Binary Weight Distribution of Non-Binary LDPC Codes

被引:7
|
作者
Andriyanova, Iryna [1 ]
Rathi, Vishwambhar [2 ]
Tillich, Jean-Pierre [3 ]
机构
[1] Univ Cergy Pontoise, CNRS, ENSEA, ETIS Grp, F-95015 Cergy, France
[2] KTH Royal Inst Technol, Sch Elect Engn, Stockholm, Sweden
[3] INRIA Roquencourt, SECRET Project, Le Chesnay, France
来源
2009 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1- 4 | 2009年
关键词
LDPC codes; Galois fields; general linear groups; ML decoding; binary weight distribution; error probability; PARITY-CHECK CODES; DENSITY;
D O I
10.1109/ISIT.2009.5205662
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
(1) This paper is the first part of an investigation if the capacity of a binary-input memoryless symmetric channel under ML decoding can be achieved asymptotically by using non-binary LDPC codes. We consider (l, r)-regular LDPC codes both over finite fields and over the general linear group and compute their asymptotic binary weight distributions in the limit of large blocklength and of large alphabet size. A surprising fact, the average binary weight distributions that we obtain do not tend to the binomial one for values of normalized binary weights to smaller than 1 - 2(-1/r). However, it does not mean that non-binary codes do not achieve the capacity asymptotically, but rather that there exists some exponentially small fraction of codes in the ensemble, which contains an exponentially large number of codewords of poor weight. The justification of this fact is beyond the scope of this paper and will be given in [1].
引用
收藏
页码:65 / 69
页数:5
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