Investigation of Forward Error Correction Coding Schemes for a Broadcast Communication System

This thesis investigates four FEC (forward error correction) coding schemes for their suitability for a broadcast system where there is one energy-rich transmitter and many energy-constrained receivers with a variety of channel conditions. The four coding schemes are: repetition codes (the baseline scheme); Reed-Solomon (RS) codes; Luby-Transform (LT) codes; and a type of RS and LT concatenated codes. The schemes were tested in terms of their ability to achieve both high average data reception success probability and short data reception time at the receivers (due to limited energy). The code rate (Rc) is fixed to either 1/2 or 1/3. Two statistical channel models were employed: the memoryless channel and the Gilbert-Elliott channel. The investigation considered only the data-link layer behaviour of the schemes. During the course of the investigation, an improvement to the original LT encoding process was made, the name LTAM (LT codes with Added Memory) was given to this improved coding method. LTAM codes reduce the overhead needed for decoding short-length messages. The improvement can be seen for decoding up to 10000 number of user packets. The maximum overhead reduction is as much as 10% over the original LT codes. The LT-type codes were found to have the property that can both achieve high success data reception performance and flexible switch off time for the receivers. They are also adaptable to different channel characteristics. Therefore it is a prototype of the ideal coding scheme that this project is looking for. This scheme was then further developed by applying an RS code as an inner code to further improve the success probability of packet reception. The results show that LT&RS code has a significant improvement in the channel error tolerance over that of the LT codes without an RS code applied. The trade-off is slightly more reception time needed and more decoding complexity. This LT&RS code is then determined to be the best scheme that fulfils the aim in the context of this project which is to find a coding scheme that both has a high overall data reception probability and short overall data reception time. Comparing the LT&RS code with the baseline repetition code, the improvement is in three aspects. Firstly, the LT&RS code can keep full success rate over channels have approximately two orders of magnitude more errors than the repetition code. This is for the two channel models and two code rates tested. Secondly, the LT&RS code shows an exceptionally good performance under burst error channels. It is able to maintain more than 70% success rate under the long burst error channels where both the repetition code and the RS code have almost zero success probability. Thirdly, while the success rates are improved, the data reception time, measured in terms of number of packets needed to be received at the receiver, of the LT&RS codes can reach a maximum of 58% reduction for Rc = 1=2 and 158% reduction for Rc = 1=3 compared with both the repetition code and the RS code at the worst channel error rate that the LT&RS code maintains almost 100% success probability