In this study, a fair user‐scheduling method is considered for an underlay cognitive radio system, in which the secondary users (SUs) are sharing the licenced frequency spectrum of a single primary user (PU), where the PU and SUs utilise Alamouti orthogonal space‐time block coding (OSTBC). The impacts of some important practical issues are investigated in the system. First, it is assumed that the signal‐to‐noise‐ratios of the SUs are independent non‐identically distributed. Second, the transmit antennas for OSTBC corresponding to the SUs are assumed to be equally correlated. Third, the interference from the PU to SUs as well as the interferences from SUs to the PU are taken into consideration. To investigate the outage performance of the SUs, a closed‐form expression for the cumulative distribution function of the SUs signal‐to‐interference‐noise‐ratio is obtained and then used to derive an expression for evaluating the secondary system outage performance. The numerically evaluated results, validated by computer simulations, provide insights about system outage performance under various practical situations on the impacts of the spatial antennas correlation and the PU interference on to SUs.

This study presents an analysis for evaluating the physical layer (PHY) security performance of a two‐hop amplify‐and‐forward cooperative relaying system employing Alamouti orthogonal space–time block coding (OSTBC) in the presence of an eavesdropper, where the transmit antennas for OSTBC are assumed to be spatially correlated. It is also assumed that the authorised main channels as well as the non‐authorised eavesdropper channels follow Rayleigh fading distribution. Closed‐form mathematical expressions are derived for three performance metrics for evaluating the PHY security, namely the probability of non‐zero secrecy capacity, the secrecy outage probability, and the average secrecy capacity. Using the extensive numerical results obtained from the derived mathematical expressions, the impact of antennas correlation on the PHY secrecy performance of the system is studied and evaluated under different parameters. It is also shown that the antennas correlation corresponding to the main channels has more impact than the antennas correlation corresponding to the eavesdropper channels.

This study presents a performance analysis for a cognitive radio network with multi‐user scheduling in which a primary user can share its licenced spectrum with several secondary users (SUs), each employing Alamouti orthogonal space‐time block coding (OSTBC) with spatially correlated antennas over Rayleigh fading channels. Closed‐form formulae are obtained for the cumulative density function of the signal‐to‐noise‐ratio of SUs with multi‐user scheduling under correlated antennas. Closed‐form mathematical expressions are then derived for three important system performance metrics: the average channel capacity, outage probability, and the average bit error rate of the system. From the numerical results obtained from the derived mathematical expressions, the system performances with different parameters are studied, evaluated and compared showing the effects of spatial correlation on the performance of the system. It is observed that spatially correlated antennas can improve the average channel capacity of the cognitive radio system with user scheduling.

In this paper, we investigate the achievable rate and the average sum capacity of an underlay cognitive radio (CR) (also known as a secondary) system. We consider single user (SU) and multiple users (MU) secondary systems that deploy spread spectrum as the signaling technique which utilizes the whole available spectrum. The objective is to maximize the achievable rate and the average sum capacity of the SU and MU secondary systems, respectively, by allocating the optimum power to the secondary transmitter(s) (STs), such that the instantaneous (aggregate) interference power from STs is below a certain threshold at the primary receiver (PR), to guarantee the quality of service (QoS) of the primary system. Numerical and Monte-Carlo Simulation results show that the achievable rate of the SU system and the average sum capacity of the MU system can be enhanced significantly compared to other signaling techniques, because of the fact that in spread spectrum the signal's power is spread over a wider bandwidth, which gives the secondary system more freedom to allocate power to enhance the data rate.

In this study, the authors analyse the impact of spatial correlation on the average bit error‐rate (BER) performance of amplify‐and‐forward cooperative relay networks employing Alamouti orthogonal space‐time block coding (OSTBC) over Rayleigh fading channels. Closed‐form expressions are derived for the moment generating function of the total signal‐to‐noise‐ratio (SNR). The authors then obtain closed‐form expressions for the average BER of the system as well as asymptotic expressions for the average BER at high SNRs. To quantify the effects of antenna correlation on the system performance, numerical results are provided and compared for different cases.

This study analyses the impact of antenna correlation on orthogonal space–time block coding in amplify‐and‐forward cooperative relay networks in conjunction with different adaptive transmission techniques over Rayleigh fading channels. Closed‐form expressions are derived for the cumulative distribution function, and probability distribution function of the total signal‐to‐noise ratio. For each considered adaptive transmission technique, the authors derive closed‐form expressions for the average channel capacity, outage probability, average spectral efficiency and the average bit error rate of the system. Using numerical evaluations, the performances for different cases are compared in order to evaluate and quantify the effects of spatial correlation on the system performance.

Cognitive radio (CR) systems allow unlicensed secondary users to transmit on the licensed frequency bands without degrading the transmissions of licensed primary users. Combining CR with other emerging techniques such as multi‐antenna relaying may bring many benefits for the secondary transmissions. In this study, the authors propose and investigate a new relay‐based cooperation scheme for a CR network to improve the secondary access to the licensed spectrum band without causing additional interference to the simultaneous primary transmission. The proposed scheme considers one multi‐antenna relay node that can assist either the primary or the secondary transmission using beam‐forming (BF). In the proposed new scheme, the BF weights are designed in the presence of imperfect channel state information (CSI). Simulation results show that the secondary's channel capacity is significantly improved and outperforms conventional transmission schemes. The results also reveal the impact of imperfect CSI on the primary outage performance and the efficiency of the proposed solution for minimising the interference due to imperfect CSI.

