{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-optimal-recovery-threshold-of-coded","title":"On the Optimal Recovery Threshold of Coded Matrix Multiplication","arxiv_id":"1801.10292","date":"2018-01-31","proceeding":null,"authors":["Sanghamitra Dutta","Mohammad Fahim","Farzin Haddadpour","Haewon Jeong","Viveck Cadambe","Pulkit Grover"],"abstract":"We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent \"Polynomial code\" constructions in recovery threshold, i.e., the required number of successful workers. When $m$-th fraction of each matrix can be stored in each worker node, Polynomial codes require $m^2$ successful workers, while our MatDot codes only require $2m-1$ successful workers, albeit at a higher communication cost from each worker to the fusion node. We also provide a systematic construction of MatDot codes. Further, we propose \"PolyDot\" coding that interpolates between Polynomial codes and MatDot codes to trade off communication cost and recovery threshold. Finally, we demonstrate a coding technique for multiplying $n$ matrices ($n \\geq 3$) by applying MatDot and PolyDot coding ideas.","url_abs":"https://arxiv.org/abs/1801.10292v2","url_pdf":"https://arxiv.org/pdf/1801.10292v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-the-optimal-recovery-threshold-of-coded","repo_url":"https://github.com/nitishmital/distributed_storage_computing","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"on-the-optimal-recovery-threshold-of-coded","repo_url":"https://github.com/nitishmital/nitish","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"on-the-optimal-recovery-threshold-of-coded","repo_url":"https://github.com/nitishmital/phd_thesis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1801.10292","atlas_url":"https://app.syntology.ai/?focus=1801.10292","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}