Effective Capacity of Retransmission Schemes - A Recurrence Relation Approach

Research paper by Peter Larsson, James Gross, Hussein Al-Zubaidy, Lars K. Rasmussen, Mikael Skoglund

Indexed on: 28 Jan '16Published on: 28 Jan '16Published in: Computer Science - Information Theory


We consider the effective capacity performance of retransmission schemes that can involve any combination of multiple transmissions per packet, multiple communication states, or multiple packet communication. We present a novel unified analytical approach, based on a recurrence relation formulation, and give an exact effective capacity expression. The expression is based on the spectral radius of a special block companion matrix given in terms of the state transition probabilities and renewal rate(s). We apply this approach to analyze the performance of hybrid automatic repeat request (HARQ), network-coded ARQ (NC-ARQ), and ARQ operating in a block Gilbert-Elliot channel. We extend the analysis of HARQ to wireless block fading channels, specified by a probability density function, and give closed-form effective capacity expressions of HARQ in general, and of repetition redundancy-HARQ in Rayleigh fading in particular. Finally, we determine the optimal effective capacity, wrt the initial rate, of ARQ, as well as the effective capacity of multilayer-ARQ. Apart from handling a wide class of retransmission schemes, the recurrence relation framework developed for computing the moment-generating function, or moments, may be applicable to other fields of time-series analysis.