Analysis of the finite length performance of spatially coupled convolutional codes

Sammanfattning: Error control coding is an essential part of any well-designed digital communication system. It has been used in structures to protect the information, by enabling reliable delivery of digital data over unreliable communication channels. Even though this is an old topic, enlisted by Shannon in the late 40's, a lot of research is still going on. There have been recently some interesting approaches about spatially coupled LDPC codes and it promises excellent performance over a broad range of channels. Part of the current research by the Department of Electrical and Information Technology is the construction of spatially coupled turbo like codes, including braided convolutional codes (BCC) and their generalization. The behavior of this type of codes when the length approaches infinity has been analyzed and looks very promising. In this thesis we have investigated such codes in the finite length regime. The first thing that we do is implementing two decoders of rate 1/2 and rate 2/3 based on the BCJR algorithm for convolutional codes. This is then used as a component decoder for all constructions. Then we implement two different kinds of codes, parallel concatenated codes (PCC) and braided convolutional codes (BCC). Furthermore we constructed three different ensembles for coupled codes, spatially coupled parallel concatenated codes and spatially coupled braided convolutional code for two different types which we call Type I and Type II. We also implement a sliding window decoder for the spatially coupled ensembles. In order to visualize the results we implement a simulation environment, we estimated the bit error probability with different values of E_b/N_0 for all the constructions. Since the computation time for these simulations was high, we used the Alarik lunarc cluster facilities based in Lund university. We started by implementing everything in Matlab but after evaluating the processing time, we decided to implement the BCJR algorithm in C++. By doing this we managed to save a lot of simulation time. We plot all the points for the different constructions in different figures. With the help of the figures we analyze the performance of the different constructions. We can see that braided convolutional codes do not present an error floor, which is one of the drawback of parallel concatenated turbo like codes. This investigation enables us to observe that the performance of spatial coupling for finite length gives a significant BER performance for approaching the Shannon limit. We can also observe that spatial coupling for braided convolutional codes gives better performance than spatially coupled parallel codes.