Modelling the memory of the free space optical channel for use in the design of Error correcting codes

Abstract

Free Space Optics based communication links are an attractive potential approach for solving the last mile challenge, which will enable social advancement in more rural areas. Turbulence, however, remains a significant challenge in the use of Free Space Optical (FSO) channels. While models exist to predict how the turbulence affects the signal, these models often do not account for the memory in the channel. Furthermore, typical fading models accurately predict the average effect of the channel on a signal but not the distribution of the errors and the individual length of events such as deep fades. To better model and study the channel, this research demonstrates an alternative approach to modelling the channel: Fritchman Markov modelling. Fritchman Markov models capture the memory of a channel allowing for simulations and designs based thereon to be more accurate. A short-range link has been established and used to train a three state Fritchman Model to allow channel simulation. The models developed have accomplished better approximations of the digital behaviour of the channel when compared to traditional Probability Distribution Function (PDF)-based models. The techniques used to train the models have been demonstrated. The trained models capture the system’s memory, allowing for better utilisation of channel capacity, which proves vital for the design of efficient Error Correcting Codes (ECC) for the channel. FSO channels are packet erasure channels that are best suited by rateless codes. The aforementioned models have been used to simulate the application of ECC for the channel in the form of Luby Transform (LT) codes to show the efficacy of the models. This research has shown that rateless codes are not only suitable for the FSO channel but also that rateless code based transmission methods would be more suited for the channel. It is shown that the use of rateless codes results in similar throughput for a fixed overhead in comparison to a traditional method that would utilise retransmission. The performance of the LT code based system does, however, improve significantly with increased overhead allowing for a predicted better channel utilisation with increased turbulence strengths compared to retransmission based methods. The use of the Fritchman models had also shown that the memory of the channel could be utilised when the models are used to capture this memory. The short-range nature of the link means that the models and the resulting ECC do not fully predict behaviour in very high turbulence situations. Consequently, the work presented is not comprehensive for a full system design for use on real-world links, but it serves as crucial steps towards using and improving FSO links.