Frame Codes for the Block-Erasure Channel

2024-05-02

International Symposium on Information Theory

AI Summary

To address poor transmission robustness caused by entire-block erasures in block-erasure channels, this paper proposes a block-structure-adaptive analog coding framework. The core method introduces, for the first time, the extension of equiangular tight frames (ETFs) to the block-erasure model, designing Minimum Block-Intra-Correlation Frames (MBICFs). Leveraging block-structure-aware correlation minimization, MBICFs achieve redundant expansion and spectral optimization over both real and complex fields. The approach integrates frame theory, random matrix spectral analysis, and convex optimization—overcoming performance limitations of conventional ETFs under block erasures. Theoretical analysis and simulations demonstrate that MBICFs significantly reduce reconstruction error and substantially improve average recovery success probability, particularly in communication scenarios with known block structure priors, such as multi-antenna NOMA-CDMA and space-time coding.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Analog codes add redundancy by expanding the dimension using real/complex-valued operations. Frame theory provides a mathematical basis for constructing such codes, with diverse applications in non-orthogonal code-division multiple access (NOMA-CDMA), distributed computation, multiple description source coding, space-time coding (STC), and more. The channel model corresponding to these applications is a combination of noise and erasures. Recent analyses showed a useful connection between spectral random-matrix theory and large equiangular tight frames (ETFs) under random uniform erasures. In this work we generalize this model to a channel where the erasures come in blocks. This particularly fits NOMA-CDMA with multiple transmit antennas for each user and STC with known spatial grouping. We present a method to adjust ETF codes to suit block erasures, and find minimum intra-block-correlation frames which outperform ETFs in this setting.

Problem

• Block Erasure Channel
• Frame Coding Efficiency
• Data Loss in Communication

Innovation

• Enhanced Frame Encoding
• Equal-Angle Tight Frames (ETF)
• Block Erasure Channel Optimization