16 research outputs found
Communication over an Arbitrarily Varying Channel under a State-Myopic Encoder
We study the problem of communication over a discrete arbitrarily varying
channel (AVC) when a noisy version of the state is known non-causally at the
encoder. The state is chosen by an adversary which knows the coding scheme. A
state-myopic encoder observes this state non-causally, though imperfectly,
through a noisy discrete memoryless channel (DMC). We first characterize the
capacity of this state-dependent channel when the encoder-decoder share
randomness unknown to the adversary, i.e., the randomized coding capacity.
Next, we show that when only the encoder is allowed to randomize, the capacity
remains unchanged when positive. Interesting and well-known special cases of
the state-myopic encoder model are also presented.Comment: 16 page
Generalized List Decoding
This paper concerns itself with the question of list decoding for general
adversarial channels, e.g., bit-flip () channels, erasure
channels, (-) channels, channels, real adder
channels, noisy typewriter channels, etc. We precisely characterize when
exponential-sized (or positive rate) -list decodable codes (where the
list size is a universal constant) exist for such channels. Our criterion
asserts that:
"For any given general adversarial channel, it is possible to construct
positive rate -list decodable codes if and only if the set of completely
positive tensors of order- with admissible marginals is not entirely
contained in the order- confusability set associated to the channel."
The sufficiency is shown via random code construction (combined with
expurgation or time-sharing). The necessity is shown by
1. extracting equicoupled subcodes (generalization of equidistant code) from
any large code sequence using hypergraph Ramsey's theorem, and
2. significantly extending the classic Plotkin bound in coding theory to list
decoding for general channels using duality between the completely positive
tensor cone and the copositive tensor cone. In the proof, we also obtain a new
fact regarding asymmetry of joint distributions, which be may of independent
interest.
Other results include
1. List decoding capacity with asymptotically large for general
adversarial channels;
2. A tight list size bound for most constant composition codes
(generalization of constant weight codes);
3. Rederivation and demystification of Blinovsky's [Bli86] characterization
of the list decoding Plotkin points (threshold at which large codes are
impossible);
4. Evaluation of general bounds ([WBBJ]) for unique decoding in the error
correction code setting
Dirty Paper Arbitrarily Varying Channel with a State-Aware Adversary
In this paper, we take an arbitrarily varying channel (AVC) approach to
examine the problem of writing on a dirty paper in the presence of an
adversary. We consider an additive white Gaussian noise (AWGN) channel with an
additive white Gaussian state, where the state is known non-causally to the
encoder and the adversary, but not the decoder. We determine the randomized
coding capacity of this AVC under the maximal probability of error criterion.
Interestingly, it is shown that the jamming adversary disregards the state
knowledge to choose a white Gaussian channel input which is independent of the
state
Effect of Jitter on the Settling Time of Mesochronous Clock Retiming Circuits
It is well known that timing jitter can degrade the bit error rate (BER) of
receivers that recover the clock from input data. However, timing jitter can
also result in an indefinite increase in the settling time of clock recovery
circuits, particularly in low swing mesochronous systems. Mesochronous clock
retiming circuits are required in repeaterless low swing on-chip interconnects.
We first discuss how timing jitter can result in a large increase in the
settling time of the clock recovery circuit. Next, the circuit is modelled as a
Markov chain with absorbing states. The mean time to absorption of the Markov
chain, which represents the mean settling time of the circuit, is determined.
The model is validated through behavioural simulations of the circuit, the
results of which match well with the model predictions. We consider circuits
with (i) data dependent jitter, (ii) random jitter, and (iii) combination of
both of them. We show that a mismatch between the strengths of up and down
corrections of the retiming can reduce the settling time. In particular, a 10%
mismatch can reduce the mean settling time by up to 40%. We leverage this fact
toward improving the settling time performance, and propose useful techniques
based on biased training sequences and mismatched charge pumps. We also present
a coarse+fine clock retiming circuit, which can operate in coarse first mode,
to reduce the settling time substantially. These fast settling retiming
circuits are verified with circuit simulations.Comment: 23 pages, 40 figure
Correlated Jamming in a Joint Source Channel Communication System
We study correlated jamming in joint source-channel communication systems. An
i.i.d. source is to be communicated over a memoryless channel in the presence
of a correlated jammer with non-causal knowledge of user transmission. This
user-jammer interaction is modeled as a zero sum game. A set of conditions on
the source and the channel is provided for the existence of a Nash equilibrium
for this game, where the user strategy is uncoded transmission and the jammer
strategy is i.i.d jamming. This generalizes a well-known example of uncoded
communication of a Gaussian sources over Gaussian channels with additive
jamming. Another example, of a Binary Symmetric source over a Binary Symmetric
channel with jamming, is provided as a validation of this result