Study On The Structure And Properties Of Multi-Polarization Code Kernel Matrix

In 2009,Erdal Arikan published a paper“Channel polarization:A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels" in "IEEE Transaction On Information Theor".In this dissertation,the channel polarization was described in detail.Polarization code is a new channel coding technique which can reach the channel capacity theoretically under symmetric binary input discrete memoryless channel.Polarization code has two important processes:channel synthesis and channel splitting.Channel synthesis is the composition of N independent copies of the original channel W into a new channel WN.After channel synthesis,channel WN splits into channel WN(i)(i=0,1,…,N-1).As the code length N increases,part of the split channel tends to be noiseless channel whose channel capacity is close to one.The other part tends to be a pure noisy channel with channel capacity approaching zero.Arikan studied polarization codes on the basis of kernel matrix(?).However,later studies showed that when the order of kernel matrix increases,its polarizability will be higher.Therefore,higher order kernel matrix has better performance.Based on the above theory,this dissertation discusses and studies the 3rd order kernel matrix and related properties on finite field F3 in the following aspects:1.The development course of channel coding and the origin of polarization code are introduced.The research status and application of polarization codes at home and abroad are briefly described too.2.Some basic theories related to polarization codes are explained.The principle of polarization code to achieve channel capacity is explained,and the two processes of channel synthesis and channel splitting are elaborated in detail.3.The selection principle and generating process of the third order kernel matrix on the finite field F3 are described in detail.Beyond that this dissertation studies the construction process of third order kernel matrix.Taking(?)as an example,this dissertation introduces the relevant properties of polarization codes and draws relevant conclusions.4.Based on channel polarization theory,the channel degradation is explained in detail.The properties of channel degradation and the relationship between channel degradation and babbitt parameters are studied.We also define the image permutation and obtain the degradation relation of split channel under image permutation.