Chase Decoding for Space-Time Codes David J. Love School of Electrical and Computer Engr. Purdue University West Lafayette, IN 47907 djlove@ecn.purdue.edu Srinath Hosur and Anuj Batra DSPS R&D Center Texas Instruments Dallas, TX {hosur, batra}@ti.com Robert W. Heath, Jr. Dept. of Electrical and Computer Engr. The University of Texas at Austin Austin, TX 78712 rheath@ece.utexas.edu Abstract— Multiple antenna wireless systems are known to provide a higher capacity than traditional single antenna systems. Over the past few years, space-time signaling schemes that make use of this increased capacity have been studied. Because of the large capacity of multiple-input multiple-output channels, the multidimensional constella- tions used by these space-time techniques are large in size making it impractical to perform optimal maximum like- lihood decoding even for a moderate number of transmit antennas. In this paper, we propose a space-time version of the binary Chase decoder. The decoder generates an initial estimate of the transmitted bit sequence from successive detection and then uses this bit estimate to generate a reduced search space (or list) to perform minimum distance decoding. Three algorithms for constructing the space-time reduced search space are overviewed. I. I NTRODUCTION Multiple-input multiple-output (MIMO) wireless sys- tems, which use multiple antennas at the transmitter and receiver, provide substantial gains in capacity compared to single antenna systems. As well, MIMO systems can offer an increase in diversity, the rolloff factor of the probability of error curve on a log-log scale. To achieve maximum diversity advantage, space-time transmission techniques must be optimally decoded [1], [2]. Unfortunately, the optimal decoder complexity of most space-time signaling methods grows exponentially with the number of transmit antennas. Thus maximum likelihood (ML) decoding is often impractical even for a modest number of transmit antennas. Several reduced complexity decoding schemes have been proposed to solve this implementation problem. Because most space-time transmission is based on the idea of transmitting multiple substreams (see for example spatial multiplexing [3], [4]), multiuser communication receivers can be employed by thinking of each substream as a user and the intereference between substreams as interference between users. Successive detection tech- niques (see [3]–[5], etc.) avoid computationally expen- sive joint detection by detecting and then cancelling the effect of each substream. Unfortunately, the bit error rate performance of successive detection schemes is inferior to that provided by ML decoding. Sphere decoding [6]– [8] is a low complexity symbol decoding technique that provides performance close to that of ML symbol decoding by performing minimum distance decoding over a small number of symbol vectors that fall within a metric ball around the received signal vector. The sphere decoder, however, has several serious problems that make its implementation challenging. First, the optimal ML vector within the metric ball might be the first or last vector searched meaning that the worst case complexity of the sphere decoder is always equal to that of ML decoding. Second, there is no simple algorithm for choosing the sphere radius. As well, a list- based sphere decoder must be used to allow the sphere decoding algorithm to generate the log-likelihood, or soft bit, information that is critical to error control codes [8], [9]. In this paper, we propose space-time Chase (ST Chase) decoding for MIMO wireless systems as a solu- tion to the MIMO decoding problem. ST Chase decoding is a modification of existing successive detection de- coders that operates in two-stages: successive detection and reduced search space ML decoding. We design our decoder to attempt to minimize the raw (uncoded) bit error rate by refining, in some sense, the initial bit estimates returned from the successive detection decoder. The initial bit estimate is used to generate a list of candidate symbol vectors over which minimum distance decoding can be performed. We present three differ- ent algorithms for constructing these candidate symbol vectors based on the binary block decoding algorithms proposed in Chase’s famous work [10]. The ST Chase- 1 decoding algorithm performs maximum likelihood de- coding on symbol vectors corresponding to bit sequences lying in a predetermined radius Hamming ball around an initial estimate of the transmitted bit sequence. The second decoding algorithm, known as the ST Chase- 2 decoder, uses soft bit information from a successive detection stage to construct a reduced search space