We characterize the secrecy capacity region of a fast Fading Binary 2-user Z-Interference Channel (FBZIC), assuming that only the Statistical Channel State Information is available at the Transmitters (S-CSIT). The converse is proved by constructing a new channel which is stochastically stronger than both the direct and cross-links emerging from the interfering transmitter. We also show that a capacity optimal code for a point-to-point binary erasure channel can be used at the non-interfering transmitter, a secrecy capacity optimal code for a binary erasure wiretap channel can be used at the interfering transmitter, and received signals can be decoded treating interference as erasure, to achieve all the secrecy rate pairs within the secrecy capacity region of the FBZIC. It turns out that the secrecy capacity region is a trapezoid and we explicitly characterize its corner points in terms of erasure probabilities of the various links of the channel. Comparing it with the capacity region of a fast fading no-secrecy binary 2-user ZIC, we quantify the loss due to the additional secrecy constraint. Our results reveal that, when the non-interfering user operates at its maximum rate, the interfering user cannot operate at a non-zero secrecy rate.

We consider a fast fading 2-receiver Broadcast channel (BC), where one of the receivers is legitimate and the other is malicious/unintended. The instantaneous Channel State Information (CSI) is assumed to be known only at the receivers (CSIR). The secrecy capacity of this channel is characterized within 11 bits irrespective of fading statistics and Signal-to- Noise Ratios (SNRs). This is achieved by deriving a new upper bound to the secrecy capacity of the channel and two new lower bounds. The upper bound is derived by approximating Complementary Cumulative Distribution Functions (CCDFs) of the two links by corresponding staircase functions and has the desirable property of easy computability for arbitrary fading statistics. The smaller lower bound, although looser, has a form which can be analytically compared with the upper bound and facilitates the approximate secrecy capacity characterization. It is proved that, the so called Binary Expansion Signaling with Reverse Stripping (BES-RS) scheme can achieve a secrecy rate larger than both these lower bounds. This result establishes BES-RS scheme as a practically implementable coding scheme that can achieve the secrecy capacity of the FWC within a constant number of bits, where the constant is universal across all fading statistics and SNR. Explicit numerical computation of these bounds shows that the difference between the secrecy rate achievable by the BES-RS scheme and the upper bound is much smaller than the aforementioned universal constant. This in turn suggests that, much of the gap of 11 bits originates from the looseness introduced to bring the two bounds in a compatible form.

We characterize the generalized degrees of freedom (GDoF) region of an ergodic fading 2-user interference channel (IC) with multiple antennas at each node (MIMO) under the assumption that the channel realizations are known only at the receivers and not at the transmitters (No CSIT). We consider the weak interference scenario where the ratio - denoted by α - of the signal strength of the interfering links to that of the corresponding direct links in dB scale is assumed to be smaller than half. Assuming that transmitters and receivers have Mi, M2and N1, N2, antennas respectively, except from a small class where (M2+ N2) > min{M1, N1} > N2> M2, we characterize the GDoF region of the weak IC for all other antenna configurations. We derive newer outer bounds to the GDoF which enable us bypass the use of full CSIT GDoF bounds as outer bounds for the No-CSIT scenario and therefore has the potential to be useful for analyzing other networks for which full-CSIT GDoF characterization is not available. The achievability of these upper bounds are then proved specifying explicit coding-decoding schemes.

We characterize the secrecy capacity region of a Layered Erasure 2-user Z interference channel (LEZIC) with arbitrary distribution for the numbers of layers that gets erased on any particular link. It is assumed that the instantaneous channel state information (CSI), i.e., the number of surviving layers on any particular link is available only at the receivers. We prove the capacity result in two steps; In the first step, we show that a polygon with one vertex at origin and two sides coinciding with the rate axes contains the secrecy capacity region of the LEZIC. Characterization of this polygon involves defining an intermediate enhanced channel. In the second step, we prove that all the non-zero vertexes of the aforementioned polygon can be achieved by point-to-point coding by the non-interfering transmitter and decoding its message at the interfered receiver by treating interference as erasure. The interfering transmitter on the other hand, sends Bernoulli i.i.d. bits only at layers that have a better chance of reaching the desired receiver than the interfered receiver.

