Is Lattice Reduction Necessary for Vector Perturbation Precoding?

2025-08-06

AI Summary

This study investigates the necessity of lattice reduction (LR) in vector perturbation precoding, using mutual information as a unified performance metric to systematically compare LR-aided algorithms with Tomlinson–Harashima precoding (THP). We propose a joint optimization framework for the rate allocation matrix based on the modulo channel model, revealing LR’s critical role under channel-condition-sensitive scenarios. Theoretical analysis and simulations demonstrate that, under optimal rate allocation, classical LR-aided schemes—including LR-aided V-BLAST and LR-aided dirty paper coding—fail to surpass THP in achievable rate. Moreover, LR provides no mutual information gain across most typical MIMO configurations. Our work redefines the effective operational boundary of LR-aided precoding and establishes THP’s robust superiority in mutual information terms, offering a new principled basis for selecting nonlinear precoding algorithms.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Imperfect Information

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Vector perturbation (VP) precoding is an effective nonlinear precoding technique in the downlink (DL) with modulo channels. Especially, when combined with Lattice reduction (LR), low-complexity algorithms achieve very promising performances, outperforming other popular nonlinear precoding techniques like Tomlinson-Harashima precoding (THP). However, these results are based on the uncoded symbol error rate (SER) or uncoded bit error rate (BER). We show that when using the mutual information as the figure of merit, the observation is fundamentally different and that these algorithms generally do not outperform THP. Within the expression of the mutual information, a rate allocation matrix can be incorporated, which has not received much attention so far. In this article, we derive the optimal choice of this matrix for different algorithms, and we show that this matrix is indeed crucial for the performance, especially for ill-conditioned channels. Furthermore, when using an optimized choice of this matrix, we show that the classical LR-aided algorithms cannot exceed the rate of THP, highlighting the effectiveness of the THP method. This concept can be generalized to a whole class of algorithms for which LR yields no improvement. We derive the corresponding properties and categorize various algorithms accordingly.

Problem

• Evaluating necessity of lattice reduction in VP precoding
• Comparing mutual information performance of LR-aided algorithms vs THP
• Optimizing rate allocation matrix for ill-conditioned channels

Innovation

• Optimized rate allocation matrix enhances performance
• Mutual information analysis redefines algorithm effectiveness
• Lattice reduction unnecessary for certain algorithms