Higher-Order Staircase Codes: A Unified Generalization of High-Throughput Coding Techniques
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913661543514112 |
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| author | Shehadeh, Mohannad Kschischang, Frank R. |
| author_facet | Shehadeh, Mohannad Kschischang, Frank R. |
| contents | We introduce a unified generalization of several well-established high-throughput coding techniques including staircase codes, tiled diagonal zipper codes, continuously interleaved codes, open forward error correction (OFEC) codes, and Robinson-Bernstein convolutional codes as special cases. This generalization which we term "higher-order staircase codes" arises from the marriage of two distinct combinatorial objects: difference triangle sets and finite-geometric nets, which have typically been applied separately to code design. We illustrate one possible realization of these codes, obtaining powerful, high-rate, low-error-floor, and low-complexity coding schemes based on simple iterative syndrome-domain decoding of coupled Hamming component codes. We study some properties of difference triangle sets having minimum scope and sum-of-lengths, which correspond to memory-optimal higher-order staircase codes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_16504 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-Order Staircase Codes: A Unified Generalization of High-Throughput Coding Techniques Shehadeh, Mohannad Kschischang, Frank R. Information Theory We introduce a unified generalization of several well-established high-throughput coding techniques including staircase codes, tiled diagonal zipper codes, continuously interleaved codes, open forward error correction (OFEC) codes, and Robinson-Bernstein convolutional codes as special cases. This generalization which we term "higher-order staircase codes" arises from the marriage of two distinct combinatorial objects: difference triangle sets and finite-geometric nets, which have typically been applied separately to code design. We illustrate one possible realization of these codes, obtaining powerful, high-rate, low-error-floor, and low-complexity coding schemes based on simple iterative syndrome-domain decoding of coupled Hamming component codes. We study some properties of difference triangle sets having minimum scope and sum-of-lengths, which correspond to memory-optimal higher-order staircase codes. |
| title | Higher-Order Staircase Codes: A Unified Generalization of High-Throughput Coding Techniques |
| topic | Information Theory |
| url | https://arxiv.org/abs/2410.16504 |