The generalized diversity-multiplexing tradeoff (GDMT) of the two-user, quasi-static fading, multi-input, multi-output (MIMO) Z interference channel (Z-IC) is established for the general case with an arbitrary number of antennas at each node under the assumptions of full channel state information at the transmitters (CSIT) and a short-term average power constraint. In the GDMT framework, which captures the rate versus reliability tradeoff in the high signal-to-noise ratio (SNR) regime, the direct link SNR and cross-link interference-to-noise ratio (INR) are allowed to be disparate, so that their ratios relative to a nominal SNR in the decibel scale, i.e., the SNR and INR exponents, are arbitrary and fixed. It is shown that a simple Han-Kobayashi message-splitting/partial interference decoding scheme that uses only partial CSIT-in which the second transmitter's signal depends only on its cross-link channel matrix and the first user's transmit signal does not need any CSIT-can achieve the full-CSIT GDMT of the MIMO Z-IC. The GDMT of the MIMO Z-IC under the No-CSIT assumption is also obtained for some range of multiplexing gains. The size of this range depends on the numbers of antennas at the four nodes and the SNR and INR exponents of the direct and cross links, respectively. For certain classes of channels including those in which the interfered receiver has more antennas than do the other nodes, or when the INR exponent is greater than a certain threshold, the GDMT of the MIMO Z-IC under the No-CSIT assumption is also completely characterized.

The diversity multiplexing-gain tradeoff (DMT) of a Rayleigh faded relay network (RN) with a single source-destination pair and n half-duplex relay nodes, all with single antennas, is characterized and shown to be equal to the DMT of an (n + 1) × 1 MISO point-to-point channel. Further, it is shown that the quantize map-and-forward (QMF) scheme with fixed, channel independent scheduling for the relays can achieve the fundamental DMT of the RN. An interesting consequence is that the DMT of the RN can be achieved without any channel state information (CSI) at the relay nodes.

The capacity region of the two-user multi-input multioutput (MIMO) Gaussian interference channel (IC) is characterized to within a constant gap that is independent of the channel matrices for the general case of the MIMO IC with an arbitrary number of antennas at each node. An achievable rate region and an outer bound to the capacity region of a class of interference channels were obtained in previous work by Telatar and Tse as unions over all possible input distributions. In contrast to that previous work on the MIMO IC, a simple and an explicit achievable coding scheme are obtained here and shown to have the constantgap-to-capacity property and in which the sub-rates of the common and private messages of each user are explicitly specified for each achievable rate pair. The constant-gap-to-capacity results are thus proved in this work by first establishing explicit upper and lower bounds to the capacity region. A reciprocity result is also proved which is that the capacity of the reciprocal MIMO IC is within a constant gap of the capacity region of the forward MIMO IC.

The generalized multiplexing gain region (GMGR) of the slow-fading MIMO interference channel is obtained under the assumption of perfect channel state information at the transmitters (CSIT) in the general case where there are an arbitrary number of antennas at each of the four nodes. It is shown that a simple Han-Kobayashi (HK) linear Gaussian superposition coding scheme with a public/private message split at each transmitter can achieve the GMGR of the channel if the covariance matrices associated with the private and public sub-message codewords at each transmitter are certain functions of the null-space of the respective cross-link channel matrix. Moreover, in such a coding scheme, the multiplexing gains of the sub-messages can be chosen without any CSIT. Building on this result, and with Miand Nidenoting the numbers of transmit and receive antennas at the ithtransmitter and receiver, respectively, it is shown that at transmitter i an approximate version of the associated null-space expressed in terms of Nj(Mi-Nj)+log(INRij) bits per channel realization is sufficient to achieve the perfect CSIT GMGR of the channel, where INRijis the interference-to-noise ratio at receiver j. Furthermore, under the assumption of no CSIT, the GMGR is characterized for two sub-classes of MIMO ICs.

