Markov Chain Model for the Decoding Probability of Sparse Network Coding

Abstract

Abstract-Random Linear Network Coding (RLNC) has been proved to offer an efficient communication scheme, leveraging an interesting robustness against packet losses. However, it suffers from a high computational complexity and some novel approaches, which follow the same idea, have been recently proposed. One of such solutions is Tunable Sparse Network Coding (TSNC), where only few packets are combined in each transmissions. The amount of data packets to be combined in each transmissions can be set from a density parameter/distribution, which could be eventually adapted. In this work we present an analytical model that captures the performance of SNC on an accurate way. We exploit an absorbing Markov process where the states are defined by the number of useful packets received by the decoder, i.e the decoding matrix rank, and the number of non-zero columns at such matrix. The model is validated by means of a thorough simulation campaign, and the difference between model and simulation is negligible. A mean square error less than 4 · 10 −4 in the worst cases. We also include in the comparison some of more general bounds that have been recently used, showing that their accuracy is rather poor. The proposed model would enable a more precise assessment of the behavior of sparse network coding techniques. The last results show that the proposed analytical model can be exploited by the TSNC techniques in order to select by the encoder the best density as the transmission evolves.

Improving wireless multicast communications with NC: Performance assessment over a COTS platform

“…where α is a constant value, which does not depend on the generation size, when k 1, but it varies with the Galois Field, as it is derived in [12]. For the binary case, GF (2), α ≈ 1.6, being almost negligible as the Galois Field length increases.…”

“…In [12] we introduced a semi-analytical model that accurately captures the performance of Sparse Network Coding (SNC). It is based on an Absorbing Markov Process, S, where the states are defined by the decoding matrix rank, i.e number of useful packets received, and the non-zero columns at such matrix (i.e.…”

“…The model is characterized by the corresponding fundamental matrix N = (I − Q) −1 , where Q is a matrix that includes the transition probabilities between the transient states. Since they are used in this work, we recall some of the results that were derived in [12], in particular Corollary 7:…”

The full-state reliability model and evaluation technology of mechatronic product based on meta-action unit

“…For example, Guo et al 24 built the reliability model using Markov chains and the recursive method to evaluate modular multilevel converters under different redundancy schemes. Garrido et al 25 presented a semi-analytical model by exploiting an absorbing Markov process. Meanwhile, there are many different methods in the reliability region, such as subset- simulation-based reliability analysis approach, 26 evidence-based reliability optimization method, 27 and fatigue accumulation model based on probabilistic framework.…”

Caracterización experimental del comportamiento de Network Coding para comunicaciones multicast

“…donde α es una constante que no depende del tamaño de la generación pero sí del cuerpo de Galois elegido, como se demuestra en [14] y, que en el caso binario (GF (2)), α ≈ 1,6, para ir aproximándose a cero a medida que el tamaño del cuerpo crece. Hay que destacar que bajo esquemas de codificación RLNC no es importante qué paquetes han sido recibidos, sino recibir suficientes paquetes de información para decodificar.…”