Finding optimal/short-span Convolutional Self-Doubly Orthogonal (CDO) codes and Simplified-CDO (S-CDO) codes for a specified order J is computationally very challenging. This paper describes several optimizations that were applied to an implicitly-exhaustive search algorithm in order to reduce the time required for finding these types of codes. The resulting high-performance parallel implementation provides an impressive speedup that is greater than 16 300 (CDO,${\rm J} = 7$) and 6300 (S-CDO,${\rm J} = 8$) over the reference implicitly-exhaustive search algorithm, and greater than 2000$({\rm J} = 17)$over the fastest published CDO validation function used in high-performance pseudorandom search algorithms. These speedups are achieved through enhancements in the deterministic search-space reduction, and a vastly improved validation function that makes use of a novel data structure for enabling data-reuse and incremental computations. The resulting validation function speedup is greater than 60 000 (S-CDO,${\rm J} = 17$) and 190 000 (CDO,${\rm J} = 17$) when compared to its reference implementation. The combination of optimizations and load-balancing techniques allowed us to leverage hundreds of processor cores in order to complete an exhaustive search over a search space that is some$10^{14}$times larger than what was previously possible.

In this paper, we examine the problem of secondary access blocking in cognitive radio networks when secondary transmissions cause unacceptably high interference to primary transmissions. In general, the access of secondary users (SUs) to a licensed spectrum band is only allowed when this access does not alter the performance of primary users that can be defined by the primary QoS requirement. In this paper, we propose a cooperative scheme that allows SUs to increase their access to the spectrum band and access the spectrum even when the primary QoS is not satisfied. Using relay selection and a proper power allocation method, we show that the secondary outage performance can be significantly improved, whereas the primary outage performance is either not altered or slightly improved. Moreover, closed-form expressions of the primary and secondary outage probabilities are derived, and the achieved diversity order is calculated. Finally, analytical and simulation results illustrate the primary outage performance and secondary outage performance of the proposed scheme and show its advantages compared with conventional schemes.

ABSTRACT User cooperation has evolved as a popular coding technique in wireless relay networks (WRNs). Using the neighboring nodes as relays to establish a communication between a source and a destination achieves an increase of the diversity order. The relay nodes can be seen as a distributed multi‐antenna system, which can be exploited for transmit diversity by using distributed space–time block coding (STBC). In this paper, we investigate the bit error rate (BER) of multi‐hop WRNs employing distributed STBC at the relay nodes. We develop the general model of WRNs using distributed STBC, and we derive the pairwise error probability and an approximation of the BER. We examine the impact of several parameters, such as distributed STBC at the relays, the number of relays, the distances between the nodes, and the channel state information available at the receivers, on the BER performance of the multi‐hop WRN. The obtained results provide guidelines about the expected error performance and the design of channel estimation for these networks. Copyright © 2011 John Wiley & Sons, Ltd.

Secondary access to the licensed primary spectrum band at the same time as the primary nodes is generally conditioned on the satisfaction of a Quality-of-Service (QoS) requirement at the primary transmission (such as a Signal-to-Noise-Ratio -SNR- threshold or a primary outage probability threshold). Consequently, at low primary SNR that is below a cut-off value, secondary transmissions are totally blocked. In this paper, we propose a new cooperative scheme for cognitive radio networks, where secondary access to the primary spectrum band is granted whether or not the primary transmission satisfies its QoS requirement thanks to the utilization of secondary relay nodes. Using relay selection and proper power allocation at the secondary nodes, we show that the proposed scheme allows secondary access with low secondary outage performance without degrading the primary outage performance. We also compare the proposed scheme to other ones presented in the literature and we study the impact of the number of available relay nodes and the primary outage threshold value on the primary and secondary outage probabilities.

Cognitive radio (CR) systems allow unlicensed secondary users to transmit on the licensed frequency bands without degrading the licensed primary transmissions. Combining CR with other emerging transmission techniques, such as user cooperation may have many benefits on both the primary and secondary transmissions. In this study, the authors propose and investigate an adaptive relay‐based cooperation scheme for CR networks that improves the secondary outage performance, while respecting a primary outage probability threshold. The proposed adaptive scheme considers one multi‐antenna relay node that, by selecting the antenna(s) to use, can assist either the primary, the secondary or both transmissions simultaneously. Expressions of the conditional primary outage probability for Rayleigh fading channels are derived and used to investigate the associated power allocation problem. Simulation results show that both primary and secondary outage probabilities of the proposed scheme are significantly improved and outperform non‐cooperative and cooperative schemes given in the literature.

Convolutional doubly orthogonal (CDO) codes constitute a recent group of binary error correcting codes for additive white gaussian noise channel, achieving very good error performance at moderate values of E b / N 0 under the threshold decoding algorithm. Inspired by the low‐density parity‐check codes over the finite fields, this study extends the construction and decoding of single shift register CDO codes from binary field to the finite fields GF ( q ) for q > 2, referred to as the q ‐ary CDO codes. The threshold decoding algorithm is modified to accommodate the decoding requirement for this set of codes. Superior error performance has been observed for q ‐ary CDO codes over their binary counterparts, especially in the error floor region.

The impact of outdated channel state information (CSI) on the performance of variable‐rate adaptive M ‐ary quadrature amplitude modulation in amplify‐and‐forward (AF) opportunistic relaying systems over time‐variant Rayleigh fading channels is analysed. Two rate‐adaptive modulation techniques are considered. In the first scheme, the relay and the transmission rate are selected according to the CSI at the receiver side. In the second scheme, whereas selection of the relay is based on the receiver's CSI, the transmission rate is selected based on the predicted CSI at the transmitter after the feedback delay. The impact of imperfect CSI prediction on the system performance is also evaluated. For each scheme, analytical expressions are derived for the average spectral efficiency, outage probability and the average bit‐error rate under outdated CSI. Using numerical evaluations the performances of the considered rate‐adaptive modulation schemes are analysed to illustrate the impact of outdated CSI on AF opportunistic relaying systems.

A novel parallel and implicitly-exhaustive search algorithm for finding, in systematic form, rate R=1/2 optimal-span Convolutional Self-Doubly Orthogonal (CDO) codes and Simplified Convolutional Self-Doubly Orthogonal (S-CDO) codes is presented. In order to obtain high-performance low-latency codecs with these codes, it is important to minimize their constraint length (or "span") for a given J number of generator connections. The proposed exhaustive algorithm uses algorithmic enhancements over the best previously published searching techniques, yielding new and improved codes: we were able to obtain new optimal-span CDO/S-CDO codes (having order J∈{9} and J∈{10,11} respectively), as well as new codes having the shortest spans published to date for higher values of J (J∈{10,12,...,17} and J∈{12,...,20} for CDO and S-CDO codes respectively). The new codes and their error performance are provided. An analysis of the evolution of the CDO/S-CDO code error performance as J increases is presented, and the shortest CDO/S-CDO code span values for each given J are compared.

