Soft Decision Decoding of Reed-Solomon Product Codes

Reed-Solomon codes are a class of non-binary cyclic codes which have strong burst and erasure error correction capabilities. Their current uses include deep-space communications, compact disc recordings, cellular communications, and digital broadcast[1]. Their popularity stems in part from the existence of encoding and decoding algorithms that are simple to implement in hardware. In addition to their practical uses, these codes also have a nice theoretical structure for proving the feasibility of certain coding and storage schemes [2] [3]. Product codes are a method for constructing longer codes from shorter component codes. The information symbols can be thought of entering the encoder as a 2-dimensional array as shown in Figure 1 [4]. The rows are first encoded individually according to a code C1 and then the columns of the result are encoded according to a code C2. If the codes C2 and C2 have minimum distances d1 and d2 respectively, then the product code has minimum distance d1d2. In this project, we investigate a very restricted class of product codes in which the row and column code are both Reed-Solomon codes. These Reed-Solomon Product Codes (RS-PC) are used in the encoding of data for DVDs. Much of the recent research about Reed-Solomon codes has come from a new approach to decoding Reed-Solomon codes, developed initially by Sudan [5]. These algorithms attempt to bridge the often significant gap between maximum likelihood (ML) decoding and previous algebraic decoding techniques. In particular, the recent result of Kötter and Vardy [6] allows soft-decision