Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2011, Article ID 653506, 9 pages doi:10.1155/2011/653506 Research Article Full-Diversity Space-Time Error Correcting Codes with Low-Complexity Receivers Mohamad Sayed Hassan and Karine Amis Signals and Communications Department, TELECOM Bretagne, 29238 BREST, France Correspondence should be addressed to Mohamad Sayed Hassan, mohamad-sayed@hotmail.com Received 3 August 2010; Revised 9 November 2010; Accepted 11 January 2011 Academic Editor: Wolfgang H. Gerstacker Copyright © 2011 M. S. Hassan and K. Amis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We propose an explicit construction of full-diversity space-time block codes, under the constraint of an error correction capability. Furthermore, these codes are constructed in order to be suitable for a serial concatenation with an outer linear forward error correcting (FEC) code. We apply the binary rank criterion, and we use the threaded layering technique and an inner linear FEC code to define a space-time error-correcting code. When serially concatenated with an outer linear FEC code, a product code can be built at the receiver, and adapted iterative receiver structures can be applied. An optimized hybrid structure mixing MMSE turbo equalization and turbo product code decoding is proposed. It yields reduced complexity and enhanced performance compared to previous existing structures. 1. Introduction Space-time block (STB) code designs have recently attracted considerable attention, since they improve the reliability of communication systems over fading channels. Tarokh et al. [1] developed some criteria for designing STB codes (for the high SNR regime), in order to minimize the pairwise error probability. Among the resulting proposed schemes (based on these criteria), orthogonal space-time block (OSTB) codes, introduced by Alamouti [2] and generalized by Tarokh et al. [3], are attractive due to their low optimal decoding complexity. Their practical use is limited to the Alamouti scheme (two transmit antennas) as their rate decreases rapidly with an increase in the number of transmit antennas, and they cannot achieve the MIMO system capacity. Hassibi and Hochwald proposed the linear dispersion codes (LDCs) [4] that maximize the mutual information between transmit- ted and received signals in order to achieve the maximum ergodic capacity of the equivalent MIMO system. Then full rate and full diversity STB codes were designed. The application of the threaded layering principle yielded the threaded algebraic space-time (TAST) codes [5]. Belfiore et al. added a nonvanishing determinant constraint [6–8] to achieve the optimal diversity/multiplexing tradeoff [9] and defined the perfect space-time block codes [10, 11]. However, in any transmission system the forward error correction coding is used in conjunction with interleaving. All the above STB codes deal with the forward error correct- ing code as an independent entity of the transmitter scheme. A joint design of FEC, modulation, and space-time scheme was considered in [1], in order to construct the space-time trellis codes (STTCs) that provide maximum diversity and maximum coding gain. STTCs exhibit higher coding gains than STB codes, but due to their trellis nature, the optimal decoding has a high computational cost incompatible with a practical implementation. An interesting method to design full diversity space- time block codes with an error correction capability has been developed in [12–14]. In the current paper, these codes are referred as space-time error correcting codes (STECCs) in order to stress on their ability to correct errors due to the transmission. We name also concatenated STECC the serial concatenation of a STECC and an outer linear FEC code. In [12], a binary rank criterion has been introduced in order to construct full diversity STECCs for binary phase shift keying (BPSK) modulation. A generalization of this