Impact of the decoder connection schemes on iterative decoding of GPCB codes Fouad Ayoub, Mohammed Lahmer, Mostafa Belkasmi, and El Houssine Bouyakhf Abstract—In this paper we present a study of the impact of connection schemes on the performance of iterative decoding of Generalized Parallel Concatenated block (GPCB) constructed from one step majority logic decodable (OSMLD) codes and we propose a new connection scheme for decoding them. All iterative decoding connection schemes use a soft-input soft-output threshold decoding algorithm as a component decoder. Numerical result for GPCB codes transmitted over Additive White Gaussian Noise (AWGN) channel are provided. It will show that the proposed scheme is better than Hagenauer’s scheme and Lucas’s scheme [1] and slightly better than the Pyndiah’s scheme. Keywords—Generalized Parallel concatenated block codes, OSMLD codes, threshold decoding, iterative decoding scheme, and performance. I. I NTRODUCTION T HE decoding process of turbo codes is a suboptimal iterative processing in which each component decoder takes advantage of the extrinsic information produced by the other component decoder at the previous step. The way the extrinsic information is conveyed and how it is exploited by the component decoders to make their decision has not been closed yet. The original works in this context are due to Berrou [2] and Robertson [3] for convolutional codes, Pyndiah [4] and Lucas [5] for block codes. Hagenauer [6] gave an extrapolation of Robertson’s scheme for block codes by using a trellis decoder. In this work the impact of the connection scheme on the performance of iterative decoding of Generalized Parallel Concatenated block codes (GPCB) [1] constructed from OSMLD codes is considered. These codes have proven to be a very good performance. On the other hand we will use the same component decoder for all schemes namely soft-in soft-out threshold algorithm [7] with a slight modification. The organization of the paper is as follows. In Section II, we start with a description of the basic concept GPCB codes, and then we describe the soft-in soft-out decoding algorithm in section III. The connection schemes studied in this work are given in Section IV. Section V is dedicated to simulation results and analysis for different GPCB-OSMLD codes. Section VI concludes this paper. F. Ayoub is with Faculty of Sciences, University Mohamed V Agdal, Rabat, Morocco. ayoubfouadn@gmail.com. M. Lahmer is with High School of Technology, Moulay Ismal University, Meknes, Morocco. lahmer@est-umi.ac.ma. M. Belkasmi is with National School of Computer Science and Systems Analysis, Rabat, Morocco. belkasmi@ensias.ma. E. H. Bouyakhf is with Faculty of Sciences, University Mohamed V Agdal, Rabat, Morocco. bouyakhf@fsr.ac.ma. II. GPCB CODES A. One-step majority-logic decodable codes One step majority logic decodable codes are based on orthogonal parity check sums for each bit. We relied on the work of [8] to develop algorithm for constructing various codes shown in table I . In this table we present some examples, using the abbreviation DSC for Difference Set Cyclic codes, EG for Euclidean Geometry codes and BCH for Bose Chaudhuri and Hocquenghem codes. TABLE I SET OF OSMLD CODES. n k J Minimal distance Rate Code family 7 3 3 4 0.42 DSC 15 7 4 5 0.46 BCH 21 11 5 6 0.52 DSC 63 37 8 9 0.58 EG 73 45 9 10 0.61 DSC 255 175 16 17 0.68 EG 273 191 17 18 0.69 DSC 1023 781 32 33 0.76 EG 1057 813 33 34 0.76 DSC 4161 3431 65 66 0.82 DSC B. Structure of GPCB codes The structure of generalized parallel concatenated block codes is shown in figure 1; it was introduced independently by Nilson et al [9] and Benedetto et al [10]. A block of N data bits at the input of the GPCB encoder is subdivided into M sub-blocks. Each sub-block of length k is encoded using a component encoder in order to produce parity check bits. The input block is scrambled by the interleaver, denoted by Π , before entering the second encoder. The codeword of GPCB code consists of the input block followed by the parity check bits of both encoders. A systematic GPCB code is based on two systematic block component codes, C 1 with parameters (n 1 ,k), and C 2 with parameters (n 2 ,k). The length of the information word to be encoded by the GPCB code is given by the size of the interleaver N = M × k. The first encoder produces P 1 = M × (n 1 − k)= M × p 1 parity check bits. The second encoder produces P 2 = M × (n 2 − k)= M × p 2 parity check bits. Thus the total number of parity bits generated by the GPCB encoder is P = P 1 + P 2 = M × (n 1 + n 2 − 2 × k). The length of the GPCB codeword is given by L = N + P = M × (n 1 + n 2 − k). Consequently, the World Academy of Science, Engineering and Technology 37 2010 876