ABSTRACT In this paper, the performance of variable‐rate adaptive modulation schemes in the amplify‐and‐forward cooperative systems with relay selection is analyzed over Rayleigh fading channels. We consider constant power and discrete‐rate adaptive multi‐level modulation techniques. The switching levels required for discrete‐rate adaptive modulation have been determined for two schemes, namely fixed switching levels and optimum switching levels, both respecting a target bit error rate requirements, where in the later scheme, the switching levels are optimally determined in a way that the average spectral efficiency of the system is maximized. Two M‐ary modulation schemes, namely quadrature amplitude modulation and phase shift keying, are considered. Closed‐form expressions are derived for three performance metrics, namely average spectral efficiency, outage probability, and average bit error rate, for two cases: independent and identically distributed fading relay links and independent and non‐identically distributed links. It is shown that, compared with using fixed switching levels, employing optimum switching levels provides a slight improvement in the spectral efficiency and moderate improvements in the signal‐to‐noise ratio gain and in the outage probability of the system. It is also shown that compared with the independent and identically distributed links, independent and non‐identically distributed relay links yield a slight increase in the signal‐to‐noise ratio gain and a slight decrease in the diversity order of the system. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, we investigate and evaluate the performance of incremental relaying and relay selection, when used in the context of cognitive radio networks. Assuming that a number of cognitive radio relay nodes N (N ≥ 2) are co-located with simultaneous primary and secondary transmissions, the “best” relays are chosen to assist the primary and/or the secondary transmission(s) (in case of decoding failure at the destination(s) using the direct link source-destination). The outage probability of both primary and secondary systems is investigated and the associated power allocation problem analyzed. Results show that incremental relaying allows to improve greatly the secondary outage probability with respect to a primary outage probability threshold, compared to the non-cooperative case. Moreover, they suggest that selecting at first the “best” relay to assist the primary transmission before the one that would assist the secondary transmission is more beneficial than choosing at first the “best” relay that would help the secondary transmission. Finally, by proposing an adequate transmit power allocation scheme, we bypass the secondary transmissions' blocking at low primary Signal-to-Noise-Ratio.

Combining cognitive radio technology with user cooperation could be advantageous to both primary and secondary transmissions. In this paper, we propose a first relaying scheme for cognitive radio networks (called “Adaptive relaying scheme 1”), where one relay node can assist the primary or the secondary transmission with the objective of improving the outage probability of the secondary transmission with respect to a primary outage probability threshold. Upper bound expressions of the secondary outage probability using the proposed scheme are derived over Rayleigh fading channels. Numerical and simulation results show that the secondary outage probability using the proposed scheme is lower than that of other relaying schemes. Then, we extend the proposed scheme to the case where the relay node has the ability to decode both the primary and secondary signals and also can assist simultaneously both transmissions. Simulations show the performance improvement that can be obtained due to this extension in terms of secondary outage probability.

In this paper, we investigate several relaying schemes for cooperative communications in Cognitive Radio Networks (CRNs) in order to improve the performances of secondary transmissions while respecting a certain Quality of Service (QoS) requirement at the primary transmissions. We propose relaying schemes where a number of relay nodes, randomly located, may help either the primary or the secondary transmission. By defining proper relay selection criteria and power allocation schemes, we illustrate the secondary outage probability performance while guaranteeing the primary QoS. Using simulations, we present the impact of different parameters, such as the QoS requirement, the chosen relay selection criteria, the number of available relays, the positions of the relays, etc., on the secondary transmission performance. The obtained results show the potential of the proposed relaying schemes, and provide guidelines about the expected secondary performance under the impact of several parameters.

In this article, the impact of outdated channel information on the average bit error rate (BER) performance of the opportunistic relay selection in amplify-and-forward cooperative systems is analysed and evaluated over Rayleigh fading channels. Using the moment generating function (MGF)-based approach closed-form analytical expressions are derived for the average BER performance of M-ary modulations and the average signal-to-noise-ratio (SNR) gain obtained from opportunistic relaying. Numerical evaluation results obtained from the analytical expressions are provided to study and quantify the deteriorating effects of outdated channel information on the BER performance and on the achievable diversity and SNR gain obtained from relay selection.

A novel implicitly-exhaustive search algorithm for finding, in systematic form, rate R=\frac{1}{2} optimal-span Convolutional Self-Doubly Orthogonal (CDO) codes and Simplified Convolutional Self-Doubly Orthogonal (S-CDO) codes is presented. In order to build high-performance low-latency codecs with these codes, it is important to minimize their constraint length (or "span") for a given J number of generator connections. The proposed algorithm is exhaustive in nature and its improvements over the best previously published searching techniques allowed it to yield new optimal-span CDO/S-CDO codes (having order J ∈ {6,7,8} and J ∈ {9} respectively), as well as a span reduction for codes with a higher J value (J ∈ {10,11} and J ∈ {14,15} for CDO and S-CDO respectively).

In underlay cognitive radio networks, unlicensed secondary users are allowed to share the spectrum with licensed primary users when the interference induced on the primary transmission is limited. In this paper, we propose a new cooperative transmission scheme for cognitive radio networks where a relay node is able to help both the primary and secondary transmissions. We derive exact closed-form and upper bound expressions of the conditional primary and secondary outage probabilities over Rayleigh fading channels. Furthermore, we proposed a simple power allocation algorithm. Finally, using numerical evaluation and simulation results we show the potential of our cooperative transmission scheme in improving the secondary outage probability without harming the primary one.

