Zero-error list capacities of discrete memoryless channels

We define zero-error list capacities for discrete memoryless channels. We find lower bounds to, and a characterization of these capacities. As is usual for such zero-error problems in information theory, the characterization is not generally a single-letter one. Nonetheless, we exhibit a class of channels for which a single letter characterization exists. We also show how the computational cutoff rate relates to the capacities we have define

Exponential bounds for list size moments and error probability

We consider list decoding with a variable list size for discrete memoryless channels. We obtain simultaneous upper bounds on the error probability and the moments of list siz

On the universality of Burnashev's error exponent

We consider communication over a time-invariant discrete memoryless channel (DMC) with noiseless and instantaneous feedback. We assume that the transmitter and the receiver are not aware of the underlying channel, however, they know that it belongs to some specific family of DMCs. Recent results show that for certain families (e.g., binary-symmetric channels and Z channels) there exist coding schemes that universally achieve any rate below capacity while attaining Burnashev's error exponent. We show that this is not the case in general by deriving an upper bound to the universally achievable error exponent

The behavior of certain stochastic processes arising in window protocols

Window based network flow control protocols, such as TCP, modulate the number of unacknowledged packets the protocol is allowed to have outstanding. Such protocols change the size when they receive positive or negative acknowledgements, where the latter kind may be inferred from timeouts. Together with a communications channel that loses packets at random, such a protocol induces a stochastic process on the window size. We consider a broad class of window based protocols, and analyze various statistics of the induced stochastic process. We demonstrate that all these protocols can be treated analytically using the theory of semi-Markov processe

Optimal feedback schemes over unknown channels

Communication over unknown discrete memoryless channels with instantaneous and perfect feedback is considered. For a given set of channels we define a notion of optimal coding schemes in terms of achievable rate and error exponent, and prove the existence of such coding schemes for two families of channels

Kurtosis Constraints In Communication Over Fading Channels

The kurtosis of a signal is a quantitative measure of how `peaky' it is. In this paper we consider two scenarios of communication over fading channels with kurtosis constraints: in the first, we analyze a non-coherent Rayleigh fading channel where the input signal is required to satisfy a kurtosis constraint in addition to a power constraint. In the second, we find the `worst' fading process that satisfies a kurtosis constraint and has a given second moment, while the fading coefficients are assumed to be known at the receiver. In both cases the transmitter is assumed ignorant of the instantaneous fading realization. The technique that enables our analysis is based on bounding mutual information between random variables which satisfy kurtosis and second moment constraints; the bound is tight in the low second moment regime and can be extended to multi-antenna communications

The behavior of stochastic processes arising in window protocols

Window based network flow control protocols, such as TCP, modulate the number of unacknowledged packets the protocol is allowed to have outstanding. Such protocols change the window size when they receive positive or negative acknowledgments, where the latter kind may be inferred from timeouts. Together with a communications channel that loses packets at random, such a protocol induces a stochastic process on the window size. For a broad class of window based protocols, the induced stochastic process can be analyzed using the theory of semi-Markov processe

A feedback strategy for binary symmetric channels

Communication over unknown binary symmetric channels with instantaneous and perfect feedback is considered. We describe a universal scheme based on a decision feedback strategy

Capacity and mutual information of wideband multipath fading channels

We investigate the capacity and mutual information of a broadband fading channel consisting of a finite number of time-varying paths. We show that the capacity of the channel in the wideband limit is the same as that of a wideband Gaussian channel with the same average received power. However, the input signals needed to achieve the capacity must be “peaky” in time or frequency. In particular, we show that if white-like signals are used instead (as is common in spread-spectrum systems), the mutual information is inversely proportional to the number of resolvable paths L˜ with energy spread out, and in fact approaches 0 as the number of paths gets large. This is true even when the paths are assumed to be tracked perfectly at the receiver. A critical parameter L˜crit is defined in terms of system parameters to delineate the threshold on L over which such overspreading phenomenon occurs

Measurement of time--varying Multiple--Input Multiple--Output Channels

We derive a criterion on the measurability / identifiability of Multiple--Input Multiple--Output (MIMO) channels based on the size of the so-called spreading support of its subchannels. Novel MIMO transmission techniques provide high-capacity communication channels in time-varying environments and exact knowledge of the transmission channel operator is of key importance when trying to transmit information at a rate close to channel capacity