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

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.