Arbitrarily varying multiple access channels with conferencing encoders: List decoding and finite coordination resources

Abstract

Communication over channels that may vary in an arbitrary and unknown manner from channel use to channel use is studied. Such channels fall in the framework of arbitrarily varying channels (AVCs), for which it has been shown that the classical deterministic approaches with pre-specified encoder and decoder fail if the AVC is symmetrizable. However, more sophisticated strategies such as common randomness (CR) assisted codes or list decoding are capable to resolve the ambiguity induced by symmetrizable AVCs. AVCs further serve as the indispensable basis for modeling adversarial attacks such as jamming in information theoretic security related communication problems. In this paper, we study the arbitrarily varying multiple access channel (AVMAC) with conferencing encoders, which models the communication scenario with two cooperating transmitters and one receiver. This can be motivated for example by cooperating base stations or access points in future systems. The capacity region of the AVMAC with conferencing encoders is established and it is shown that list decoding allows for reliable communication also for symmetrizable AVMACs. The list capacity region equals the CR-assisted capacity region for large enough list size. Finally, for fixed probability of decoding error the amount of resources, i.e., CR or list size, is quantified and shown to be finite.

The secrecy capacity of the arbitrarily varying wiretap channel under list decoding

“…List codes are a special class of uncorrelated codes, in which the decoder outputs a list of L possible messages, instead of deciding on exactly one message. Such codes have been used for the AVC without secrecy constraints to overcome the problem of uncorrelated codes with symmetrizability and the need of correlated random codes to a shared common randomness [4,16,22,6]. We start by presenting the following definition.…”