Marat V. Burnashev

On the zero-rate error exponent for a BSC with noisy feedback

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 outputs of the forward channel via the feedback channel. Transmission of non-exponentially many messages is considered (i.e., the transmission rate is zero). The achievable decoding error exponent for this 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 similar error exponent of the no-feedback channel. The described transmission method and the corresponding lower bound for the error exponent can be improved, as well as extended to positive transmission rates.

Differential preamble detection in packet-based wireless networks

A novel hypothesis-based preamble detection method for uncoordinated, high-density packet-based communication over an additive white Gaussian noise channel is proposed and analyzed. Received samples are observed over a window of length equal to that of the preamble and a metric is computed for each sample shift of the window. A metric exceeding a noise dependent pre-computed threshold flags the presence of a preamble. The preamble sequence consists of concatenated sections of spreading sequences whose length is at most the coherence time of the channel. These sections are then differentially combined. A differential correlation-based detection is employed to locate the boundaries of the preamble. A theoretical framework is developed to provide exact analytical solutions for missing and falsely detecting a preamble using matrix analysis of quadratic Gaussian statistics. Furthermore, the robustness of the proposed methodology in a two path channel is studied. The effects of frequency and timing offsets on the system performance is evaluated. Simulation results are presented to validate the analytical expressions. Additionally, a performance comparison of the proposed differential detection scheme with that of a noncoherent square-law detector is presented.

Error exponents for the two-user Poisson multiple-access channel

The error exponent of the two-user Poisson multiple-access channel under peak and average power constraints, but unlimited in bandwidth, is considered. First, a random coding lower bound on the error exponent is obtained, and an extension of Wyners (1988) single-user codes is shown to be exponentially optimum for this case as well. Second, the sphere-packing bounding technique suggested by Burnashev and Kutoyants (see Probl. Inform. Transm., vol.35, no.2, p.3-22, 1999) is generalized to the case at hand and an upper bound on the error exponent, which coincides with the lower bound, is derived. Thus, this channel joins its single-user partner as one of very few for which the reliability function is known.

On the probability of error in linear multiuser detection

The problem of determining the bit-error probability in linear multiuser detection analytically is considered. A number of upper and lower bounds are developed, some of which are very tight, and issues of asymptotic behavior, optimality, and Gaussian approximation are explored. Several special cases, including those of equi-energy and equi-correlated signals, are treated in some detail.

On the reliability function for a BSC with noisy feedback

A binary symmetric channel is used for information transmission. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all outputs of the forward channel via the feedback channel. Transmission of an exponential number of messages is considered (i.e., the transmission rate is positive). The achievable decoding error exponent for this combination of channels is studied. 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 a channel without feedback.

Sharpening of an Upper Bound for the Reliability Function of a Binary Symmetric Channel

An upper bound for the reliability function of a binary symmetric channel is improved.

Noisy feedback improves the BSC reliability function

For the 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 overall transmission time is fixed. The transmission of a 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 best known lower bound for the error exponent of the no-feedback channel.

A new lower bound for the a-mean error of parameter transmission over the white Gaussian channel

Upper and lower bounds are derived on the exponential behavior of the \alpha -mean error for parameter transmission over the additive white Gaussian noise channel. The method of proving the lower bound may be used in many information theory and mathematical statistics problems.

Two-stage detection of partitioned random CDMA

Random Code Division Multiple Access (CDMA) with low complexity two-stage joint detection/decoding is considered. A sequence partitioning approach is used for modulation, where every spreading sequence is divided into M sections (partitions) which are interleaved prior to transmission. This setup, called partitioned CDMA, can be understood as a generalisation of (chip) interleave division multiple access (IDMA). An analysis of a low-complexity iterative cancellation receiver is presented for arbitrary received power distributions. It is shown that for equal rate and equal power users the asymptotic performance of partitioned CDMA is equal to the performance of CDMA with optimal a posteriori probability (APP) detection for system loads K/N < 1.49. Effects of asynchronous signal transmission are quantified for standard pulse shaping filters and it is shown that the signal-to-noise ratios achievable in an asynchronous system are improved with respect to fully synchronous transmission. The effect of unequal received powers is examined and considerable gains in performance are obtained by judicious choices of power distributions. For certain power distribution, partitioned CDMA with iterative detection can achieve arbitrary system loads, that is detection is no longer fundamentally interference limited. The practical near-far resistance of the proposed system is illustrated using an example of a receiver with a circular receive footprint and uniformly distributed transmitters (single cell system). Copyright

On BSC, noisy feedback and three messages

A binary symmetric channel is considered. A transmitter observes without delay all the outputs of the forward channel via a noisy binary symmetric channel (a feedback). For illustrative purposes, we consider the transmission of only three messages. The best achievable 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 some positive level, then the achievable error exponent is better than the similar error exponent of the no-feedback channel. In particular, it is the case if the crossover probability of the feedback channel is eight (or more) times smaller than the crossover probability of the forward channel. The transmission strategy described in this talk and the corresponding lower bound for the error exponent can be strengthened and extended to the positive transmission rates as well.