# Probabilistic forwarding of coded packets on networks

### Vinay Kumar B. R.

**Research Overview**

IoT is the new emerging technology in the networking market. It involves different types of physical devices - like sensors, actuators, routers, mobiles etc.- communicating with each other over a network. Broadcast mechanisms are crucial in such ad-hoc networks to disburse key network related information. A typical example is over-the-air (OTA) programming of IoT nodes. As part of my PhD, I am looking at a novel algorithm for broadcast which is light-weight and energy efficient. This is described here. Consider a connected graph with a particular node designated as the source. The source node has k message packets which need to be broadcast in the network. The source encodes the k message packets into n (> k) coded packets using a Maximum Distance Separable (MDS) code. This ensures that any node that receives at least k out of the n packets can retrieve the original k message packets that the source intended to convey. The source then transmits all the n packets to its neighbours. Every other node in the network follows a probabilistic forwarding mechanism: a node on reception of a new packet forwards it to its neighbours with some probability p and does nothing with probability 1-p. We are interested in finding the minimum value of the forwarding probability p for which a large fraction of the nodes are able to obtain the information from the source. Call this p*. The performance metric of interest is the expected total number of transmissions when the forwarding is done using this minimum value of the forwarding probability p*.

**Work done in previous years**

- Simulation of the probabilistic forwarding protocol with coded packets on different underlying graph structures like tree, grids etc.
- Analysis of the probabilistic forwarding protocol on a rooted binary tree: It was shown that probabilistic forwarding with coded packets is not beneficial on trees with respect to the expected total number of transmissions in the network. Introducing coded packets increases the number of transmissions in the network.
- Analysis of the probabilistic forwarding protocol on a square grid: Probabilistic forwarding with coded packets decreases the expected total number of transmissions when the forwarding probability and the number of coded packets is chosen wisely as compared to a mechanism with no coding.

**Work done in the current year (2019-2020)**

- Refined analysis for the grid.: Simplification of expressions for the minimum forwarding probability and better estimates for the same on the grid.
- Extensive simulations on the Random Geometric Graph (RGG): RGGs are widely used to model deployments of ad-hoc networks. Understanding behaviour of the probabilistic forwarding protocol on them is key for practical implementation.
- Partial analysis of the probabilistic forwarding protocol on RGGs: Analytical expression for the expected number of transmissions has been obtained and is being verified.

**Future work

- A complete analysis of the probabilistic forwarding mechanism on RGGs: Obtain an analytical expression for p*. The challenge is to obtain an estimate of the expected number of receivers when the nodes transmit with some forwarding probability p