I 121 "I PERFORMANCE OF REED-SOLOMON BLOCK TURBO CODE Omar AIT.SAB and Ramesh PYNDIAH T616com Bretagne, Technop8le Brest Iroise, BP-832,29285 BREST, FRANCE. (Tel : (33) 98 00 10 70, Fax : (33) 98 00 10 98) (Email : Omar.Aitsab@enst-bretagne.fr, Ramesh.Pyndiah@enst-bretagneh) k2 kI Information symbols Checks on rows M I' CT - Thanks to recent progress in the iterative of concatenated codes, several new fields of In this paper, we present a first of the iterative decoding of Reed-Solomon (RS) codes: "Turbo codes RS". Two methods to construct ponent codes. The performance of RS turbo codes evaluated on the Gaussian and Rayleigh channels e of powerful source coding which are more and more sensitive to transmission hermore, the progress in VLSI technology opens the f more complex algorithms. So with an iterative decoding algorithm based on soft f the component codes and soft decision of decoded e succes of convolutional turbo codes encouraged R. turbo code. R. codes and soft decision of decoded bits [3]. re, this work has shown that the BCH block turbo to evaluate the performance of block turbo codes 11, we present two methods for the constuction codes and in section 111, we describe the soft decoding algorithm and give some results of RS soft decoding. In section IV, we give the soft decision algorithm derived from the theoretical Log-Likelihood-Ratio and in section V we describe the iterative algorithm for decoding RS product codes. Section VI and VI1 are dedicated to simulation results of BER function of signal to noise ratio for different RS turbo codes over Gaussian and Rayleigh channels while in section WI we discuss the results of RS turbo codes. 11. CONSTRUCTION OF PRODUCT CODE 11.1. Reed-Solomon codes RS codes are BCH codes with non binary elements belonging to GF q = 2" . Each q-ary symbol of the Galois field can be mapped to m binary elements. The main parametres of a RS code are (n, k, 6), where n is the code word lenght, k is the number of information symbols and 6 its minimal Hamming distance. 0 11.2. Product codes Let us consider two linear block codes t1 having parametres (nl , kl, 61) and t2 having parametres (n2, k2,62). The product code ? =fl @ t2 is obtained by : 1) placing ( kl x k2) information symbols in an array of kl rows and k2 columns, 2) coding the kl rows using code t2, 3) coding the n2 columns using code t2, as illustrated in figure 1. Checks on columns 11 j%l Figure 1 : Construction of product code 9 =fl 6 f2 It is shown [4] that the (nl - kl) last rows of the matrix are code words of t2 exactly as the ( n2 - k2) last columns are code words of t1 by construction. The parameters of the resulting product code 9 are given by n = nl x n 2 , k = kl x k 2 , 6=61 x62 and the code rate R is given by R = R1 x R2 where Ri is the code rate of code ti.