摘要
This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.
This paper studies the nonsystematic Low-Density Parity-Check（LDPC）codes based on Symmetric Balanced Incomplete Block Design（SBIBD）.First,it is concluded that the performance degradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes constructed based on SBIBD is presented.Their characteristics include：both generator matrices and parity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbitrary rate codes can be easily constructed,so they are rate-compatible codes.Because there are sparse generalized inverses of generator matrices,the performance of the proposed codes is only 0.15dB away from that of the traditional systematic LDPC codes.
基金
the National Natural Science Foundation of China(No.60272009,No.60472045,and No.60496313).
