Research On Polar Code Rate Matching Algorithm Based On Channel Reliability

Polar Code is a new type of channel coding that can reach the Shannon limit based on the phenomenon of Channel Polarization proposed by Professor Arikan.It has a clear construction method and compiled code structure,and the compiled code algorithm has low complexity,so it is expected to be applied in the communication field and has high research value.However,the size of the kernel matrix used to construct polar codes is usually 2 × 2,leading to its coding length will be limited to the nth power of 2,which hinders the adaptation of polar code to flexible channel conditions.In order to solve the problem of variable polar code length in practical applications,this thesis investigates the rate matching of polar codes,where the main research work and innovations are in the following aspects.First,the coding construction of polar code is closely related to the decoding performance,and the key point is to select the sub-channel with high reliability in the polarization channel to transmit the information bits.Therefore,in this thesis,the existing Gaussian Approximation(GA)construction is optimized from the polar code construction.The GA construction is viewed as a product of a tangent function and a Gaussian function,and the tangent function in the composite function is weakened by a segmentation method to obtain a trivial approximation alternative that does not depend on the integral form.The optimized GA construction algorithm makes the calculated sub-channel capacity more accurate,and compared with the standard GA construction method,it can have a performance gain of 0.1 d B in the case of insufficient polarization for short code lengths,and the performance gain increases with code rate for the same code length.Second,the existing ways to change the code length of polar codes are punctured or shortened under the original code length,while the polar code are originally constructed based on uniform channels.In the case of punctured polar code,the punctured bits are not transmitted through the channel,but rather they are considered to be transmitted in a different way,i.e.,through a zero-capacity channel.Thus,puncture polar code can be considered as a special case where they are constructed on the basis of a non-uniform channel,i.e.the original base channel and a zero capacity channel.Where the location of the puncture bits is constructed by directly assigning the Log-Likelihood Ratio(LLR)to zero at their locations,and the remaining subchannels are subjected to non-uniform polarization operation,from which the channel with high reliability is selected to transmit the information bits.The feasibility of the non-uniform polarization theory is verified in the thesis,and compared with the existing classical punctured scheme.The rate-matched polar code under the optimized GA construction proposed in this paper,for example,has a performance gain of about 0.2 d B at a code length of 512,a code rate of 2/3,and a signal-to-noise ratio greater than 2.5 d B.Third,to address the problem that the degree of degradation of the polarization subchannel due to puncturing affects the reliability of the polarization sub-channel,the channel degradation due to puncturing during channel construction is considered in this thesis.On the polar codes constructed based on uniform channels,channel reliability parameters are used to assist in selecting some channels that are less affected by channel degradation to puncture,so that the desired channels are more stable and reliable.Considering the difference in the initial values of the channels after punching,a non-uniform polarization reconstruction operation is used to pick the information bits,thus further improving the performance of the rate-matching polar codes.Experiments show that the performance of the improved puncture polar codes under the same decoding conditions is better than that of the classical puncture polar codes.The higher the code rate,the more obvious the improvement of the decoding performance of this channel reliability screening puncture bit polar code.for example,at a code length of 512,a code rate of 2/3,and a BER of 10-2,there is a performance gain of about 1 d B for SC decoding and 1.2 d B for CA-SCL decoding.