The impact of outdated channel state information (CSI) on the performance of variable-rate adaptive M-ary quadrature amplitude modulation (M-QAM) in an amplify-and-forward (AF) opportunistic relaying system over Rayleigh fading channels is analyzed. Closed-form expressions are derived for the average spectral efficiency, outage probability and the average bit error rate under outdated CSI. Using numerical evaluations, the performances of different cases are compared showing the impact of outdated CSI on the performance of the considered rate-adaptive modulation scheme in AF opportunistic relaying systems.

The system performance of the opportunistic relaying technique in amplify-and-forward cooperative systems with adaptive transmission over Rayleigh fading channels is analysed. Two rate-adaptive modulation techniques, continuous-rate and discrete-rate adaptive techniques, are considered. Closed-form expressions are derived for the average spectral efficiency, outage probability and the average bit error rate for two cases: independent and identically distributed (i.i.d.) fading links and independent and non-identically distributed (i.ni.d.) links. Using numerical evaluations, the performances of different cases are compared showing the advantages of each adaptive modulation technique in conjunction with the opportunistic relaying in a cooperative communication over both i.i.d. and i.ni.d. fading links.

In this study, the performance of user selection diversity for rate-adaptive multiuser multiple-input multiple-output (MIMO) systems employing orthogonal space time block coding (OSTBC) is analysed and evaluated. An antenna selection scheme is used to overcome the drawback of channel hardening effects in multiuser MIMO systems. Closed-form expressions for the average spectral efficiency and outage probability of the system are derived. Using numerical evaluations the considered schemes are compared in terms of outage probability and spectral efficiency. The effects of antenna correlation at the receiver ends on the performance of the system are analysed and evaluated, indicating that spatial correlation may be beneficial for the spectral efficiency of the multiuser OSTBC MIMO systems employing user selection.

In this letter, a performance analysis is presented for a joint multiuser scheduling and antenna selection in MIMO systems employing orthogonal space-time block coding (OSTBC) over Rayleigh fading channels under a general case of heterogeneous scenario. Using numerical evaluations the performance of different cases of the considered scheme are compared for heterogeneous and homogeneous scenarios.

In this paper, we derive probability density function (PDF) and cumulative distribution function (CDF) expressions for the end-to-end signal-to-noise ratio (SNR) of an opportunistic relaying amplify-and-forward (AF) cooperative diversity system over independent and non-identically distributed (i.ni.d.) Rayleigh fading links where outdated channel state information (CSI) is used for relay selection. Based on these expressions, we derive the analytical capacity and outage probability expressions for four classical adaptive transmission techniques, namely, optimal power and rate adaptation (OPRA), constant power with optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR) and truncated channel inversion with fixed rate (TIFR). Numerical evaluations results are presented showing the impact of relay selection with outdated CSI and i.ni.d. links on the performance of each adaptive transmission technique in AF opportunistic relaying systems.

In this paper we present an attractive alternative to construct time-invariant Low-Density Parity-Check Convolutional Codes (LDPC-CC) of coding rate-b/c from a simple recursive systematic convolutional encoder design. The proposed Recursive Convolutional Doubly-Orthogonal (RCDO) encoders have a corresponding Tanner graph for which the girth is controlled by the doubly-orthogonal conditions that are imposed onto the set of generators that represent the encoder. Therefore, RCDO encoders can be decoded using simply a cascade of the same threshold decoder. The convergence behavior of the iterative decoder is then controlled by the position and by the number of forward and feedback connections that constitute the encoder. RCDO encoders give rise to a class of capacity approaching codes that use simple encoder and decoder structures.

The error performance, in terms of Bit Error Rate (BER), of multi-stage (multi-hop) Wireless Relay Networks (WRNs) with distributed STBC at the relay stages is presented. One relay stage is defined by a set of relays located at the same distance from the source node where the distance is measured by the number of hops. We develop the multi-stage WRN model for Amplify-and-Forward (AF) and Decode-and-Forward (DF) procedures at the relaying nodes. The system's performance with imperfect Channel State Information (iCSI) at the receivers is also examined. Simulation results show that the tolerated error on the channel estimation increases when iCSI occurs at the channels between nodes that are far from the source node rather than close to it. This result gives good guidelines about the design of CSI knowledge at the receivers in such a way to reduce delay time and increase data rate.

A performance analysis for cooperative diversity systems with best relay selection over Rayleigh fading channels is presented. The authors obtain analytical expressions for the probability density function (PDF), cumulative density function (CDF) and the moment generating function (MGF) of end-to-end signal-to-noise ratio (SNR) of the system under study for independent and non-identically distributed (i.ni.d.) fading links. Using these expressions the authors derive lower bound closed-form expressions for the average symbol error rate (SER), the outage probability, and an upper bound closed-form expression for the average channel capacity. Using numerical evaluation of the mathematical expressions, system performances of different cases are evaluated and compared for both non-identically and identically distributed links showing the impact of the relay selection in cooperative communication systems.

Abstract In this paper, we present a finite‐signal‐to‐noise ratio (finite‐SNR) framework to establish tight bounds on the diversity‐multiplexing tradeoff of a multiple input multiple output (MIMO) system. We focus on a more realistic propagation environment where MIMO channel fading coefficients are correlated and where SNR values are finite. The impact of spatial correlation on the fundamental diversity‐multiplexing tradeoff is investigated. We present tight lower bounds on the outage probability of both spatially uncorrelated and correlated MIMO channels. Using these lower bounds, accurate finite‐SNR estimates of the diversity‐multiplexing tradeoff are derived. These estimates allow to gain insight on the impact of spatial correlation on the diversity‐multiplexing tradeoff at finite‐SNR. As expected, the diversity‐multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a spectral efficiency ofRbps/Hz and at an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at the same spectral efficiency and at an SNR of 10 dB in a highly correlated channel, when the multiplexing gainris greater than 0.8. Another interesting point is that provided that the spatial correlation channel matrix is of full rank, the maximum diversity gain is not affected by the spatial correlation. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper, we present a performance analysis for the user scheduling for the multiuser MRC MIMO systems exploiting the user and antenna diversities. We consider two scheduling schemes including absolute SNR-based scheduling and normalized SNR-based scheduling schemes. We propose the utilization of an antenna selection scheme to overcome the drawback of channel hardening in multiuser MIMO systems and to improve the system performance. We derive new closed-form expressions for the average bit error rate of the presented schemes for two scenarios: heterogeneous (independent nonidentically distributed SNRs-i.n.i.d.) and homogeneous (independent identically distributed SNRs- i.i.d.) cases. Using mathematical analysis and numerical simulations, we compare the presented schemes.