The fundamental diversity-multiplexing tradeoff of the three-node, multi-input, multi-output (MIMO), quasi-static, Rayleigh faded, half-duplex relay channel is characterized for an arbitrary number of antennas at each node and in which opportunistic scheduling (or dynamic operation) of the relay is allowed, i.e., the relay can switch between receive and transmit modes at a channel dependent time. In this most general case, the diversity-multiplexing tradeoff is characterized as a solution to a simple, two-variable optimization problem. This problem is then solved in closed form for special classes of channels defined by certain restrictions on the numbers of antennas at the three nodes. The key mathematical tool developed here that enables the explicit characterization of the diversity-multiplexing tradeoff is the joint eigenvalue distribution of three mutually correlated random Wishart matrices. Besides being relevant here, this distribution result is interesting in its own right. Previously, without actually characterizing the diversity-multiplexing tradeoff, the optimality in this tradeoff metric of the dynamic compress-and-forward protocol based on the classical compress-and-forward scheme of Cover and El Gamal was shown by Yuksel and Erkip. However, this scheme requires global channel state information at the relay. In this paper, the so-called quantize-map and forward (QMF) coding scheme is adopted as the achievability scheme with the added benefit that it achieves optimal tradeoff with only the knowledge of the (channel dependent) switching time at the relay node. Moreover, in special classes of the MIMO half-duplex relay channel, the optimal tradeoff is shown to be attainable even without this knowledge. Such a result was previously known only for the half-duplex relay channel with a single antenna at each node, also via the QMF scheme. More generally, the explicit characterization of the tradeoff curve in this study enables the in-depth comparisons herein of full-duplex versus half-duplex relaying as well as static versus dynamic relaying, both as a function of the numbers of antennas at the three nodes.

The generalized degrees of freedom (GDoF) region of the MIMO Gaussian interference channel (IC) is obtained for the general case of an arbitrary number of antennas at each node and where the signal-to-noise ratios (SNRs) and interference-to-noise ratios vary with arbitrary exponents to a nominal SNR. The GDoF-optimal coding scheme involves message splitting and partial interference decoding and consists of linear Gaussian superposition coding of the private and common submessages that can be seen as jointly performing signal-space and signal-level interference alignment. The admissible degree of freedom (DoF)-splits between the private and common messages are also specified. A study of the GDoF region reveals various insights through the joint dependence of optimal interference management techniques at high SNR on the SNR exponents and the numbers of antennas at the four terminals. For instance, it reveals that, unlike in the scalar IC, treating interference as noise is not always GDoF-optimal even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beamforming and time sharing is not GDoF optimal (and thus has an unbounded gap to capacity), the precise characterization of the very strong interference regime-where single-user DoF performance can be achieved simultaneously for both users-depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the single-input single-output case. For asymmetric numbers of antennas at the four nodes, the shape of the symmetric GDoF curve can be a “distorted W” curve to the extent that for certain multiple-input multiple-output ICs it is a “V” curve.

The capacity region of the 2-user multi-input multi-output (MIMO) Gaussian interference channel (IC) is characterized to within a constant gap that is independent of the signal-to-noise ratio (SNR) and all channel parameters. The general MIMO IC is considered with an arbitrary number of antennas at each node. For a class of MIMO ICs characterized by the relation between the numbers of antennas at the different nodes this gap is strictly smaller than the gap in a previous result obtained by Telatar and Tse. For instance, the gap for the SIMO IC with single antenna transmitters and N-antenna receivers obtained here is 1 bit, instead of N bits. Moreover, a simple (or universal) and an explicit achievable coding scheme are given here that have the constant-gap-to-capacity property. Consequently, explicit upper and lower bounds to the capacity region are obtained. A reciprocity result is also proved which is that the capacity of the reciprocal MIMO IC is within a constant gap of the capacity region of the forward MIMO IC.

The generalized degrees of freedom (GDoF) region of the MIMO Gaussian interference channel is obtained for the general case with an arbitrary number of antennas at each node and where the SNR and interference-to-noise ratios (INRs) vary with arbitrary exponents to a nominal SNR. The GDoF region reveals various insights through the joint dependence of optimal interference management techniques at high SNR on the SNR exponents that determine the relative strengths of direct-link SNRs and cross-link INRs and the numbers of antennas at the four terminals. For instance, it permits an in-depth look at the issue of rate-splitting and partial decoding at high SNR and it reveals that, unlike in the SISO case, treating interference as noise is not GDoF optimal always even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beam-forming and time-sharing is not GDoF optimal (and thus has an unbounded gap to capacity) the precise characterization of the very strong interference regime, where single-user DoF performance can be achieved simultaneously for both users, depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the SISO case. For asymmetric numbers of antennas at the four nodes the shape of the symmetric GDoF curve can be a “distorted W” curve to the extent that for certain MIMO ICs it is a “V” curve.

