We initiate the study of error correcting codes over the multi-party adversarial broadcast channel. Specifically, we consider the classic information dissemination problem where $n$ parties, each holding an input bit, wish to know each other's input. For this, they communicate in rounds, where, in each round, one designated party sends ... more >>>

We show how to convert any circuit of poly-logarithmic depth and polynomial size into a functionally equivalent circuit of polynomial size (and polynomial depth) that is resilient to adversarial short-circuit errors. Specifically, the resulting circuit computes the same function even if up to $\epsilon d$ gates on every root-to-leaf path ... more >>>

Kol and Raz [STOC 2013] showed how to simulate any alternating two-party communication protocol designed to work over the noiseless channel, by a protocol that works over a stochastic channel that corrupts each sent symbol with probability $\epsilon>0$ independently, with only a $1+\mathcal{O}(\sqrt{\H(\epsilon)})$ blowup to the communication. In particular, this ... more >>>

Single-hop radio networks (SHRN) are a well studied abstraction of communication over a wireless channel. In this model, in every round, each of the $n$ participating parties may decide to broadcast a message to all the others, potentially causing collisions. We consider the SHRN model in the presence of stochastic ... more >>>

In a celebrated result from the $60$'s, Berlekamp showed that feedback can be used to increase the maximum fraction of adversarial noise that can be tolerated by binary error correcting codes from $1/4$ to $1/3$. However, his result relies on the assumption that feedback is "continuous", i.e., after every utilization ... more >>>

Much of today's communication is carried out over large wireless systems with different input-output behaviors. In this work, we compare the power of central abstractions of wireless communication through the general notion of boolean symmetric $f$-channels: In every round of the $f$-channel, each of its $n$ parties decides to either ... more >>>

We study boolean constraint satisfaction problems (CSPs) $\mathrm{Max}\text{-}\mathrm{CSP}^f_n$ for all predicates $f: \{ 0, 1 \} ^k \to \{ 0, 1 \}$. In these problems, given an integer $v$ and a list of constraints over $n$ boolean variables, each obtained by applying $f$ to a sequence of literals, we wish ... more >>>

We consider the Max-Cut problem, asking how much space is needed by a streaming algorithm in order to estimate the value of the maximum cut in a graph. This problem has been extensively studied over the last decade, and we now have a near-optimal lower bound for one-pass streaming algorithms, ... more >>>

In this work, we design an interactive coding scheme that converts any two party interactive protocol $\Pi$ into another interactive protocol $\Pi'$, such that even if errors are introduced during the execution of $\Pi'$, the parties are able to determine what the outcome of running $\Pi$ would be in an ... more >>>

We give an $\widetilde{O}(\sqrt{n})$-space single-pass $0.483$-approximation streaming algorithm for estimating the maximum directed cut size (Max-DICUT) in a directed graph on $n$ vertices. This improves over an $O(\log n)$-space $4/9 < 0.45$ approximation algorithm due to Chou, Golovnev, Velusamy (FOCS 2020), which was known to be optimal for $o(\sqrt{n})$-space algorithms.

In the reliable transmission problem, a sender, Alice, wishes to transmit a bit-string x to a remote receiver, Bob, over a binary channel with adversarial noise. The solution to this problem is to encode x using an error correcting code. As it is long known that the distance of binary ... more >>>

We initiate a study of the streaming complexity of constraint satisfaction problems (CSPs) when the constraints arrive in a random order. We show that there exists a CSP, namely Max-DICUT, for which random ordering makes a provable difference. Whereas a $4/9 \approx 0.445$ approximation of DICUT requires $\Omega(\sqrt{n})$ space with ... more >>>

Given a Boolean circuit $C$, we wish to convert it to a circuit $C'$ that computes the same function as $C$ even if some of its gates suffer from adversarial short circuit errors, i.e., their output is replaced by the value of one of their inputs [KLM97]. Can we ... more >>>

Let $\Pi$ be a protocol over the $n$-party broadcast channel, where in each round, a pre-specified party broadcasts a symbol to all other parties. We wish to design a scheme that takes such a protocol $\Pi$ as input and outputs a noise resilient protocol $\Pi'$ that simulates $\Pi$ over the ... more >>>

We study the error resilience of the message exchange task: Two parties, each holding a private input, want to exchange their inputs. However, the channel connecting them is governed by an adversary that may corrupt a constant fraction of the transmissions. What is the maximum fraction of corruptions that still ... more >>>

Interactive error correcting codes are codes that encode a two party communication protocol to an error-resilient protocol that succeeds even if a constant fraction of the communicated symbols are adversarially corrupted, at the cost of increasing the communication by a constant factor. What is the largest fraction of corruptions that ... more >>>

We give an almost quadratic $n^{2-o(1)}$ lower bound on the space consumption of any $o(\sqrt{\log n})$-pass streaming algorithm solving the (directed) $s$-$t$ reachability problem. This means that any such algorithm must essentially store the entire graph. As corollaries, we obtain almost quadratic space lower bounds for additional fundamental problems, including ... more >>>

We study the $n$-party noisy broadcast channel with a constant fraction of malicious parties. Specifically, we assume that each non-malicious party holds an input bit, and communicates with the others in order to learn the input bits of all non-malicious parties. In each communication round, one of the parties broadcasts ... more >>>

The field of Interactive Coding studies how an interactive protocol can be made resilient to channel errors. Even though this field has received abundant attention since Schulman's seminal paper (FOCS 92), constructing interactive coding schemes that are both deterministic and efficient, and at the same time resilient to adversarial errors ... more >>>

Interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication. What is the maximum fraction of errors that such codes can protect against?

For the non-adaptive channel, where the parties must agree ... more >>>

We consider the celebrated radio network model for abstracting communication in wireless networks. In this model, in any round, each node in the network may broadcast a message to all its neighbors. However, a node is able to hear a message broadcast by a neighbor only if no collision occurred, ... more >>>

We study the effect of noise on the $n$-party beeping model. In this model, in every round, each party may decide to either `beep' or not. All parties hear a beep if and only if at least one party beeps. The beeping model is becoming increasingly popular, as it offers ... more >>>

A set of $n$ players, each holding a private input bit, communicate over a noisy broadcast channel. Their mutual goal is for all players to learn all inputs. At each round one of the players broadcasts a bit to all the other players, and the bit received by each player ... more >>>