1,403 research outputs found
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
On AVCs with Quadratic Constraints
In this work we study an Arbitrarily Varying Channel (AVC) with quadratic
power constraints on the transmitter and a so-called "oblivious" jammer (along
with additional AWGN) under a maximum probability of error criterion, and no
private randomness between the transmitter and the receiver. This is in
contrast to similar AVC models under the average probability of error criterion
considered in [1], and models wherein common randomness is allowed [2] -- these
distinctions are important in some communication scenarios outlined below.
We consider the regime where the jammer's power constraint is smaller than
the transmitter's power constraint (in the other regime it is known no positive
rate is possible). For this regime we show the existence of stochastic codes
(with no common randomness between the transmitter and receiver) that enables
reliable communication at the same rate as when the jammer is replaced with
AWGN with the same power constraint. This matches known information-theoretic
outer bounds. In addition to being a stronger result than that in [1] (enabling
recovery of the results therein), our proof techniques are also somewhat more
direct, and hence may be of independent interest.Comment: A shorter version of this work will be send to ISIT13, Istanbul. 8
pages, 3 figure
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