Design And Implementation Of Rate-Compatible QC-LDPC Codes

Low-Density Partiy-Check (LDPC) codes, a type of error control codes, canachieve error correcting performance which is very close to the Shannon limit. LDPCcodes become one of the popular research fields in recent years. QC-LDPC(Quasi-Cyclic LDPC) codes are a kind o f very impor tant LDPC cod es. Comparing withthe other LDPC codes, QC-LDPC codes exhibit less encod ing and decoding complexity,which is very suitable for practical applications and implementations. Moreover,QC-LDPC codes can achieve very outstanding performance through particular designs.As a result, QC-LDPC codes have recently been one of the promising choices forchannel coding scheme in various standa rds, incluc ing the deep space communicationsystem, DVB-S2, WIMAX, etc. Practical communication systems are often required tooperate at several different rates according to channel conditions,therefore the study ofdesign and implementation of rate-compatible(RC) QC-LDPC codes is very importantin real applications.Through the design of a group of the parity check matrics, the RCQC-LDPC codes may operate on the same encoder and decoder architecture, whilemaintaing good performance.In this paper, the basic concept of LDPC codes and quasi circulation characteristicsof QC-LDPC codes are introduced first, considering the engineering problemsencounted in field applications. Based on the finite field, an algebric method ofconstructing QC-LDPC codes is proposed, with which the constructed QC-LDPC codescan achieve a lower error floor with a girth number higher than four. On the basis of theabove discussion, a design method of irregular QC-LDPC codes is discussed.Meanwhile, the fast encoding algorithms are introduced for QC-LDPC codes.Last but not least, the design and implementation of the rate-compatible QC-LDPCcodes are proposed and discussed in details. The rate-compatible QC-LDPC codesconstructed through parity matrix extanding are able to operate on the same encoder anddecoder articture, while maintaing a good correcting performance.