Orthogonal LDPC Base Matrices for Parallel Decoding With Lower Error Floors
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Solution Overview
Problem
Protograph-based low-density parity-check (LDPC) codes face high error floors when using large expansion factors, which degrade performance, while smaller base matrices with medium expansion factors offer better parallelization but at the cost of reduced decoding efficiency.
Innovation Solution
Implementing multiple expansion steps with smaller factors to maintain parallelism and reduce error floors, and constructing z-row-orthogonal base matrices to achieve higher row decoder parallelization and efficient encoding/decoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a large expansion factor is used to achieve better parallelization, then the parallelization efficiency is improved, but the error floor increases and performance degrades
Solution Approach 1:
The patent divides the single large expansion operation into multiple smaller expansion steps. Instead of expanding the base matrix once by a large factor q, the method performs multiple expansions with smaller factors q1, q2, ..., qm where q1×q2×...×qm=q. This segmentation allows the code to achieve the same overall parallelization benefit while avoiding the high error floors associated with large single-step expansions, as each smaller expansion step maintains better code properties.
2Reliability
If a small base matrix with medium expansion factor is used, then the error floor is reduced, but the decoding parallelization efficiency decreases
Solution Approach 1:
The patent introduces dynamic adaptability by allowing the selection of different expansion factor combinations (q1, q2, ..., qm) based on performance requirements. The system can dynamically choose to use multiple expansion steps when high parallelization is needed, or use fewer steps when error floor performance is the priority, making the code construction flexible and adaptable to different operational scenarios.
3Reliability
If multiple expansion steps are used to maintain parallelism and reduce error floors, then the code performance is improved, but the code construction complexity increases
Solution Approach 1:
The patent creates a universal code construction framework that can handle both single-step and multi-step expansions through the same base matrix and systematic procedure. The method maintains universality by using the same base matrix B and following the same expansion algorithm regardless of whether one uses a single large expansion factor or multiple smaller factors, thus improving performance without proportionally increasing construction complexity.
Data Source
AI summary
Protograph-based LDPC codes are obtained from z-row-orthogonal base matrices with some additional structure constraints, such as a diagonal and/or double-diagonal structure, in order to allow a high parallelization that is a multiple of z, while having an efficient encoding or decoding. A “big” base matrix is constructed from a structured square submatrix in order to have a WiMAX-like structure and a z-row-orthogonality. Also, starting from a “smaller” base matrix having a part arranged in a double-diagonal shape with tail-biting one, an expansion by a factor equal to z can be performed, followed by an addition of a single one-entry into the last column at a specific location, thereby obtaining a three-degree column, and followed by a row and/or column permutation in order to obtain a base matrix in a WiMAX-like structure.