| Polar codes is the first structure code to prove that can achieve shannon limit under the B- DMC channe ls, and the comple xity o f encoding and decoding of Polar codes is very low. Because of Polar codes having these advantages, a lot of attention of the researchers have been payed to Polar codes. C hannel polarizat ion is the basis of Polar codes, this paper firstly analyze d the forming princip le of cha nne l polar izatio n. In BEC channe l, polar izat ion has much to do wit h channel type, channe l number N and erase probabilit y p. In this paper, we stud ied these factors. The calculat ion method s of polar izat ion are different w hen t he channels t ype is different. In t his paper, we stud ied the transmiss ion of informat ion on t he three kinds of channels, ana lyzed their polar izatio n process respective ly. The encoding process is expressed in matr ix to to discribe the channe l combinat ion and decomposit ion. The most important of the coding process is the calculat ion of ge nerator matr ix. This paper ana lyzed the calc ulat ion formula of generator matr ix, talked about the encoding process of Polar codes in detail.The decoding o f Polar codes using SC decoding algorithm, is a series of iterative decoding process.The tradit ional SC decoding algorit hm has low comp lexit y. This paper first analyze d the basic SC decoding algorit hm and studied the application of Polar codes over different channels. In BEC and BSC channe l, respective ly explores the relat ions hips between error rate and code rate, code lengt h and erase the probability. U nder the gauss ian channe l, the gauss ian approximat ion method was adopted to do the channel po larizat ion t hat P olar codes could be used in gauss ian channe l. Then the relat ionship between the perfor mance of Polar codes and code rate, code le ngt h and signa l to no ise ratio was studied, and ber cur ve was obtained. O n the basis of SC decoding, the perfor mance of the list SC decoding algor ithm(SC L) and C A-SC L over gauss ian channe l was studied, compared wit h the tradit iona l SC decoding algorit hm, the comp lexit y of t he latter two decoding a lgor it hm is increased. The s imulat ion results show t hat these two kinds of a lgor it hm is superior to the basic SC algorithm.Fina lly by observing the structure of decoding, find ing that there ma y be isolated code ele ment and put forward an improved algorit hm. Delet ing t he corresponding c hanne l can reduce the calc ulatio n of decoding algorithm w hen encoding. Simulat ion was conducted to verify t he effect of improved algor it hm. The result shows that in t he presence of iso lated nodes, the proposed algor ithm could reduce the complexity of decoding algorithm. |
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