Sparse Network Coding (SNC) has been a promising network coding scheme as an improvement for Random Linear Network Coding (RLNC) in terms of the computational complexity. However, in this literature, there has been no analytical expressions for the probability of decoding a fraction of source messages after transmission of some coded packets. In this work, we looked into the problem of the probability of decoding a fraction of source messages, i.e., partial decoding, in the decoder for a system which uses SNC. We exploited the Principle of Inclusion and Exclusion to derive expressions of partial decoding probability. The presented model predicts the probability of partial decoding with an average deviation of 6 . Our results show that SNC has a great potential for recovering a fraction of the source message, especially in higher sparsity and lower Galois Field size. Moreover, to achieve a better probability of partial decoding throughout transmissions, we define a sparsity tuning scheme that significantly increases the probability of partial decoding. Our results show that this tuning scheme achieves a 16 improvement in terms of probability of decoding a fraction of source packets with respect to traditional SNC.
Another interesting research is Instantly Decodable Network Coding (IDNC) @cite_12 . In this scheme, the packets are sent in a way that an instant decoding of at least one of the source packets is guaranteed. However, the analysis on the partial decoding probability of this family of codes, such as @cite_16 and @cite_24 , is only valid for binary Galois Field and the presence of feedback in the system. Moreover, the IDNC family of codes heavily rely on feedbacks, though in our work, the system is considered to be feedback-free.
@cite_24 @cite_16 @cite_12
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This paper investigates the use of instantly decodable network coding (IDNC) for minimizing the mean decoding delay in multicast cooperative data exchange systems, where the clients cooperate with each other to obtain their missing packets. Here, IDNC is used to reduce the decoding delay of each transmission across all clients. We first introduce a new framework to find the optimum client and coded packet that result in the minimum mean decoding delay. However, since finding the optimum solution of the proposed framework is NP-hard, we further propose a heuristic algorithm that aims to minimize the lower bound on the expected decoding delay in each transmission. The effectiveness of the proposed algorithm is assessed through simulations. In this paper, we consider the problem of min- imizing the multicast decoding delay of generalized instantly decodable network coding (G-IDNC) over persistent forward and feedback erasure channels with feedback intermittence. In such an environment, the sender does not always receive acknowledgement from the receivers after each transmission. Moreover, both the forward and feedback channels are subject to persistent erasures, which can be modelled by a two state (good and bad states) Markov chain known as Gilbert-Elliott channel (GEC). Due to such feedback imperfections, the sender is unable to determine subsequent instantly decodable packets combination for all receivers. Given this harsh channel and feedback model, we first derive expressions for the probability distributions of decoding delay increments and then employ these expressions in formulating the minimum decoding problem in such environment as a maximum weight clique problem in the G-IDNC graph. We also show that the problem formulations in simpler channel and feedback models are special cases of our generalized formulation. Since this problem is NP-hard, we design a greedy algorithm to solve it and compare it to blind approaches proposed in literature. Through extensive simulations, our adaptive algorithm is shown to outperform the blind approaches in all situations and to achieve significant improvement in the decoding delay, especially when the channel is highly persistent. Index Terms—Multicast Channels, Persistent Erasure Chan- nels, G-IDNC, Decoding Delay, Lossy Intermittent Feedback, Maximum Weight Clique Problem. This work aims at introducing two novel packet retransmission techniques for reliable multicast in the framework of Instantly Decodable Network Coding (IDNC). These methods are suitable for order- and delay-sensitive applications, where some information is of high importance for an earlier gain at the receiver's side. We introduce hence an Unequal Error Protection (UEP) scheme, showing by simulations that the Quality of Experience (QoE) for the end-users is improved even without complex encoding and decoding. In this paper, we consider the problem of minimizing the completion delay for instantly decodable network coding (IDNC) in wireless multicast and broadcast scenarios. We are interested in this class of network coding due to its numerous benefits, such as low decoding delay, low coding and decoding complexities, and simple receiver requirements. We first extend the IDNC graph, which represents all feasible IDNC coding opportunities, to efficiently operate in both multicast and broadcast scenarios. We then formulate the minimum completion delay problem for IDNC as a stochastic shortest path (SSP) problem. Although finding the optimal policy using SSP is intractable, we use this formulation to draw the theoretical guidelines for the policies that can minimize the completion delay in IDNC. Based on these guidelines, we design a maximum weight clique selection algorithm, which can efficiently reduce the IDNC completion delay in polynomial time. We also design a quadratic-time heuristic clique selection algorithm, which can operate in real-time applications. Simulation results show that our proposed algorithms significantly reduce the IDNC completion delay compared to the random and maximum-rate algorithms, and almost achieve the global optimal completion delay performance over all network codes in broadcast scenarios.