Parham Noorzad

On the power of cooperation: Can a little help a lot?

In this paper, we propose a new cooperation model for discrete memoryless multiple access channels. Unlike in prior cooperation models (e.g., conferencing encoders), where the transmitters cooperate directly, in this model the transmitters cooperate through a larger network. We show that under this indirect cooperation model, there exist channels for which the increase in sum-capacity resulting from cooperation is significantly larger than the rate shared by the transmitters to establish the cooperation. This result contrasts both with results on the benefit of cooperation under prior models and results in the network coding literature, where attempts to find examples in which similar small network modifications yield large capacity benefits have to date been unsuccessful.

Can negligible cooperation increase network reliability

In network cooperation strategies, nodes work together with the aim of increasing transmission rates or reliability. This paper demonstrates that enabling cooperation between the transmitters of a two-user multiple access channel via a cooperation facilitator that has access to both messages, always results in a network whose maximal- and average-error sum-capacities are the same-even when the information shared with the encoders is negligible. Thus, for a multiple access channel whose maximal- and average-error sum-capacities differ, the maximal-error sum-capacity is not continuous with respect to the output edge capacities of the facilitator. This shows that for some networks, sharing even a negligible number of bits per channel use with the encoders can yield a non-negligible benefit.

The unbounded benefit of encoder cooperation for the k-user MAC

Cooperation strategies that allow communication devices to work together can improve network capacity. This paper generalizes the “cooperation facilitator” (CF) model from the 2-user to the k-user multiple access channel (MAC), extending capacity bounds, characterizing all k-user MACs for which the sum-capacity gain of encoder cooperation exceeds the capacity cost that enables it, and demonstrating an infinite benefit-cost ratio in the limit of small cost.

On the cost and benefit of cooperation

In cooperative communication, network nodes that would otherwise act independently instead coordinate their efforts with the aim of improving communication performance. To better understand cooperation, we consider communication over a multiple access channel using a “cooperation facilitator”, a node that receives rate-limited message descriptions from the transmitters and sends rate-limited message descriptions back. This model includes the conferencing encoders model and a prior model from the current authors as special cases. We characterize a class of multiple access channels for which there is no gain in sum-capacity under current or prior cooperation models. We then show that for all other multiple access channels, the gain in sum-capacity can be far greater than the capacity of the cooperation facilitators output links. These channels violate the edge removal property. The Gaussian multiple access channel is an important special case for which we explicitly characterize the sum-rate cooperation gain.

Can Negligible Rate Increase Network Reliability

In network cooperation strategies, nodes work together with the aim of increasing transmission rates or reliability. This paper demonstrates that enabling cooperation between the transmitters of a two-user multiple access channel via a cooperation facilitator that has access to both messages results in a network whose maximal- and average-error capacity regions are the same; this benefit ensues even when the information received by each transmitter is negligible. From this result, it follows that if a multiple access channel with no transmitter cooperation has different maximal- and average-error sum-capacities, then the maximal-error sum-capacity of the network consisting of this channel and a cooperation facilitator is not continuous with respect to the output edge capacities of the facilitator. Thus, there exist networks where adding negligible rate yields a non-negligible benefit.

The benefit of encoder cooperation in the presence of state information

In many communication networks, the availability of channel state information at various nodes provides an opportunity for network nodes to work together, or “cooperate.” This work studies the benefit of cooperation in the multiple access channel with a cooperation facilitator, distributed state information at the encoders, and full state information available at the decoder. Under various causality constraints, sufficient conditions are obtained such that encoder cooperation through the facilitator results in a gain in sum-capacity that has infinite slope in the information rate shared with the encoders. This result extends the prior work of the authors on cooperation in networks where none of the nodes have access to state information.

The birthday problem and zero-error list codes

As an attempt to bridge the gap between classical information theory and the combinatorial world of zero-error information theory, this paper studies the performance of randomly generated codebooks over discrete memoryless channels under a zero-error constraint. This study allows the application of tools from one area to the other. Furthermore, it leads to an information-theoretic formulation of the birthday problem, which is concerned with the probability that in a given population, a fixed number of people have the same birthday. Due to the lack of a closed-form expression for this probability when the distribution of birthdays is not uniform, the resulting computation is not feasible in some applications; the information-theoretic formulation, however, can be analyzed for all distributions.