The generalized degrees of freedom region (GDoF) of the multiple-input multiple-output (MIMO) interference channel (IC) is studied under the “no CSIT” assumption under which there is perfect channel state information (CSI) at the receivers and no CSI at the transmitters (CSIT). In the very weak interference regime, where the ratio of channel gains (in dB) of the interfering and direct links, α, is ≤ 0.5, the GDoF regions are characterized for the two classes of the MIMO ICs defined by (a) M1= N1>; M2≥ N2and (b) M1= N1>; N2>; M2(where Miis the number of antennas at transmitter i and Niis the number of antennas at receiver i, i ∈ {1, 2}). In particular, inner-bounds are obtained by developing CSI-independent coding schemes using which it is shown that for each of the two classes a significant portion of the perfect-CSIT GDoF region can be achieved even without CSIT. Furthermore, tight outer-bounds to the no-CSIT GDoF regions are obtained that simultaneously account for the interference encountered by both the receivers. These bounds are thus fundamentally different from those derived in earlier works which deal with the case of α = 1, i.e., the degrees of freedom (DoF) regions. Interestingly, it is found that the loss of DoFs due to lack of CSIT is much less pronounced for the α ≤ 1 over 2 than it is for α = 1.

It is well known that the space-time block codes (STBCs) from complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD). The weight matrices of the square CODs are all unitary and obtainable from the unitary matrix representations of Clifford Algebras when the number of transmit antennasnis a power of 2. The rate of the square CODs forn= 2ahas been shown to be [(a+1)/(2a)] complex symbols per channel use. However, SSD codes having unitary-weight matrices need not be CODs, an example being the minimum-decoding-complexity STBCs from quasi-orthogonal designs. In this paper, an achievable upper bound on the rate of any unitary-weight SSD code is derived to be [(a)/(2a-1)] complex symbols per channel use for 2aantennas, and this upper bound is larger than that of the CODs. By way of code construction, the interrelationship between the weight matrices of unitary-weight SSD codes is studied. Also, the coding gain of all unitary-weight SSD codes is proved to be the same for QAM constellations and conditions that are necessary for unitary-weight SSD codes to achieve full transmit diversity and optimum coding gain are presented.

The diversity-multiplexing tradeoff of the dynamic decode-and-forward protocol is characterized for the half-duplex three-terminal (m,k,n)-relay channel where the source, relay and the destination terminals havem,kandnantennas, respectively. The tradeoff curve is obtained as a solution to a simple, two-variable, convex optimization problem which is explicitly solved in closed-form for certain special classes of relay channels, namely, the (1,k, 1) relay channel, the (n, 1,n) relay channel and the (2,k, 2) relay channel. Moreover, the tradeoff curves for a certain class of relay channels, such as the (m,k,n>;k) channels, are found to be identical to those for the decode-and-forward protocol for the full duplex channel while for other classes of channels they are marginally lower at high multiplexing gains. Our results also show that for some classes of relay channels and at low multiplexing gains the diversity orders of the dynamic decode-and-forward protocol are greater than those of the static compress-and-forward protocol which in turn is known to be tradeoff optimal over all static half duplex protocols. In general, the dynamic decode-and-forward protocol has a performance that is comparable to that of the static compress-and-forward protocol which, unlike the dynamic decode-and-forward protocol, requires global channel state information at the relay node. Its performance is also close to that of the decode-and-forward protocol over the full-duplex relay channel thereby indicating that the half-duplex constraint can be compensated for by the dynamic operation of the relay wherein the relay switches from the receive to the transmit mode based on the source-relay channel quality.

The diversity-multiplexing tradeoff (DMT) is obtained for the symmetric MIMO half-duplex (HD) relay channel where the source and the destination have n antennas each and the relay node has m antennas (hereafter, such a channel is referred to as an (n, m)-relay channel). The characterization of the DMT requires the joint eigenvalue distribution of three specially correlated central Wishart random matrices, which is derived using a related result in. The explicit characterization of the DMT, besides providing the theoretical benchmark for evaluating performance of practical cooperative protocols on this channel, reveals several interesting facts such as: a) the HD operation of the relay fundamentally limits relay channel performance in the sense that the DMT of the full-duplex (FD) relay channel can be strictly greater than that of the HD relay channel; b) an extra antenna at the relay node on a HD relay channel does not always improve the achievable diversity order, unlike that on an FD relay channel. While the fundamental DMTs of the two channels (FD and HD) coincide for a range of low multiplexing gains (MG), this range becomes smaller and the gap between the two (HD and FD) at higher MGs become larger with increasing number of antennas at the relay node, thus potentially justifying the extra cost of an FD relay. It is also proved that the DMTs of the HD and FD (n, 1)-relay channels are the same. Finally, it is shown that the DMT of the (1, m) relay channel can be achieved over different ranges of multiplexing gains by the dynamic decode-and-forward (DDF) and the quantize-and-forward (QF) protocols.

