International Symposium on Information Theory and its Applications, ISITA2008 Auckland, New Zealand, 7-10, December, 2008 Hybrid ARQ for Non-Orthogonal Space-Time Block Codes Rui Lin, Philippa A. Martin Department of Electrical and Computer Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand E-mail:{rli24@student, p.martin@elec}.canterbury.ac.nz Abstract We propose a novel hybrid automatic repeat-request (HARQ) scheme for non-orthogonal space-time block codes based on BCH and Reed Solomon codes. We use list decoding techniques to significantly reduce the decoding complexity. We obtain significant gains in terms of dropped packet rate and throughput spectral efficiency at the cost of increased complexity. 1. Introduction Modern wireless communication networks typically transmit information in a packet by packet fashion. A packet is declared dropped if it still contains errors after the maximum allowed number of transmissions, m max . Automatic-repeat-request (ARQ) schemes can be used to improve the dropped packet rate (DPR) at the cost of throughput spectral efficiency (TSE). In order to maintain high spectral efficiency, the average number of transmissions for each packet needs to be minimized and the code rate needs to be maximized. This requires the use of powerful high rate codes. Space-time codes (STCs) are an effective way to combat fading. Most existing hybrid ARQ (HARQ) schemes designed for STCs use an error control code, such as a convolutional [1] or turbo [2] code. The en- coded packets are then transmitted using BPSK and/or an orthogonal space-time block code (OSTBC) [3], which limits the achievable spectral efficiency. The non-OSTBCs (NOSTBCs) of [4] allow much higher rates and obtain significant coding gains com- pared to OSTBCs at the cost of increased decoding complexity. In this paper, we design a HARQ scheme for these NOSTBCs and a list decoding algorithm to reduce the resulting decoding complexity. This list de- coding algorithm can be applied to other HARQ schemes. 2. System Description We consider a MIMO system with n t transmit and n r receive antennas. We assume a quasi-static channel model and so the same n r × n t channel matrix, H, is used for an entire frame. We assume it varies indepen- dently for each transmission/ frame. The n r × T frame baseband received signal matrix corresponding to the transmission of a frame of T frame time slots is given by Y = HX + N, (1) where X is the n t ×T frame transmitted matrix and N is the n r × T frame additive white Gaussian noise matrix. Each element of H, h j,i , is an independent identically distributed (i.i.d.) complex Gaussian random variable with zero mean and variance 0.5 per dimension, repre- senting the channel coefficient between the j th receive and i th transmit antenna. Each element of N is an i.i.d. complex Gaussian random variable with zero mean and variance N 0 /2 per dimension. Here we focus on the design of HARQ schemes for the NOSTBCs of [4]. The NOSTBCs are encoded us- ing a (n, k) eRS/BCH code, where n is the number of encoded symbols, k is the number of data symbols and the code’s symbols are defined over GF (q), q =2, 4, 16. In the GF (16) case, the binary information bits are mapped to GF (16) symbols (0, 1, ··· , 15) and every k symbols are encoded to generate an eRS codeword. The encoded symbols are mapped to 16-QAM as [4] 0 8 5 15 14 1 9 4 7 13 2 10 11 6 12 3 (2) After this mapping, the constellation points chosen by each codeword are written into the NOSTBC matrix column by column. Therefore, there is a one to one mapping between NOSTBC matrices and eRS/BCH codewords. The NOSTBC decoder picks the codeword with smallest squared Euclidean distance using [4] ˆ X k = arg min {Xo} kτ  t=(k−1)τ +1 nr  j=1      y j,t − nt  i=1 h j,i x i,t      2 , k =1, 2, ··· ,T frame /τ, (3) Authorized licensed use limited to: University of Canterbury. Downloaded on June 14,2010 at 09:19:25 UTC from IEEE Xplore. Restrictions apply.