The average weight enumerator and the maximum likelihood performance of product codes

Author

El-Khamy, Mostafa

Author_Institution

Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA

Volume

2

fYear

2005

fDate

13-16 June 2005

Firstpage

1587

Abstract

Product codes are widely used in data-storage, optical and wireless applications. Performance analysis of the product codes in the literature relied on the truncated union lower bounds due to lack of the knowledge of the weight enumerator of most product codes. In this paper, average weight enumerators of arbitrary product codes over F_q are derived. The split weight enumerators of some linear codes are studied and are used in the analysis. The average binary weight enumerator of product Reed Solomon codes is derived. The relationship between the codeword weight and the coordinate weight is discussed for product codes. Consequently, tight bounds on the performance of product codes at low signal to noise ratios are shown.

Keywords

Reed-Solomon codes; binary codes; linear codes; maximum likelihood estimation; product codes; arbitrary product codes; average weight enumerator; binary weight enumerator; codeword weight; data-storage; linear codes; maximum likelihood performance; optical applications; performance analysis; product Reed Solomon codes; signal to noise ratios; wireless applications; AWGN; Bit error rate; Galois fields; Iterative decoding; Linear code; Maximum likelihood decoding; Performance analysis; Product codes; Reed-Solomon codes; Signal to noise ratio;

fLanguage

English

Publisher

ieee

Conference_Titel

Wireless Networks, Communications and Mobile Computing, 2005 International Conference on

Print_ISBN

0-7803-9305-8

Type

conf

DOI

10.1109/WIRLES.2005.1549650

Filename

1549650