The fundamental diversity-multiplexing tradeoff (DMT) of the quasi-static fading, MIMO Z interference channel (ZIC), with M1and M2antennas at the transmitters and N1and N2antennas at the corresponding receivers, respectively, is derived. Channel state information at the transmitters (CSIT) and a short-term average power constraint is assumed. The achievability of the DMT is proved by showing that a simple Gaussian superposition coding scheme can achieve a rate region which is within a constant (independent of signal-to-noise ratio (SNR)) number of bits from an upper bound to the capacity region of the ZIC. We also characterize an achievable DMT of the ZIC with No-CSIT and show that in a small region of multiplexing gains (MG), the full CSIT DMT of the ZIC can be achieved with no CSIT at all. The size of this MG region depends on the system parameters such as the number of antennas at the four nodes (referred to hereafter as “antenna configuration”), SNRs and interference-to-noise ratio (INR) of the direct and cross links. Interestingly, for some antenna configurations this MG region covers the entire MG region of the ZIC. Thus, under these circumstances, the optimal DMT of the MIMO ZIC with F-CSIT is same as that of a corresponding ZIC with No-CSIT and availability of CSIT can not further improve the DMT. Finally, we identify a class of ZICs with M1= M2= M ≤ N1over 2, N1≤ N2and SNR ≤ INR where the achievable DMT with No-CSIT coincides with the optimal DMT with F-CSIT.

The fundamental diversity-multiplexing tradeoff (DMT) of the quasi-static fading, symmetric 2-user MIMO interference channel (IC) with channel state information at the transmitters (CSIT) and a short term average power constraint is obtained. The general case is considered where the interference-to-noise ratio (INR) at each receiver scales differently from the signal-to-noise ratio (SNR) at the receivers. The achievability of the DMT is proved by showing that a simple Han-Kobayashi coding scheme can achieve a rate region which is within a constant (independent of SNR) number of bits from a set of upper bounds to the capacity region of the IC. In general, only part of the DMT curve with CSIT can be achieved by coding schemes which do not use any CSIT (No-CSIT). A result in this paper establishes a threshold for the INR beyond which the DMT with CSIT coincides with that with No-CSIT. Our result also settles one of the conjectures made in. Furthermore, the fundamental DMT of a class of non-symmetric ICs with No-CSIT is also obtained wherein the two receivers have different numbers of antennas.

We compute the diversity-multiplexing tradeoff (DMT) curve for a three node multi-input-multi-output (MIMO) half-duplex (HD) relay network, operating in the dynamic decode-and-forward (DDF) mode. We consider the case where the source and the destination have n antennas each and the single relay node has m antennas. Denoting such a channel as a (n, m)-relay channel, we provide an analytical characterization of the DMT curve for certain simple configurations such as (n, 1), (1, m) and (2, 2). We employ a numerical method to compute the DMT for more general channel configurations. Interestingly, for low multiplexing gains the achievable diversity orders of the HD-DDF protocol coincides with the diversity orders achieved by the full-duplex decode-and-forward (FDDF) protocol analyzed in. In fact, the HD-DDF and FDDF protocols achieve the same diversity orders for all integer multiplexing gains. Thus, the half duplex constraint does not significantly affect the achievable DMT for the DF protocol when the source and the destination have the same number of antennas.

A space-time block code (STBC) inKsymbols (variables) is called ag-group decodable STBC if its maximum-likelihood (ML) decoding metric can be written as a sum ofgterms, for some positive integerggreater than one, such that each term is a function of a subset of theKvariables and each variable appears in only one term. In this paper, we provide a general structure of the weight matrices of multigroup decodable codes using Clifford algebras. Without assuming that the number of variables in each group is the same, a method of explicitly constructing the weight matrices of full-diversity, delay-optimal multigroup decodable codes is presented for arbitrary number of antennas. For the special case of2anumber of transmit antennas, we construct two subclass of codes: 1) a class of2a-group decodable codes with rate[(a)/(2(a-1))], which is, equivalently, a class of single-symbol decodable codes, and 2) a class of(2a-2)-group decodable codes with rate[((a-1))/(2(a-2))], i.e., a class of double-symbol decodable codes.

