Construction Algorithm Research Of LDPC Codes With Low Error Floor Based On Tapping Sets

LDPC codes with its excellent performance which is near the Shannon limit are widely applicated in modern communication systems.But under iterative decoding algorithms,LDPC codes with middle length are always present error floor phenomenon.It will limit its further applications in communication systems which require extremely low bit error rate.Cycles and trapping sets in Tanner graph of LDPC codes are the major reasons that why LDPC codes have error floor.Trapping sets which are consist of single or various cycles will seriously influence the origin and height of error floor.In this thesis,the researches on decoding performance and error floor are start with the characteristics of cycles and trapping sets.We studied methods to lower the error floor of LDPC codes.We firstly studied the PS-LDPC codes and progression construction methods,and then we proposed arithmetic progress and partion-shift LDPC codes construction algorithms with two kinds of structures.It will lower the error floor by optimizing cycles distribution,enlarging girth and eliminating trapping sets,and increase the decoding performance as well as save the coding storage space.The main work is organized as follows:Firstly,by deeply understanding the conception and theories of trapping sets and error floor,we get the structure characteristics of trapping sets.Their effects upon decoding performance and error floor are analyzed in detail combining the structure characters and the relationships between cycles,girth and trapping sets.We also studied the influence on application in construction algorithms of LDPC codes.Secondly,construction algorithms of LDPC codes based on trapping set elimination are deeply investigated in this dissertation.On the basis of analyzing block cycles and trapping sets in PS-LDPC code,we proposed a classification method of short cycles.And then we studied the PS-LDPC codes construction algorithms which are based on classification method of short cycles and get the new idea form Fibonacci or arithmetic progression construction algorithms with large girth.The principle analysis and proven theorem are presented in detail.Simulations are carried out to compare the identities of different algorithmsFinally,in order to eliminate trapping sets and reduce their harmful influence on decoding of LDPC codes,we proposed two construction algorithms to lower the error floor which are draw lessons from PS-LDPC codes and progression theories.They are arithmetic progress and partion-shift LDPC codes with unit diagonal and Bi-diagonal structures.The shift parameters are controlled by some simple mathematical axioms to lower the error floor,it will save the storage space,enlarge the girth of LDPC codes as well as eliminate trapping sets.Simulation experiments with varied code length and rate prove that either unit diagonal or Bi-diagonal structure arithmetic progress andpartion-shift LDPC codes can lower the error floor.The outstanding performances of these algorithms with low error floor are further illustrated by analyzing cycles,trapping sets,construction complexity and time consuming.