arXiv subjects
Publications and source records attributed to M. V. Burnashev.
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper bounds for that function are derived.
Minimax detection of Gaussian stochastic sequences (signals) with unknown covariance matrices is studied. For a fixed false alarm probability (1-st kind error probability), the performance of the minimax detection is being characterized by the best exponential decay rate of the miss probability (2-nd kind error probability) as the length of the observation interval tends to infinity. Our goal is to find the largest set of covariance matrices such that the minimax robust testing of this set (composite hypothesis) can be replaced with testing of only one specific covariance matrix (simple hypothesis) without any loss in detection characteristics. In this paper, we completely describe this maximal set of covariance matrices. Some corollaries address minimax detection of the Gaussian stochastic signals embedded in the White Gaussian noise and detection of the Gaussian stationary signals.
For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also feedback channel with independent additive Gaussian noise, and the transmitter observes without delay all outputs of the forward channel via that feedback channel. Transmission of nonexponential number of messages is considered and the achievable decoding error exponent for such a combination of channels is investigated. It is shown that for any finite noise in the feedback channel the achievable error exponent is better than similar error exponent of the no-feedback channel. Method of transmission/decoding used in the paper strengthens the earlier method used by authors for BSC. In particular, for small feedback noise, it allows to get the gain of 23.6% (instead of 14.3% earlier for BSC).
For information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that feedback channel. The transmission of an exponential number of messages (i.e. the transmission rate is positive) is considered. The achievable decoding error exponent for such a combination of channels is investigated. It is shown that if the crossover probability of the feedback channel is less than a certain positive value, then the achievable error exponent is better than the decoding error exponent of the channel without feedback.
The reliability function gives the rate of exponential convergence to zero of the error probability in a communication channel. In this paper bounds for the reliability function of a quantum pure state channel are given, reminiscent of the corresponding classical bounds. This in particular suggests an alternative proof of the coding theorem for quantum noiseless channel, which would make no use of the notion of typical subspace. Example of binary quantum channel is considered in some detail.