It has been shown that cooperative communication techniques have a great potential to increase the diversity in wireless relay networks and hence improve the Bit Error Rate (BER). When exploiting many users as relay nodes, a multi-antenna network called virtual-MIMO (Multiple Input Multiple Output) is set up. This special technique helps to solve the problem of transmission error occurrences when sending information through a low quality radio channel. Consequently, the transmission gets a better reliability and higher transmission rate. In this work, we focus on the distributed Space-Time-Block- Coding (STBC) with Amplify-and-Forward (AF) and Decode-and-Forward (DF) relays, for various network configurations and channel knowledge conditions. We investigate and evaluate the performance - in term of BER - of a cooperative communication system using multiple relays equipped with multiple antennas when DSTBC coding is employed at the relays with AF (or DF) relaying. Also, we examine the behavior of these cooperative communication techniques when the Channel State Information (CSI) available at the receivers is imperfect.

A class of orthogonal convolutional codes featuring self-doubly-orthogonal properties is analyzed under iterative decoding techniques. The self-doubly-orthogonal properties of these codes allow them to approach the asymptotic error performance using a low complexity iterative threshold decoding algorithm. It can be shown that convolutional self-doubly-orthogonal codes are also suited for iterative belief propagation (BP) decoding algorithm with typically five iterations to approach the asymptotic error performance. At a substantially reduced complexity, iterative threshold decoding requires the same number of iterations as iterative BP decoding to achieve practically the asymptotic error performance at moderate signal-to-noise ratios.

A performance analysis for cooperative diversity system with best relay selection over Rayleigh fading channels is presented. We obtain analytical expressions for the probability density function (PDF), cumulative density function (CDF), and the moment generating function (MGF) of end-to-end SNR of the system under study. Using these expressions we derive closed-form expressions for the average symbol error rate (SER), the outage probability and the average end-to-end SNR gain obtained form relay selection. Using numerical simulations and calculation of the mathematical expressions, the performances of different cases are evaluated and compared to show the significant advantages of the relay selection in a cooperative communication.

A performance analysis for the average channel capacity and average bit error rate (BER) of user scheduling schemes for multiuser MIMO systems exploiting the multiuser and antenna diversities over non-identically distributed Nakagami-m fading channels is presented. We consider different scheduling schemes including absolute SNR-based scheduling and normalized SNR-based scheduling schemes for both heterogeneous and homogeneous wireless networks. We derive expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the signal-to-noise-ratio (SNR) in non-identical Nakagami-m MIMO channels for each scheduling scheme. These expressions are used to obtain analytical expressions for the average channel capacity and average bit error rate (BER) of the system under study. Finally, the performances of different schemes are evaluated and compared.

A new class of convolutional self-doubly orthogonal codes which can be decoded by an iterative threshold decoder is presented. This new type of codes, called simplified convolutional self-doubly orthogonal codes (S-CSO2C), are obtained by simplifying some of the conditions on the double orthogonality of the convolutional self-doubly orthogonal codes (CSO2C). The relaxing of these conditions yields a substantial reduction of the total decoding delay induced by the memory length of the convolutional encoder at a cost of any a small degradation of the error performances. These simplified codes are also amenable to high coding rates R = b/(b + 1), b > 1 by puncturing a rate 1/2 systematic convolutional encoder. These new simplified CSO2C provide an interesting alternative for low complexity implementation error correcting schemes.

An algebraic construction for a class of low-density parity-check (LDPC) convolutional codes is presented on the basis of difference families associated with the code generator matrix. It can be shown that these codes have girth of at least 10 on the Tanner graph which is independent of either the size of the code generator matrix or the minimum Hamming distance of the codes. The code construction guarantees the independence of the messages exchanged in the belief propagation decoding process during two successive decoding iterations. Computer simulations show that over the additive white Gaussian noise channel, the best error performance of these codes at moderate signal-to- noise ratio values is practically obtained using only three to five iterations.

We address the capacity of a discrete-time memoryless Gaussian channel, where the channel state information (CSI) is neither available at the transmitter nor at the receiver. The optimal capacity- achieving input distribution at low signal-to-noise ratio (SNR) is precisely characterized, and the exact capacity of a non-coherent channel is derived. The derived relations allow to better understanding the capacity of non-coherent channels at low SNR. Then, we compute the non- coherence penalty and give a more precise characterization of the sub- linear term in SNR. Finally, in order to get more insight on how the optimal input varies with SNR, upper and lower bounds on the non-zero mass point location of the capacity-achieving input are given.

The complexities of iterative belief propagation decoding techniques for randomly constructed low-density parity-check (LDPC) block codes and nonrecursive convolutional self-doubly-orthogonal codes (CSO2Cs) are analyzed and compared on the basis of their decoding latencies expressed in the number of code symbols. Although, in principle, they have the same computational complexities, the pipeline decoder structure for CSO2Cs has a much smaller implementation complexity than the block decoder structure for LDPC block codes, but at a cost of small loss in the error performance of decoding.

The capacity of a discrete-time memoryless Gaussian channel, where the channel state information (CSI) is neither available at the transmitter nor at the receiver, is addressed. A closed form expression of the optimal capacity-achieving input distribution at low signal-to-noise ratio (SNR) is derived, and the exact capacity of a non-coherent Single Input Single Output (SISO) channel is given. The derived relations allow to better understanding the capacity of non-coherent channels at low SNR. Then, we compute the non-coherence penalty and give a more precise characterization of the sub-linear term in SNR. Finally, upper and lower bounds on the capacity of a multiple input multiple output (MIMO) channel are derived in terms of its counterpart SISO channel capacity. We show that these bounds are sufficient to characterize the MIMO channel capacity at low SNR.

