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 ($\textsf{XOR}$) channels, erasure channels, $\textsf{AND}$ ($Z$-) channels, $\textsf{OR}$ channels, real adder channels, noisy typewriter channels, etc. We precisely characterize when exponential-sized (or positive rate) $(L-1)$-list decodable codes (where the list size $L$ 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 $(L-1)$-list decodable codes if and only if the set of completely positive tensors of order-$L$ with admissible marginals is not entirely contained in the order-$L$ 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 $L$ 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