Effective Capacity of Retransmission Schemes: A Recurrence Relation Approach

Abstract

Abstract-We consider the effective capacity performance measure of persistent-and truncated-retransmission schemes that can involve any combination of multiple transmissions per packet, multiple communication modes, or multiple packet communication. We present a structured unified analytical approach, based on a random walk model and recurrence relation formulation, and give exact effective capacity expressions for persistent hybrid automatic repeat request (HARQ) and for truncated-retransmission schemes. For the latter, effective capacity expressions are given for systems with finite (infinite) time horizon on an algebraic (spectral radius-based) form of a special block companion matrix. In contrast to prior HARQ models, assuming infinite time horizon, the proposed method does not involve a non-trivial per case modeling step. We give effective capacity expressions for several important cases that have not been addressed before, e.g. persistent-HARQ, truncated-HARQ, network-coded ARQ (NC-ARQ), two-mode-ARQ, and multilayer-ARQ. We propose an alternative QoSparameter (instead of the commonly used moment generating function parameter) that represents explicitly the target delay and the delay violation probability. This also enables closedform expressions for many of the studied systems. Moreover, we use the recently proposed matrix-exponential distributed (MED) modeling of wireless fading channels to provide the basis for numerous new effective capacity results for HARQ.

Effective Capacity in Wireless Networks: A Comprehensive Survey

“…Traditional ARQ [117] Selective Repeat ARQ (SR-ARQ) [160] Network Coded ARQ (NC-ARQ) [226] Two-Mode ARQ [226] Multi-Layer ARQ [226] Traditional HARQ [49] Type-1 HARQ [173] Chase combining HARQ (CC-HARQ) [173] Incremental redundancy HARQ (HARQ-IR) [173], [200], [296] Persistent HARQ [226] Truncated HARQ [226]…”

“…To communicate multiple packets over the same time slot, concept of network-coded ARQ (NC-ARQ) has been proposed. Authors in [226], have provided a comparative view of different retransmissions schemes while considering the concept of EC model. In this study, NC-ARQ has been proposed and compared with other versions of ARQ and HARQ.…”

“…Performance analysis of NC-ARQ based on achievable EC, shows that NC-ARQ outperforms the other state-of-the-art retransmission schemes. 4) Two-Mode ARQ: In [226], the maximization of EC with two-mode ARQ in comparison to traditional ARQ with Gilbert-Elliot block fading channel has been investigated in detail. In this two-states or two-mode ARQ, a channel always assumes either of the two states and these two states at any time can be, bad-to-good, bad-to-bad, good-to-bad, and goodto-good.…”

“…This EC analysis shows that, the performance of HARQ-IR is same either using buffer-aided diamond relaying or decode-and forward relaying. 5) Persistent HARQ: Performance of persistent HARQ has also been tested while using EC concept [226]. In this technique, a transmitter persistently resends packets for a given duration of a time (frame).…”

Effective Capacity for Renewal Service Processes With Applications to HARQ Systems

“…K < ∞. To address this issue, the outage effective capacity is proposed in [9], [10]. Unlike the maximum arrival rate studied in Subsection V-A1, the reward of each renewal is a two-value function for the truncated HARQ schemes.…”