In this paper, we present a performance analysis of user scheduling for multiuser MIMO systems exploiting the multiuser and antenna diversities while maintaining the fairness among the users. We consider different scheduling schemes including absolute throughput-based scheduling, absolute SNR-based scheduling, and normalized SNR-based scheduling schemes. We also propose the utilization of an antenna selection scheme to overcome the drawback of channel hardening in multiuser MIMO systems. This also improves the system performance and reduces the system complexity. We derive closed-form expressions for the average spectral efficiency of the system under study for each scheduling scheme. Using the results obtained from the closed-form expressions, we compare the presented schemes and show their significant advantages in terms of fairness of scheduling and spectral efficiency.

A novel approach for the algebraic construction of low-density parity-check (LDPC) convolutional codes is presented. It is based on the orthogonality structures of the codes. The proposed code construction leads to a girth of at least 10 in the Tanner graph. The error performance of these codes compares favorably with the usual LDPC convolutional codes, especially at low signal-to-noise ratio range.

In this paper, we present a multiuser scheduling technique for the MIMO-OFDM system over multipath frequency-selective fading channels to exploit the multiuser, space and frequency diversities. Two scenarios including full-feedback and limited-feedback channel information have been considered. A discrete-rate adaptive modulation is employed to increase the spectral efficiency of the system. Performance analysis and numerical simulation are conducted to evaluate the average bit error rate (BER) and average spectral efficiency (ASE) and to show the significant advantages of the proposed scheme. It is also shown that when the number of active users is moderately high and is above 30, even 10% feedback load is sufficient to get the benefits of the proposed scheme.

In this paper, we present a performance analysis of the user scheduling for the multiuser MIMO systems exploiting the multiuser and antenna diversities while maintaining the fairness among the users. We present different scheduling schemes including absolute throughput-based scheduling, normalized throughput-based scheduling, absolute SNR-based scheduling, and normalized SNR-based scheduling schemes. We use an antenna selection scheme to overcome the drawback of channel hardening in multiuser MIMO systems. This also improves the system performance and reduces the system complexity. Using mathematical analysis and numerical simulations, we compare the presented schemes and show their significant advantages.

In this paper, we present a multiuser scheduling technique for MIMO-OFDM system over multipath frequency- selective fading channels to exploit the multiuser, space and frequency diversities. A continuous-rate adaptive modulation is employed to increase the spectral efficiency of the system. A proportional fair scheduler is also considered to maintain the fairness among the users while exploiting the multiuser diversity. We also use a scheme to reduce the required feedback channel information. Using mathematical analysis and numerical simulations, the significant advantages of the proposed scheme have been shown. It is also shown that when the number of active users is moderately high and is above 30, even 10% feedback load is sufficient to get the benefits of the proposed scheme.

User cooperation enables single antenna terminals to benefit from spatial diversity by partnering with other users to create a virtual transmit antenna array. A promising form of cooperation is called coded cooperation which integrates cooperation with channel coding, showing great performance gains. However, the optimal degree of cooperation between the users changes with the channel conditions and there is no known expressions indicating the required degree of cooperation for given channel conditions. Furthermore, coded cooperation has a fixed throughput which inefficiently use the degrees of freedom of the channel, especially at high SNR. This paper proposes an adaptive coded cooperation protocol based on incremental redundancy using an ARQ/FEC scheme with rate-compatible punctured convolutional codes (RCPC). By employing a ACK/NACK feedback channel from the partner and the destination, each user adapts the size of the frames transmitted in the first and second cooperation phases in order to maximize throughput and to minimize errors due to the channel. Simulation results illustrate the gains and flexibility of our protocol for both reciprocal and non-reciprocal channels.

The complexities and latencies of iterative belief propagation (BP) and threshold decoding techniques for a new class of convolutional self-orthogonal codes are analysed using forward-only pipeline architectures. Computer simulation results show that over the additive white Gaussian noise channel at moderate signal-to-noise ratios, BP decoding yields one half the decoding delay when compared with threshold decoding at essentially the same error performances. However, the reduction in the decoding delay using BP is obtained at the cost of an increase of the implementation complexity.

The impact of spatial correlation on the performance limits of multielement antenna (MEA) channels is analyzed in terms of the diversity-multiplexing tradeoff (DMT) at finite signal-to-noise ratio (SNR) values. A lower bound on the outage probability is first derived. Using this bound accurate finite-SNR estimate of the DMT is then derived. This estimate allows to gain insight on the impact of spatial correlation on the DMT at finite SNR. As expected, the DMT is severely degraded as the spatial correlation increases. Moreover, using asymptotic analysis, we show that our framework encompasses well-known results concerning the asymptotic behavior of the DMT.

In this paper a new class of high-rate punctured convolutional codes that can be decoded using an iterative threshold algorithm is proposed. These codes are called simplified punctured convolutional self-doubly orthogonal codes (S-PCSO2C) of rate-R=b/(b+1), b>1 and are obtained by puncturing a rate 1/2 systematic convolutional mother code. S-PCSO2C are codes for which the original set of conditions, respected by PCSO2C, is simplified. Relaxing the doubly orthogonal conditions yields an important reduction of the constraint length of the systematic convolutional encoder which in turn reduce the implementation complexity and the total decoding latency at the cost of a very small performance degradation.

The forward-only iterative decoding techniques for convolutional self-doubly-orthogonal codes are systematically presented based on one-step belief propagation (BP) decoding and one-step threshold decoding. A feedback mechanism and a weighing technique are examined in order to improve both the convergence speed and error performance. Computer simulation results show that compared with the iterative threshold decoding over an additive white Gaussian noise channel, the iterative BP decoding for these codes achieves essentially the same error performance while requiring only about half the number of iterations. Therefore, these two iterative decoding techniques can provide a tradeoff between the latency and the complexity of decoding and allow for the applications of these codes in very high speed wireless communications.

