Exact decoding probability of random linear network coding for combinatorial networks

Abstract

Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in which one source sends messages to k destinations through m relays using random linear network coding over a Galois field. The formulation at a (all) sink(s) represents the impact of major parameters, i.e., the size of field, the number of relays (and sinks) and provides theoretical groundings to numerical results in the literature. Such condition maps to the receivers' capability to decode the original information and its mathematical characterization is helpful to design the coding. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized.

Distributions of random variables involved in discrete censored δ-shock models

“…Many researchers have defined and investigated modifications and generalizations of these two traditional models, such as -shock models, run shock models, and mixed shock models. In the -shock model, the system fails whenever the time between two consecutive shocks falls below a fixed threshold (Li [27], Wang and Zang [46], Xu and Li [50], Li and Kong [28], Li and Zhao [29], Li et al [30], Bai and Xiao [4], Eryilmaz and Bayramoglou [19]), whereas under the setup of the run shock model, the system fails when the magnitudes of a specified number of consecutive shocks exceed a given threshold (Sumita and Shanthikumar [45], Gut [23], Mallor and Omey [36]). The above-mentioned papers study the lifetime behavior of the system when the shocks occur according to a Poisson process, i.e.…”