Lan V. Truong

Error exponent of the common-message broadcast channel with variable-length feedback

We derive upper and lower bounds on the reliability function for the discrete memoryless broadcast channel with common message and variable-length feedback. We show that the bounds are tight when the broadcast channel is stochastically degraded. We adapt and supplement new ideas to Yamamoto and Itohs two-phase coding scheme for the direct part and Burnashevs proof technique for the converse part.

On the Gaussian MAC with stop-feedback

We characterize the information-theoretic limits of the Gaussian multiple access channel (MAC) when variable-length stop-feedback is available at the encoder and a non-vanishing error probability is permitted. Due to the continuous nature of the channel and the presence of expected power constraints, we need to develop new achievability and converse techniques. Due to the multi-terminal nature of the channel model, we are faced with the need to bound the asymptotic behavior of the expected value of the maximum of several stopping times. We do so by leveraging tools from renewal theory developed by Gut (1974) and Lai and Siegmund (1979).

On second-order asymptotics of AWGN channels with feedback under the expected power constraint

In this paper, we analyze the asymptotic expansion for additive white Gaussian noise (AWGN) channels with feedback under an expected power constraint and the average error probability formalism. We show that the ε-capacity depends on ε in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that the second-order term is bounded between -ln ln n and a term that is proportional to +√(n ln n). The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available.

The ∊-capacity region of AWGN multiple access channels with feedback

In this paper, we establish the ε-capacity region for the AWGN multiple access channel (MAC) with feedback under an expected power constraint by combining ideas from binary hypothesis testing, information spectrum analysis, Ozarows coding scheme, and power control.