8 research outputs found
The benefit of a 1-bit jump-start, and the necessity of stochastic encoding, in jamming channels
We consider the problem of communicating a message in the presence of a
malicious jamming adversary (Calvin), who can erase an arbitrary set of up to
bits, out of transmitted bits . The capacity of such
a channel when Calvin is exactly causal, i.e. Calvin's decision of whether or
not to erase bit depends on his observations was
recently characterized to be . In this work we show two (perhaps)
surprising phenomena. Firstly, we demonstrate via a novel code construction
that if Calvin is delayed by even a single bit, i.e. Calvin's decision of
whether or not to erase bit depends only on (and
is independent of the "current bit" ) then the capacity increases to
when the encoder is allowed to be stochastic. Secondly, we show via a novel
jamming strategy for Calvin that, in the single-bit-delay setting, if the
encoding is deterministic (i.e. the transmitted codeword is a deterministic
function of the message ) then no rate asymptotically larger than is
possible with vanishing probability of error, hence stochastic encoding (using
private randomness at the encoder) is essential to achieve the capacity of
against a one-bit-delayed Calvin.Comment: 21 pages, 4 figures, extended draft of submission to ISIT 201
Upper Bounds on the Capacity of Binary Channels with Causal Adversaries
In this work we consider the communication of information in the presence of
a causal adversarial jammer. In the setting under study, a sender wishes to
communicate a message to a receiver by transmitting a codeword
bit-by-bit over a communication channel. The sender and the receiver do not
share common randomness. The adversarial jammer can view the transmitted bits
one at a time, and can change up to a -fraction of them. However, the
decisions of the jammer must be made in a causal manner. Namely, for each bit
the jammer's decision on whether to corrupt it or not must depend only on
for . This is in contrast to the "classical" adversarial
jamming situations in which the jammer has no knowledge of , or
knows completely. In this work, we present upper bounds (that
hold under both the average and maximal probability of error criteria) on the
capacity which hold for both deterministic and stochastic encoding schemes.Comment: To appear in the IEEE Transactions on Information Theory; shortened
version appeared at ISIT 201
Coding against a Limited-view Adversary: The Effect of Causality and Feedback
We consider the problem of communication over a multi-path network in the
presence of a causal adversary. The limited-view causal adversary is able to
eavesdrop on a subset of links and also jam on a potentially overlapping subset
of links based on the current and past information. To ensure that the
communication takes place reliably and secretly, resilient network codes with
necessary redundancy are needed. We study two adversarial models - additive and
overwrite jamming and we optionally assume passive feedback from decoder to
encoder, i.e., the encoder sees everything that the decoder sees. The problem
assumes transmissions are in the large alphabet regime. For both jamming
models, we find the capacity under four scenarios - reliability without
feedback, reliability and secrecy without feedback, reliability with passive
feedback, reliability and secrecy with passive feedback. We observe that, in
comparison to the non-causal setting, the capacity with a causal adversary is
strictly increased for a wide variety of parameter settings and present our
intuition through several examples.Comment: 15 page
The Capacity of Online (Causal) -ary Error-Erasure Channels
In the -ary online (or "causal") channel coding model, a sender wishes to
communicate a message to a receiver by transmitting a codeword symbol by symbol via a channel
limited to at most errors and/or erasures. The channel is
"online" in the sense that at the th step of communication the channel
decides whether to corrupt the th symbol or not based on its view so far,
i.e., its decision depends only on the transmitted symbols .
This is in contrast to the classical adversarial channel in which the
corruption is chosen by a channel that has a full knowledge on the sent
codeword .
In this work we study the capacity of -ary online channels for a combined
corruption model, in which the channel may impose at most {\em errors} and
at most {\em erasures} on the transmitted codeword. The online
channel (in both the error and erasure case) has seen a number of recent
studies which present both upper and lower bounds on its capacity. In this
work, we give a full characterization of the capacity as a function of ,
and .Comment: This is a new version of the binary case, which can be found at
arXiv:1412.637
A characterization of the capacity of online (causal) binary channels
In the binary online (or "causal") channel coding model, a sender wishes to
communicate a message to a receiver by transmitting a codeword bit by bit via a channel limited to at most
corruptions. The channel is "online" in the sense that at the th step
of communication the channel decides whether to corrupt the th bit or not
based on its view so far, i.e., its decision depends only on the transmitted
bits . This is in contrast to the classical adversarial
channel in which the error is chosen by a channel that has a full knowledge on
the sent codeword .
In this work we study the capacity of binary online channels for two
corruption models: the {\em bit-flip} model in which the channel may flip at
most of the bits of the transmitted codeword, and the {\em erasure} model
in which the channel may erase at most bits of the transmitted codeword.
Specifically, for both error models we give a full characterization of the
capacity as a function of .
The online channel (in both the bit-flip and erasure case) has seen a number
of recent studies which present both upper and lower bounds on its capacity. In
this work, we present and analyze a coding scheme that improves on the
previously suggested lower bounds and matches the previously suggested upper
bounds thus implying a tight characterization
Codes Against Online Adversaries: Large Alphabets
In this paper, we consider the communication of information in the presence of an online adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x = (x(1), ... , x(n)) symbol-by-symbol over a communication channel. The adversarial jammer can view the transmitted symbols x(i) one at a time and can change up to a p-fraction of them. However, for each symbol x(i), the jammer's decision on whether to corrupt it or not (and on how to change it) must depend only on x(j) for j <= i. This is in contrast to the "classical" adversarial jammer which may base its decisions on its complete knowledge of x. More generally, for a delay parameter delta is an element of (0, 1), we study the scenario in which the jammer's decision on the corruption of x(i) must depend solely on x(j) for j <= i - delta n. In this study, the transmitted symbols are assumed to be over a sufficiently large field F. The sender and receiver do not share resources such as common randomness (though the sender is allowed to use stochastic encoding). We present a tight characterization of the amount of information one can transmit in both the 0-delay and, more generally, the delta-delay online setting. We show that for 0-delay adversaries, the achievable rate asymptotically equals that of the classical adversarial model. For positive values of delta, we consider two types of jamming: additive and overwrite. We also extend our results to a jam-or-listen online model, where the online adversary can either jam a symbol or eavesdrop on it. We present computationally efficient achievability schemes even against computationally unrestricted jammers