On the Responsiveness-Diversity-Multiplexing Tradeoff

The work analyzes the error performance of high-SNR, high-rate, point-to-point, outage-limited, wireless communications, with bursty and delay-limited information. In this setting, the bit-arrival process is stochastic and bursty, and the bits are limited by a strict delay condition. In the presence of fixed transmission rate, errors are due to both decoding and delay violations, and are attributed to sequences of atypical bursts of information and a typical fading realizations. For the case of fast Rayleigh channel fading, and compound Poisson bit-arrival process, the work presents bounds on a tradeoff between diversity and the ratio of average bit-arrival rate to ergodic-capacity. This tradeoff describes a uniform scalar effect of burstiness on the maximum amount of diversity that can be accumulated given a delay limitation. For large burstiness, the bounds are tight. As a practical consequence, the tradeoff addresses the question of how much of the maximum allowable time should be spent on coding and how much for timely and responsive accommodation of the queue.