but the upper limit of girth is restricted leading to short-length cycles
Solution Approach 1:
The patent introduces asymmetry in the permutation matrix structure by using Affine Permutation Matrices with different parameters (a, b) for different blocks. This asymmetric parameterization breaks the symmetry constraints of conventional structured LDPC codes, allowing for optimized cycle structures and increased girth while preserving encoding efficiency through the systematic parameter-based construction method.
3Device complexity
If short-length cycles are present on the Tanner graph, then device complexity remains low, but error floors occur causing performance deterioration
Solution Approach 1:
The patent converts the potential harm of structured code constraints into a benefit by systematically using Affine Permutation Matrix parameters to eliminate short cycles. The structured nature that could potentially create harmful short cycles is instead leveraged to systematically construct codes with optimized girth properties, transforming the structural constraint from a harmful factor into a beneficial design feature that prevents error floors.
Data Source
AI summary
Disclosed is an apparatus and a method for transmitting/receiving a signal in a communication system, which generates an Affine Permutation Matrix-Low Density Parity Check (APM-LDPC) codeword by encoding an information vector in an APM-LDPC encoding scheme which is a preset structured LDPC encoding scheme, and detects the information vector by decoding the signal in a decoding scheme corresponding to the APM-LDPC encoding scheme, thereby making it possible to generate a Low Density Parity Check (LDPC) code in the form of maximizing a girth while minimizing complexity.