2011/11/27 by Asaf Cohen, Cohen, Asaf, Shlomi Dolev +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cooperative Communication and Network Coding #Cryptography and Security (cs.CR) #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.CR #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1111.6244
23 pages, 5 figure
arxiv created 2011/11/27 · openalex publication_date 2011/11/27 · arxiv updated 2011/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a new family of fountain codes which overcome adversarial errors. That is, we consider the possibility that some portion of the arriving packets of a rateless erasure code are corrupted in an undetectable fashion. In practice, the corrupted packets may be attributed to a portion of the communication paths which are controlled by an adversary or to a portion of the sources that are malicious. The presented codes resemble and extend LT and Raptor codes. Yet, their benefits over existing coding schemes are manifold. First, to overcome the corrupted packets, our codes use information theoretic techniques, rather than cryptographic primitives. Thus, no secret channel between the senders and the receivers is required. Second, the encoders in the suggested scheme are oblivious to the strength of the adversary, yet perform as if its strength was known in advance. Third, the sparse structure of the codes facilitates efficient decoding. Finally, the codes easily fit a decentralized scenario with several sources, when no communication between the sources is allowed. We present both exhaustive as well as efficient decoding rules. Beyond the obvious use as a rateless codes, our codes have important applications in distributed computing.