{
  "annotation_id": "0183f876-0c14-4c8e-9d89-04c595e674cb",
  "date_created": "2026-02-17T05:53:24.216000Z",
  "date_modified": "2026-02-17T05:53:24.216000Z",
  "file_hash": "89ed32d0a12200a34b2d4113aad22b7f145690e345f700e713589fc028113e41",
  "private": false,
  "record": {
    "abstract": "We introduce the sum channel, a new channel model motivated by applications in distributed storage and DNA data storage. In the error-free case, it takes as input an $\\ell$-row binary matrix and outputs an $(\\ell+1)$-row matrix whose first $\\ell$ rows equal the input and whose last row is their parity (sum) row. We construct a two-deletion-correcting code with redundancy $2\\lceil\\log_2\\log_2 n\\rceil + O(\\ell^2)$ for $\\ell$-row inputs. When $\\ell=2$, we establish an upper bound of $\\lceil\\log_2\\log_2 n\\rceil + O(1)$, implying that our redundancy is optimal up to a factor of 2. We also present a code correcting a single substitution with $\\lceil \\log_2(\\ell+1)\\rceil$ redundant bits and prove that it is within one bit of optimality.",
    "arxiv_id": "2601.10256",
    "authors": [
      "Lyan Abboud",
      "Eitan Yaakobi"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Error-Correcting Codes for the Sum Channel",
    "url": "https://arxiv.org/abs/2601.10256",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f1b02c1c-181d-4b82-8765-dd12dab10182",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}