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.

翻译：模拟编码通过使用实/复数值运算扩展维度来增加冗余。框架理论为构建此类编码提供了数学基础，并在非正交码分多址（NOMA-CDMA）、分布式计算、多描述信源编码、空时编码（STC）等领域具有广泛应用。对应于这些应用的信道模型是噪声与擦除的组合。近期分析表明，在随机均匀擦除条件下，谱随机矩阵理论与大型等角紧框架（ETFs）之间存在有用联系。本文将该模型推广至擦除以块形式出现的信道。这尤其适用于每用户配备多个发射天线的NOMA-CDMA以及具有已知空间分组的STC。我们提出了一种调整ETF编码以适应块擦除的方法，并找到了在该场景下性能优于ETF的最小块内互相关框架。