We present tight upper bounds on the channel mutual information of spatially correlated and uncorrelated multielement antenna (MEA) channels. Using these upper bounds, accurate lower bounds on the outage probability are derived. Similarly, tight upper bounds on the outage rate are obtained. Interestingly, these bounds are even tighter as the spatial correlation increases. Simulation results show that, in a highly correlated channel, the worst gap between our outage probability lower bounds and the exact values (given by simulation) is about 0.2 and 0.3 dBs, respectively for 2 times 2 and 3 times 3 MEA systems. This tightness suggests using the derived lower bounds on the outage probability in order to characterize the performance limits of MEA in terms of the finite-SNR diversity-multiplexing tradeoff in correlated and uncorrelated spatial fading channels.

A procedure for the forward-only iterative belief propagation decoding of orthogonal convolutional codes is presented. It can be dramatically simplified to perform the iterative threshold decoding of convolutional self-doubly-orthogonal codes without interleaving. These procedures can help implement iterative decoders efficiently using a serial concatenation of one-step BP decoders or one-step threshold decoders, respectively. Simulations have shown that the error performance of orthogonal convolutional codes can be improved by iterative decoding whether based on belief propagation decoding or threshold decoding. For convolutional self-doubly-orthogonal codes, iterative threshold decoding can achieve the same error performance as iterative belief propagation decoding, but with greatly reduced decoding complexity, allowing an advantageous tradeoff between implementation complexity and latency.

A variant of convolutional self doubly orthogonal codes that can be decoded using an iterative threshold decoding algorithm is presented. These new codes are called degenerate convolutional self-doubly orthogonal codes since not all the double orthogonality conditions required to obtained convolutional self doubly orthogonal codes defined in the wide sense are satisfied. The memory lengths or spans of the degenerate convolutional self-doubly orthogonal codes are substantially shorter than those of the usual convolutional self doubly orthogonal codes defined in the wide sense, at the cost of only a slight degradation of the error performances. As a consequence, very low complexity implementations are possible with these error correcting schemes. Several new degenerate convolutional self doubly orthogonal codes have been determined and their error performances evaluated using computer simulations.

An efficient parallel processing mode is proposed for the implementation of fast forward-only iterative belief propagation decoding of orthogonal convolutional codes based on one-step decoding. In the proposed parallel processing mode, the iterative decoding of orthogonal convolutional codes makes use of the complete set of orthogonal parity-check equations on each information symbol, thus avoiding the error performance loss. The proposed parallel processing allows the speed of iterative decoding to approach that of one-step decoding. Therefore, an advantageous tradeoff can be available between data rate and latency.

We present a tight lower bound on the outage probability of a spatially correlated multielement antenna (MEA) channel. Using this lower bound, an accurate flnite-SNR estimate of the diversity-multiplexing tradeoff over a spatially correlated Rayleigh fading channel is derived. This estimate allows gaining insight on the impact of spatial correlation on the diversity-multiplexing tradeoff at finite SNR. As expected, the diversity multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a transmission rate of R = rlog2(1+ g ldr eta) bps/Hz, where r is the multiplexing gain, g is the array gain and eta is the SNR at each receive antenna, and an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at an SNR of 10 dB in a highly correlated channel, when r ges 0.8. Another interesting point is that the maximum diversity gain is unaffected by the correlation, provided that the spatial channel correlation matrix is of full rank.

This paper investigates link layer data units (frames) transmission strategies for MIMO wireless systems using spatial multiplexing. A new effective transmission strategy is proposed in this paper in order to decrease the frame error rate by making use of the multi-channel transmission characteristics provided in MIMO systems. The main idea is to select, in the context of a V-BLAST transmitter, between transmitting each frame, where a frame corresponds to an error correcting code word, from one antenna or from multiple antennas according to the channel state. Limited binary feedback information allows the transmitter to select the appropriate frame transmission policy. Analytical studies and simulations provided in this paper determine the optimal selection criterion and highlight the gains obtained by the proposed transmission strategy. This paper confirms that always transmitting each frame from multiple antennas gives quasi-optimal performances

The puncturing technique allows obtaining high-rate convolutional codes from low-rate convolutional codes used as mother codes. This technique has been successfully applied to generate good high-rate convolutional codes which are suitable for Viterbi and sequential decoding. In this paper, we investigate the puncturing technique for convolutional self-doubly orthogonal codes (CSO/sup 2/C) which are decoded using an iterative threshold-decoding algorithm. Based on an analysis of iterative threshold decoding of the rate-R=b/(b+1) punctured systematic CSO/sup 2/C, the required properties of the rate-R=1/2 systematic convolutional codes (SCCs) used as mother codes are derived. From this analysis, it is shown that there is no need for the punctured mother codes to respect all the required conditions, in order to maintain the double orthogonality at the second iteration step of the iterative threshold-decoding algorithm. The results of the search for the appropriate rate-R=1/2 SCCs used as mother codes to yield a large number of punctured codes of rates 2/3/spl les/R/spl les/6/7 are presented, and some of their error performances evaluated.

In this paper, we present new results on the search and determination of wide-sense convolutional self-doubly orthogonal codes (CSO/sup 2/C-WS) which can be decoded using a simple iterative threshold decoding algorithm without interleaving. For their iterative decoding, in order to ensure the independence of observables over the first two iterations without the presence of interleavers, these CSO/sup 2/C must satisfy specific orthogonal properties of their generator connections. The error performances of CSO/sup 2/C, depend essentially on the number of taps J of the code generators but not on the code memory length. Since the overall latency of the iterative threshold decoding process is proportional to the memory length of the codes, therefore, when searching for the best CSO/sup 2/C-WS of a given J value, the memory length of the codes should be chosen to be as small as possible. In this paper, we present a code-searching technique based on heuristic computer searching algorithms which have yielded the best known CSO/sup 2/C-WS. The construction method for CSO/sup 2/C-WS has provided the best known r=1/2 codes with the shortest memory length having J/spl les/30. Although not very complex to implement, the search method presented here is quite efficient especially in reducing very substantially the execution time required to determine the codes with the shortest spans. Furthermore, in addition to presenting the search results for the codes, error performances obtained by simulation are also provided.

