Performance Study of LDPC Codes Constrained by Weight Distribution Polynomials
Yao Chun-guang · Dianzi xuebao · 2007
Research on LDPC codes is in the ascendant nowadays.Our paper has done some work on the proposition ofperformance of different codes in the same family constrained by weight distribution polynomials.Different codes of the same weight distribution are listed,and the results indicate the upper performance bound is determined by density evolution theory and the lower performance bound by the Fill-Shift construction method.Furthermore,the codes in the set of elementary matrix transforma- tion share the same error-correction performance but different coding complexity.We can get a conclusion that codes constrained by weight distribution polynomial can be divided into many groups,performance among different groups is not the same,it depends on the loops length and distribution,and performance in the same group is identical.What we can do now is that to find the best group and do suitable transformations if given weight distribution polynomials.Through this paper,we can see that a new idea for code constructing is also presented.If the relations between big girth of LDPC codes and weight distribution polynomial are discovered, new codes can be achieved only by the weight distribution polynomial,the currently used method given in references for code con- structing will be less useful.We can think that we have found a completely different method to construct LDPC codes.