Polar coding by spatial coupling

Polar code is a type of error correction code that has been theoretically proven to reach the Shannon limit of communication channels, and has been receiving the attention of academia and industry. Encoding of polar code is based on the phenomenon of channel polarization, and its performance is gradually improved with the increase of code length. At the same time, the price paid for this purpose is only the linear complexity of encoding and decoding, which makes it possible to design polar codes with good performance. Although the polar code is a capacity-achieving code, its short block-length codewords do not perform very good. For polar codes, researches on its encoding and decoding methods have been very abundant, and their performances have been continuously improved in simulation. The subject of this dissertation, based on the spatial coupling of polar codes, from another perspective, to achieve the purpose of error correcting performance of short block-length polar codes by spatially coupling. A spatially coupled code can be obtained by associating multiple code blocks, which can obtain better error performance than a single base code. In this dissertation, the basic theory of polar codes, the structures of non-systematic polar codes and systematic polar codes, and the encoding and decoding methods of these two are shown first. Then this dissertation introduces the basic concepts and the construction methods of spatial. The first is to couple some information bits in the previous code block to the frozen position of the adjacent code blocks; the second is to couple some information bits in the code block to the information position of the adjacent code blocks. This dissertation mainly makes some modifications based on the second method for the transmission of short block-length polar codes, and gives the relevant simulation results. Simulations show that the spatial coupling scheme significantly improves the decoding performance of the polar code.Master of Science (Signal Processing