Trace Reconstruction of First-Order Reed-Muller Codewords Using Run Statistics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915597907918848 |
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| author | Rathore, Shiv Pratap Singh Kashyap, Navin |
| author_facet | Rathore, Shiv Pratap Singh Kashyap, Navin |
| contents | In this paper, we derive an expression for the expected number of runs in a trace of a binary sequence $x \in \{0,1\}^n$ obtained by passing $x$ through a deletion channel that independently deletes each bit with probability $q$. We use this expression to show that if $x$ is a codeword of a first-order Reed-Muller code, and the deletion probability $q$ is 1/2, then $x$ can be reconstructed, with high probability, from $\tilde{O}(n^2)$ many of its traces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trace Reconstruction of First-Order Reed-Muller Codewords Using Run Statistics Rathore, Shiv Pratap Singh Kashyap, Navin Information Theory Probability In this paper, we derive an expression for the expected number of runs in a trace of a binary sequence $x \in \{0,1\}^n$ obtained by passing $x$ through a deletion channel that independently deletes each bit with probability $q$. We use this expression to show that if $x$ is a codeword of a first-order Reed-Muller code, and the deletion probability $q$ is 1/2, then $x$ can be reconstructed, with high probability, from $\tilde{O}(n^2)$ many of its traces. |
| title | Trace Reconstruction of First-Order Reed-Muller Codewords Using Run Statistics |
| topic | Information Theory Probability |
| url | https://arxiv.org/abs/2501.11393 |