Comparison of various concatenated convolutional code ensembles under spatial coupling

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.Summary of comparison of various concatenated convolutional code ensembles under spatial coupling Gabriel IRO Rajeshwari KABBINALE Department of Electrical and Information Technology Lund University 23rd January, 2017 In any digital communication system, the sender sends its information to the receiver through a channel. Channels are prone to errors which reduce the reliability of the communication. These errors can be reduced through the use of error correction codes. Finding a good error correction code is a popular area of research. Error correction code is a key element in the reliability of the communication in digital communication systems. There are different classes of error correction codes and these codes have different abilities in error correction. This ability in correction is measured by a metric called the bit error rate (BER). For the coded systems, the BER is the probability of error in decoding of a bit. Typically, the stronger the code, the lower the BER. To make an error correction code stronger, we can use various techniques. One known technique is called the code concatenation. Two or more codes can be concatenated to form a stronger code, for example, serially concatenated codes (SCCs), hybrid concatenated codes (HCCs), and in general turbo-like codes (TCs). These codes are concatenations of smaller codes. Another technique to improve a code is spatial coupling. This technique was first applied on low-density parity-check (LDPC) codes. However, this technique is not limited to LDPC codes alone. Recently, there has been ongoing research at the Department of Electrical and Information Technology at Lund University on the effect of applying spatial coupling on TCs. The results from previous investigations on spatially coupled turbo-like codes (SC-TCs) indicates that these codes have a very good performance under certain conditions which are known as asymptotic. In these conditions we assume that the length of the message is extremely large, or infinite. There are four classes of SC-TCs, they are; parallel concatenated codes (PCC), serial concatenated codes (SCC), braided convolutional codes (BCC) and hybrid concatenated codes (HCC). Investigation on the performances of two classes of SC-TCs (spatially coupled parallel concatenated codes (SC-PCCs) and braided convolutional codes (BCC)) in the finite length regime, has been carried out in the department previously. However, the performances of spatially coupled serially concatenated codes (SC-SCC) and spatially coupled hybrid concatenated codes (SC-HCC) in the finite length regime was not covered in the previous investigation. In this thesis, we investigated the effects of spatial coupling on SCCs and HCCs. Then, we compared our results with those for SC-PCCs and BCCs. The results show that all investigated codes perform better when they are spatially coupled than when they are uncoupled. BCCs with spatial coupling are comparably the best performing codes overall, especially with a higher block length. Without spatial coupling, only PCCs and HCCs are better than their braided counterpart