It is well known that space-time block codes (STBCs) obtained from orthogonal designs (ODs) are single-symbol decodable (SSD) and from quasi-orthogonal designs (QODs) are double-symbol decodable (DSD). However, there are SSD codes that are not obtainable from ODs and DSD codes that are not obtainable from QODs. In this paper, a method of constructingg-symbol decodable (g-SD) STBCs using representations of Clifford algebras are presented which when specialized tog=1,2 gives SSD and DSD codes, respectively. For the number of transmit antennas2athe rate (in complex symbols per channel use) of theg-SD codes presented in this paper is[(a+1-g)/(2a-g)]. The maximum rate of the DSD STBCs from QODs reported in the literature is[(a)/(2a-1)] which is smaller than the rate[(a-1)/(2a-2)] of the DSD codes of this paper, for2atransmit antennas. In particular, the reported DSD codes for 8 and 16 transmit antennas offer rates1and3/4, respectively, whereas the known STBCs from QODs offer only3/4and1/2, respectively. The construction of this paper is applicable for any number of transmit antennas. The diversity sum and diversity product of the new DSD codes are studied. It is shown that the diversity sum is larger than that of all known QODs and hence the new codes perform better than the comparable QODs at low signal-to-noise ratios (SNRs) for identical spectral efficiency. Simulation results for DSD codes at various spectral efficiencies are provided.

The low decoding complexity structure of Linear Dispersion Space Time Block Codes (LDSTBCs) with unitary weight matrices is analyzed. It is shown that given n = 2alpha, the maximum number of groups in which the information symbols can be separated and decoded independently is (2a + 2), and as we lower the number of different groups to (2k + 2), 0 les k les alpha, we get higher rate codes. We also find the analytic expression for rates that such codes can achieve for any chosen group number, thus completely characterizing the rate-ML-decoding-complexity tradeoff for this class of codes. The proof of the result also includes a method for constructing such optimal rate achieving codes. Interestingly, this analysis produces some low decoding complexity codes with rate greater than one.

For the number of transmit antennas N = 2athe maximum rate (in complex symbols per channel use) of all the Quasi-Orthogonal Designs (QODs) reported in the literature is a/2a-1. In this paper, we report double-symbol-decodable Space- Time Block Codes with rate a-1/2a-2for N = 2atransmit antennas. In particular, our code for 8 and 16 transmit antennas offer rates 1 and 3/4 respectively, the known QODs offer only 3/4 and 1/2 respectively. Our construction is based on the representations of Clifford algebras and applicable for any number of transmit antennas. We study the diversity sum and diversity product of our codes. We show that our diversity sum is larger than that of all known QODs and hence our codes perform better than the comparable QODs at low SNRs for identical spectral efficiency. We provide simulation results for various spectral efficiencies.

It is well known that Alamouti code and, in general, space-time block codes (STBCs) from complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes are obtainable from designs that are not CODs. Recently, two such classes of SSD codes have been studied: (i) coordinate interleaved orthogonal designs (CIODs) and (ii) minimum-decoding-complexity (MDC) STBCs from quasi-ODs (QODs). In this paper, we obtain SSD codes with unitary weight matrices (but not CODs) from matrix representations of Clifford algebras. Moreover, we derive an upper bound on the rate of SSD codes with unitary weight matrices and show that our codes meet this bound. Also, we present conditions on the signal sets which ensure full-diversity and give expressions for the coding gain

Space-time block codes (STBCs) from complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD); however, SSD codes are obtainable from designs that are not CODs. Recently, two such classes of SSD codes have been studied: (i) coordinate interleaved orthogonal designs (CIODs) and (ii) minimum-decoding-complexity (MDC) STBCs from quasi-ODs (QODs). The class of CIODs have non-unitary weight matrices when written as a linear dispersion code (LDC) proposed by Hassibi and Hochwald, whereas the other class of SSD codes including CODs have unitary weight matrices. In this paper, we construct a large class of SSD codes with non-unitary weight matrices. Also, we show that the class of CIODs is a special class of our construction