Comparison of various concatenated convolutional code ensembles under spatial coupling

Abstract: A big challenge faced by the digital communication world today is increasing the reliability of information which is being transmitted. During the transmission of information, there is a possibility that the information is corrupted or distorted. If this distortion is considerably high, it becomes dicult to decode and retrieve the original information. To help mitigate this eect, the information bits are encoded and the induced errors can be reduced or completely removed after decoding. This process of protecting the information bits is called error control coding (ECC). It is introduced to provide reliable transmission of information over the channel and this is done by adding redundancy to the message that is to be transmitted. There are ongoing studies in dierent implementations of error control coding schemes based on both convolutional codes and block codes. One technique intro- duced to improve the performance of the codes is spatial coupling. This technique was rst introduced for low-density parity check codes (LDPC) codes, however, spatial coupling is a general concept, and it can be applied on other classes of error control codes such as turbo-like codes (TCs). There is research at the De- partment of Electrical and Information Technology at Lund University on dierent construction of spatially coupled turbo-like codes such as: spatially coupled paral- lel concatenated codes (SC-PCCs), braided convolutional codes (BCCs), spatially coupled serially concatenated codes (SC-SCCs) and spatially coupled hybrid con- catenated codes (SC-HCCs). These codes have shown to have asymptotically good performance, but their performances in the nite length regime is currently under investigation. In this thesis we investigated the performance of SCCs and HCCs under spatial coupling in the nite length regime. At the beginning of our investigation, we dened the spatially coupled ensembles, then, implemented these ensembles in Matlab and C++. Thereafter, we simulated the ensembles considering dierent puncturing patterns to obtain higher code rates. We then compare our results with those for BCC and SC-PCC which has been carried out previously in the department. The results show that all the investigated codes perform better when they are spatially coupled than when they are uncoupled. Among all the considered ensembles, BCC with spatial coupling is comparably the best performing code overall especially with an increased block length. Moreover, our results also shows that the pattern of puncturing applied on the code aects the performance of the code. The puncturing pattern which gives the better performance for uncoupled codes may not necessarily give the better performance for the coupled codes.