{
  "annotation_id": "68d91c69-cf35-4644-93e4-509975235369",
  "date_created": "2026-02-17T05:53:24.270000Z",
  "date_modified": "2026-02-17T05:53:24.270000Z",
  "file_hash": "00e2da36b19b1724a11fa440e94132a67721537949eed44d002384c114fc3f5b",
  "private": false,
  "record": {
    "abstract": "The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication setting in which a sender transmits a codeword and the receiver observes K independent noisy versions of this codeword. In this work, we study the problem of efficient reconstruction when each of the $K$ outputs is corrupted by a $q$-ary discrete memoryless symmetric (DMS) substitution channel with substitution probability $p$. Focusing on Reed-Solomon (RS) codes, we adapt the Koetter-Vardy soft-decision decoding algorithm to obtain an efficient reconstruction algorithm. For sufficiently large blocklength and alphabet size, we derive an explicit rate threshold, depending only on $(p, K)$, such that the transmitted codeword can be reconstructed with arbitrarily small probability of error whenever the code rate $R$ lies below this threshold.",
    "arxiv_id": "2601.09947",
    "authors": [
      "Shubhransh Singhvi",
      "Han Mao Kiah",
      "Eitan Yaakobi"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Reconstructing Reed-Solomon Codes from Multiple Noisy Channel Outputs",
    "url": "https://arxiv.org/abs/2601.09947",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2376c148-9a24-46a8-b7e0-8a55bb3ac957",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}