Research Polar Codes' Encoding And Decoding Algorithm And Its Application In Image Transmission

Polar codes, introduced by Arikan in 2009, has provided a coding scheme for achieving the symmetric capacities of binary input discrete memory-less channels(B-DMCs) with low encoding and decoding complexities. Our previous studies have shown that the polarization phenomenon was not perfect and information bits in a codeword had different error probabilities after decoding in practical systems with finite codeword length. This inborn property of polar codes provides the opportunity for unequal error protection(UEP). In recent years, several scholars have applied polar codes to multi-media transmission system, however, exploiting the UEP property of polar codes for image transmission has not been investigated so far, which motivates our work in this thesis.This thesis mainly focuses on the research of channel polarization and polar codes' encoding and decoding theory. On the basis of that, combined with the actual image transmission scenario of polar codes' application scheme is designed and implemented. Specifically, the contributions of this thesis can be summarized as follows.1) A deep research on the theory of channel polarization and polar codes' encoding and decoding is discussed. When constructing polar codes according to the Gaussian approximation method, the experiment shows that the information bits in a codeword have different error probabilities after decoding.2) Based on the phenomenon of polar codes' unequal error protection(UEP), two different methods with unequal error protection are designed and applied to image transmission. In the design, first of all, the information bits of polar codes are sorted according to the unequal post-decoding error probabilities. Then the bits after sorting are mapped to image information to reduce image distortion in our design. One of the schemes is that if we have obtained the binary matrix of image, the most significant bits(MSB, left-most bits) of each pixel in an image are transmitted through the lower error probability bit-channels(logical channel post the polar code) and the Least Significant Bits(LSB, right-most bits) of each pixel are transmitted through higher error probability bit-channels encoding with polar codes. Another scheme is that after achieving the binary matrix of the image, firstly, handle the image by Discrete Cosine Transform(DCT), quantization, and so on, then encode it with polar codes. Simulation results show that under the same conditions, compared to the traditional schemes, the two unequal protection schemes with polar codes gain higher Peak Signal to Noise Ratio(PSNR).