Research On Algorithms Of Encoding And Decoding For Polar Codes

Polar codes, as a newly emerging channel coding scheme, have always been attracting widespread attention from the academics since they were proposed by E.Arikan in year 2009. Polar codes are theoretically based on channel polarization, and are the known code family that have been strictly proven to be able to achieve Shannon Limit. In addition, polar codes have a low encoding complexity and their decoding complexity under successive cancellation (SC) algorithm is also low, both in the order of O(NlogN). Besides, they own a very simple and regular encoding structure, and we can foresee a very potential place for polar codes in the future.Although polar codes are proven to be able to achieve Shannon Limit theoretically, it is under the premise that the code block length is very large, and the performance of polar codes with short and moderate length is still unsatisfying, which restricts the practical application of polar codes. Given this, the thesis maily focus and researchs on the performance improvement and practical application in image undistorted transmission of polar codes.Firstly, the background and significance of selection of the thesis are described. Then the thesis elaborates the channel polarization phenomenon, the construction of the generation matrix of polar codes,the selection of information bits together with the encoding and decoding algorithms of polar codes.Secondly, the thesis proposes a concatenation scheme based on systematic polar codes and repeat accumulate (RA) codes, which employs systematic polar codes as outer codes and RA codes as inner codes, and takes advantage of interleaved coding to enhance the capability to resist burst errors of concatenated codes. The thesis gives the design of the concatenation scheme alone with its simulation results and provides the simulation implementation in detail.Finally, the thesis researches on the application of polar codes in image undistorted transmission. The thesis employs polar codes for image reconstruction. Besides, the thesis also employs the systematic Polar-RA concatenation scheme in image undistorted transmission and makes a contrast with the non-systematic polar codes under the same conditions, in order to validate the performance of the concatenation scheme further.