Frame Codes for the Block-Erasure Channel -- Extended Version
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929681236754432 |
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| author | Jacoby, Itamar Zamir, Ram |
| author_facet | Jacoby, Itamar Zamir, Ram |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01172 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frame Codes for the Block-Erasure Channel -- Extended Version Jacoby, Itamar Zamir, Ram Information Theory Signal Processing 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. |
| title | Frame Codes for the Block-Erasure Channel -- Extended Version |
| topic | Information Theory Signal Processing |
| url | https://arxiv.org/abs/2405.01172 |