A mapping of the Min-Sum decoder to reduction operations, and its implementation using CUDA kernels

2025-07-14

AI Summary

Traditional LDPC Min-Sum decoders suffer from strong dependence on specific parity-check matrix structures, limiting generality and hardware reusability. To address this, we propose a matrix-content-agnostic GPU decoding framework that depends solely on the matrix dimensions. Our key innovation is the first abstraction of the Min-Sum iterative process as a reduction operation, enabling the design of configurable CUDA kernels that unify row- and column-wise processing under a single parallel paradigm. The framework requires no prior knowledge of the parity-check matrix’s sparsity pattern and supports arbitrary LDPC codes—regular or irregular, across diverse code rates. Experimental results demonstrate consistently high parallel efficiency and excellent scalability across various matrix sizes. This approach significantly enhances the flexibility and hardware reuse potential of LDPC decoders, overcoming structural rigidity inherent in conventional designs.

Technology Category

Machine Learning: Matrix & Tensor MethodsConstraint Satisfaction and Optimization: Distributed CSP/OptimizationData Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systemsSystems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Decoders for Low Density Parity Check (LDPC) codes are usually tailored to an application and optimized once the specific content and structure of the parity matrix are known. In this work we consider the parity matrix as an argument of the Min-Sum decoder, and provide a GPU implementation that is independent of the content of the parity matrix, and relies only on its dimensions.

Problem

• Mapping Min-Sum decoder to reduction operations
• GPU implementation independent of parity matrix content
• Generic decoder relying only on parity matrix dimensions

Innovation

• Mapping Min-Sum decoder to reduction operations
• GPU implementation independent of parity matrix content
• Relies only on parity matrix dimensions