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Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson , Kerdock, Preparata, Goethals, and Delsarte-Goethals. It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z 4 , the integers mod 4(More)
—The design of space–time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas. The lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband(More)
—In this paper, we introduce a simple technique for analyzing the iterative decoder that is broadly applicable to different classes of codes defined over graphs in certain fading as well as additive white Gaussian noise (AWGN) channels. The technique is based on the observation that the extrinsic information from constituent maximum a posteriori (MAP)(More)
—The availability of multiple transmit antennas allows for two-dimensional channel codes that exploit the spatial transmit diversity. These codes were referred to as space–time codes by Tarokh et al. Most prior works on space–time code design have considered quasi-static fading channels. In this paper, we extend our earlier work on algebraic space–time(More)
—The information-theoretic capacity of multiple antenna systems was shown to be significantly higher than that of single antenna systems in Rayleigh-fading channels. In an attempt to realize this capacity, Foschini proposed the layered space–time architecture. This scheme was argued to asymptotically achieve a lower bound on the capacity. Another line of(More)
—Recently, the authors introduced an algebraic design framework for space–time coding in flat-fading channels [1]–[4]. In this correspondence, we extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency(More)
The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre-parata codes are shown to be linear over Z 4 , the integers mod 4. The Kerdock and Preparata codes are duals over Z 4 , and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over Z 4. This provides a simple definition for these codes and explains why their(More)
—This paper addresses the application of turbo codes for third-generation wireless services. It describes the specific characteristics of high-rate data applications in third-generation wide-band code-division multiple-access (CDMA) systems that make turbo codes superior to convolutional codes. In particular, it shows the positive effect of fast power(More)