Vinod M. Prabhakaran

We study communication with consensus over a broadcast channel—the receivers reliably decode the sender’s message when the sender is honest, and their decoder outputs agree even if the sender acts maliciously. We characterize the broadcast channels which permit this Byzantine consensus and determine their capacity. We show that communication with consensus is possible only when the broadcast channel has embedded in it a natural “common channel” whose output both receivers can unambiguously determine from their own channel outputs. Interestingly, in general, the consensus capacity may be larger than the point-to-point capacity of the common channel, i.e., while decoding, the receivers may make use of parts of their output signals on which they may not have consensus provided there are some parts (namely, the common channel output) on which they can agree.

We study a distributed computation problem in the presence of Byzantine workers where a central node wishes to solve a task that is divided into independent sub-tasks, each of which needs to be solved correctly. The distributed computation is achieved by allocating the sub-task computation across workers with replication, as well as solving a small number of sub-tasks locally, which we wish to minimize due to it being expensive. For a general balanced job allocation, we propose a protocol that successfully solves for all sub-tasks using an optimal number of local computations under no communication constraints. Closed-form performance results are presented for cyclic allocations. Furthermore, we propose a modification to this protocol to improve communication efficiency without compromising on the amount of local computation.

We study the binary hypothesis testing problem where an adversary may potentially corrupt a fraction of the samples. The detector is, however, permitted to abstain from making a decision if (and only if) the adversary is present. We consider a few natural "contamination models" and characterize for them the trade-off between the error exponents of the four types of errors -- errors of deciding in favour of the incorrect hypothesis when the adversary is present and errors of abstaining or deciding in favour of the wrong hypothesis when the adversary is absent, under the two hypotheses.

We introduce the problem of determining the identity of a byzantine user (internal adversary) in a communication system. We consider a two-user discrete memoryless multiple access channel where either user may deviate from the prescribed behaviour. Since small deviations may be indistinguishable from the effects of channel noise, it might be overly restrictive to attempt to detect all deviations. In our formulation, we only require detecting deviations which impede the decoding of the non-deviating user’s message. When neither user deviates, correct decoding is required. When one user deviates, the decoder must either output a pair of messages of which the message of the non-deviating user is correct or identify the deviating user. The users and the receiver do not share any randomness. The results include a characterization of the set of channels where communication is feasible, and an inner and outer bound on the capacity region. We also show that whenever the rate region has non-empty interior, the capacity region is same as the capacity region under randomized encoding, where each user shares independent randomness with the receiver. We also give an outer bound for this randomized coding capacity region.

We study the problem of synthesising a two-user broadcast channel using a common message, where each output terminal shares an independent source of randomness with the input terminal. This generalises two problems studied in the literature (Cuff, IEEE Trans. Inform. Theory, 2013; Kurri et.al., IEEE Trans. Inform. Theory, 2021). We give an inner bound on the tradeoff region between the rates of communication and shared randomness, and a lower bound on the minimum communication rate. Although the bounds presented here are not tight in general, they are tight for some special cases, including the aforementioned problems.

We study communication over a Multiple Access Channel (MAC) where users can possibly be adversarial. The receiver is unaware of the identity of the adversarial users (if any). When all users are non-adversarial, we want their messages to be decoded reliably. When a user behaves adversarially, we require that the honest users’ messages be decoded reliably. An adversarial user can mount an attack by sending any input into the channel rather than following the protocol. It turns out that the 2-user MAC capacity region follows from the point-to-point Arbitrarily Varying Channel (AVC) capacity. For the 3-user MAC in which at most one user may be malicious, we characterize the capacity region for deterministic codes and randomized codes (where each user shares an independent random secret key with the receiver). These results are then generalized for the k -user MAC where the adversary may control all users in one out of a collection of given subsets.