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Technical Program

Paper Detail

Paper IDD3-S7-T2.2
Paper Title Tight List-Sizes for Oblivious AVCs under Constraints
Authors Yihan Zhang, Technion - Israel Institute of Technology, Israel; Sidharth Jaggi, University of Bristol, United Kingdom; Amitalok J. Budkuley, Indian Institute of Technology Kharagpur, India
Session D3-S7-T2: Topics in Coding III
Chaired Session: Thursday, 15 July, 00:00 - 00:20
Engagement Session: Thursday, 15 July, 00:20 - 00:40
Abstract We study list-decoding over adversarial channels governed by oblivious adversaries (a.k.a. oblivious Arbitrarily Varying Channels (AVCs)). This type of adversaries aims to maliciously corrupt the communication without knowing the actual transmission from the sender. For any oblivious AVCs potentially with constraints on the sender's transmitted sequence and the adversary's noise sequence, we determine the exact value of the minimum list-size that can support a reliable communication at positive rate. This generalizes a classical result by Hughes (IEEE Transactions on Information Theory, 1997) and answers an open question posed by Sarwate and Gastpar (IEEE Transactions on Information Theory, 2012). A lower bound on the list-decoding capacity (whenever positive) is presented. Under a certain combinatorial conjecture, we also prove a matching upper bound. En route to a tight characterization of the list-decoding capacity, we propose a method for subcode construction towards the resolution of the combinatorial conjecture.