Data Stream Algorithms for Codeword Testing
Atri Rudra, Steve Uurtamo

TL;DR
This paper develops efficient one-pass data stream algorithms for local and tolerant testing of codes, including Reed-Solomon codes, with applications in storage and property testing, achieving near-optimal space complexity.
Contribution
It introduces novel one-pass, poly-log space algorithms for error detection and tolerant testing of asymptotically good codes, including Reed-Solomon and expander codes.
Findings
Existence of one-pass, log-space algorithms for error detection in good codes.
An $O(e\, ext{log}^2 n)$-space algorithm for Reed-Solomon codes distinguishing error levels.
Space and error bounds are nearly optimal, with only logarithmic improvements possible.
Abstract
Motivated by applications in storage systems and property testing, we study data stream algorithms for local testing and tolerant testing of codes. Ideally, we would like to know whether there exist asymptotically good codes that can be local/tolerant tested with one-pass, poly-log space data stream algorithms. We show that for the error detection problem (and hence, the local testing problem), there exists a one-pass, log-space data stream algorithm for a broad class of asymptotically good codes, including the Reed-Solomon (RS) code and expander codes. In our technically more involved result, we give a one-pass, -space algorithm for RS (and related) codes with dimension and block length that can distinguish between the cases when the Hamming distance between the received word and the code is at most and at least for some absolute constant .…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Data Storage Technologies · Cryptography and Data Security · DNA and Biological Computing
