Sidharth Jaggi

Polynomial time algorithms for multicast network code construction

The famous max-flow min-cut theorem states that a source node s can send information through a network (V, E) to a sink node t at a rate determined by the min-cut separating s and t. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re-encode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures.

Resilient network coding in the presence of Byzantine adversaries

Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces the first distributed polynomial-time rate-optimal network codes that work in the presence of Byzantine nodes. We present algorithms that target adversaries with different attacking capabilities. When the adversary can eavesdrop on all links and jam zO links , our first algorithm achieves a rate of C - 2zO, where C is the network capacity. In contrast, when the adversary has limited snooping capabilities, we provide algorithms that achieve the higher rate of C - zO. Our algorithms attain the optimal rate given the strength of the adversary. They are information-theoretically secure. They operate in a distributed manner, assume no knowledge of the topology, and can be designed and implemented in polynomial-time. Furthermore, only the source and destination need to be modified; non-malicious nodes inside the network are oblivious to the presence of adversaries and implement a classical distributed network code. Finally, our algorithms work over wired and wireless networks.

Resilient Network Coding in the Presence of Byzantine Adversaries

Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces the first distributed polynomial-time rate-optimal network codes that work in the presence of Byzantine nodes. We present algorithms that target adversaries with different attacking capabilities. When the adversary can eavesdrop on all links and jam zO links , our first algorithm achieves a rate of C - 2zO, where C is the network capacity. In contrast, when the adversary has limited snooping capabilities, we provide algorithms that achieve the higher rate of C - zO. Our algorithms attain the optimal rate given the strength of the adversary. They are information-theoretically secure. They operate in a distributed manner, assume no knowledge of the topology, and can be designed and implemented in polynomial-time. Furthermore, only the source and destination need to be modified; non-malicious nodes inside the network are oblivious to the presence of adversaries and implement a classical distributed network code. Finally, our algorithms work over wired and wireless networks.

RIPPLE Authentication for Network Coding

By allowing routers to randomly mix the information content in packets before forwarding them, network coding can maximize network throughput in a distributed manner with low complexity. However, such mixing also renders the transmission vulnerable to {\em pollution attacks}, where a malicious node injects corrupted packets into the information flow. In a worst case scenario, a single corrupted packet can end up corrupting {\it all} the information reaching a destination. In this paper, we propose RIPPLE, a symmetric key based in-network scheme for network coding authentication. RIPPLE allows a node to efficiently detect corrupted packets and encode only the authenticated ones. Despite using symmetric key based homomorphic Message Authentication Code (MAC) algorithms, RIPPLE achieves asymmetry by delayed disclosure of the MAC keys. Our work is the first symmetric key based solution to allow arbitrary collusion among adversaries. It is also the first to consider {\em tag pollution attacks}, where a single corrupted MAC tag can cause numerous packets to fail authentication farther down the stream, effectively emulating a successful pollution attack.

Low complexity algebraic multicast network codes

We present a low complexity algorithm for designing algebraic codes that achieve the info mation theoretic capacity for the multicast problem on directed acyclic networks. These codes operate over field sizes which are significantly smaller than those previously known, leading to significantly lower design and implementation complexity, and network link usage. These codes can be extended for networks with cycles and delays, and for robustness properties.

Correction of adversarial errors in networks

We design codes to transmit information over a network, some subset of which is controlled by a malicious adversary. The computationally unbounded, hidden adversary knows the message to be transmitted, and can observe and change information over the part of the network being controlled. The network nodes do not share resources such as shared randomness or a private key. We first consider a unicast problem in a network with |epsiv parallel, unit-capacity, directed edges. The rate-region has two parts. If the adversary controls a fraction p < 0.5 of the |epsiv edges, the maximal throughput equals (1 - p) |epsiv|. We describe low-complexity codes that achieve this rate-region. We then extend these results to investigate more general multicast problems in directed, acyclic networks

Reliable deniable communication: Hiding messages in noise

Alice may wish to reliably send a message to Bob over a binary symmetric channel (BSC) while ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie observes a “significantly noisier” transmission than Bob does, he should be unable to estimate even whether Alice is transmitting or not. Even when Alices (potential) communication scheme is publicly known to Willie (with no common randomness between Alice and Bob), we prove that over n channel uses Alice can transmit a message of length O(√n) bits to Bob, deniably from Willie. We also prove information-theoretically order-optimality of our results.

Non-adaptive group testing: Explicit bounds and novel algorithms

We present computationally efficient and provably correct algorithms with near-optimal sample-complexity for noisy non-adaptive group testing. Group testing involves grouping arbitrary subsets of items into pools. Each pool is then tested to identify the defective items, which are usually assumed to be sparsely distributed. We consider random non-adaptive pooling where pools are selected randomly and independently of the test outcomes. Our noisy scenario accounts for both false negatives and false positives for the test outcomes. Inspired by compressive sensing algorithms we introduce four novel computationally efficient decoding algorithms for group testing, CBP via Linear Programming (CBP-LP), NCBP-LP (Noisy CBP-LP), and the two related algorithms NCBP-SLP+ and NCBP-SLP- (“Simple” NCBP-LP). The first of these algorithms deals with the noiseless measurement scenario, and the next three with the noisy measurement scenario. We derive explicit sample-complexity bounds - with all constants made explicit - for these algorithms as a function of the desired error probability; the noise parameters; the number of items; and the size of the defective set (or an upper bound on it). We show that the sample-complexities of our algorithms are near-optimal with respect to known information-theoretic bounds.

Network codes resilient to jamming and eavesdropping

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time distributed network codes that are information-theoretically rate-optimal for this scenario, improving on the rates achievable in prior work by Ngai Our main contribution shows that as long as the sum of the number of links the adversary can jam (denoted by ZO) and the number of links he can eavesdrop on (denoted by ZI) is less than the network capacity (denoted by C) (i.e., ), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this scheme as a module to design codes that allow communication at the source rate of C- ZO when there are no security requirements, and codes that allow communication at the source rate of C- ZO- ZI while keeping the communicated message provably secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. We also prove that the rate-region obtained is information-theoretically optimal. In proving our results, we correct an error in prior work by a subset of the authors in this paper.

Concatenated Polar codes

Polar codes have attracted much recent attention as one of the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that for current constructions the probability of error decays sub-exponentially in the block-length (more detailed designs improve the probability of error at the cost of significantly increased computational complexity. In this work we show how the the classical idea of code concatenation - using “short” polar codes as inner codes and a “high-rate” Reed-Solomon code as the outer code - results in substantially improved performance. In particular, code concatenation with a careful choice of parameters boosts the rate of decay of the probability of error to almost exponential in the block-length with essentially no loss in computational complexity. We demonstrate such performance improvements for three sets of information-theoretic problems - a classical point-to-point channel coding problem, a class of multiple-input multiple output channel coding problems, and some network source coding problems.