Frame Codes for the Block-Erasure Channel -- Extended Version

TL;DR

This paper extends the theory of frame codes for block-erasure channels, proposing new code constructions that outperform traditional ETFs in scenarios with block erasures, relevant for NOMA-CDMA and space-time coding.

Contribution

It generalizes existing models to block erasures and introduces a method to optimize frame codes for such channels, improving performance over standard ETFs.

Findings

New frame code constructions outperform ETFs under block erasures

Method to adjust ETF codes for block erasure channels

Optimal intra-block-correlation frames enhance code robustness

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.