The structures of convolutional self-orthogonal codes and convolutional self-doubly-orthogonal codes for both belief propagation and threshold iterative decoding algorithms are analyzed on the basis of difference sets and computation tree. It is shown that the double orthogonality property of convolutional self-doubly-orthogonal codes improves the code structure by maximizing the number of independent observations over two successive decoding iterations while minimizing the number of cycles of lengths 6 and 8 on the code graphs. Thus, the double orthogonality may improve the iterative decoding in both convergence speed and error performance. In addition, the double orthogonality makes the computation tree rigorously balanced. This allows the determination of the best weighing technique, so that the error performance of the iterative threshold decoding algorithm approaches that of the iterative belief propagation decoding algorithm, but at a substantial reduction of the implementation complexity.

A class of forward-only iterative belief propagation algorithms for decoding convolutional self-orthogonal codes is presented, which perform successively a number of one-step decoding and thus have only an initial decoding delay. The one-step belief propagation decoders can be realized in a similar way to one-step threshold decoders. The error performance of the algorithms is easily improved by using a weighing technique. These iterative algorithms allow good tradeoffs between complexity, latency, and error performance of the coding scheme.

An extension of convolutional self-orthogonal codes called convolutional self-doubly orthogonal codes which are decoded using an iterative threshold decoding algorithm with no interleaver is presented. These new codes allow good error performance in addition to providing attractive trade-off between complexity and latency. Some code searching results yielding new codes are provided together with their error performance evaluation. Puncturing techniques for systematic convolutional codes that allows us to obtain high-rate R = b/(b + 1) punctured convolutional self-doubly orthogonal codes in the wide sense are also investigated. Some punctured convolutional self-doubly orthogonal codes are presented and their bit error probabilities are evaluated using computer simulations.

A novel iterative error control technique based on the threshold decoding algorithm and new convolutional self-doubly orthogonal codes is proposed. It differs from parallel concatenated turbo decoding as it uses a single convolutional encoder, a single decoder and hence no interleaver, neither at encoding nor at decoding. Decoding is performed iteratively using a single threshold decoder at each iteration, thereby providing good tradeoff between complexity, latency and error performance.

In this paper we present a novel iterative error control technique which circumvents both the complexity and latency shortcomings of the usual turbo codes. It differs from usual turbo coding techniques as it uses a single encoder (hence with no interleaver at the encoding process) and a single decoder. The technique is based on a novel class of orthogonal threshold decodable codes called convolutional self doubly orthogonal codes (CSO/sup 2/C).

The performance of suboptimal convolutional decoding over fading channels is explored. The suboptimal decoding algorithm used is the bidirectional algorithm. By estimating a "decoder weight spectrum" for the decoder, an "equivalent free distance" may be observed. Furthermore, by using this "decoder weight spectrum", useful estimations of the error probabilities are obtained and compared to computer-simulation results in the case of very slow and very fast fading. The resultant curves are shown to be very tightly related. Computer-simulation results are also shown for various signal-to-noise ratios, normalized Doppler spreads, and frame length on three typical fading channels: the Rayleigh fading channel with exponential and Bessel autocorrelation functions and the Rician fading channel with exponential autocorrelation function. We show that considerable gains (up to 4 dB) can be obtained with respect to a similar-complexity Viterbi decoder at a frame error probability P/sub e/=10/sup -3/ and a slightly smaller gain (up to 1.8 dB) at a bit error probability P/sub b/=10/sup -5/.

In this paper, an adaptive decoding algorithm for convolutional codes, which is a modification of the Viterbi algorithm (VA) is presented. For a given code, the proposed algorithm yields nearly the same error performance as the VA while requiring a substantially smaller average number of computations. Unlike most of the other suboptimum algorithms, this algorithm is self-synchronizing. If the transmitted path is discarded, the adaptive Viterbi algorithm (AVA) can recover the state corresponding to the transmitted path after a few trellis depths. Using computer simulations over hard and soft 3-bit quantized additive white Gaussian noise channels, it is shown that codes with a constraint length K up to 11 can be used to improve the bit-error performance over the VA with K=7 while maintaining a similar average number of computations. Although a small variability of the computational effort is present with our algorithm, this variability is exponentially distributed, leading to a modest size of the input buffer and, hence, a small probability of overflow.

The evaluation of the performance of partial selection networks which select a set of M elements from a set of N inputs is addressed. The partial selection problem occurs when dealing with non-exhaustive multi-path breadth-first searches, like in the M algorithm or the bidirectional algorithm. These algorithms are used in the decoding of convolutional codes. The paper presents a set of bounds to evaluate the quality of regular, Delta class, networks of depth 1gN and width N/2, with respect to their selection capabilities. The results from the bounds are compared to Monte Carlo simulations of the selection capabilities of the Banyan and Alekseyev networks. Finally, the performance degradation associated with the use of these networks on the performance of a bidirectional decoder is presented. In particular, the authors show that even with imperfect selection, the bidirectional decoder can outperform a Viterbi decoder of comparable complexity.>

Two new schemes are presented to improve the error performances of coding and modulation on slow fading channels. The first scheme consists of permuting coordinates of multidimensional modulation and trellis coded modulation (TCM) on interleaved channels. Theoretical and simulation results show that this simple permutation may provide gains of 3.8 dB on slow Rayleigh fading channels for uncoded modulation. It also improves by 5 dB the performance of fully interleaved 16-QAM TCM. The second scheme consists of using coded frequency diversity. Without bandwidth expansion, the signal is spread over different independent fading channels. For two very slow fading channels, where interleaving is impractical and coding usually does not provide any gain, coded diversity and 16-QAM TCM provides gains of 13 dB at a BER of 10/sup -4/.>

The decoding of long memory high-rate punctured convolutional codes by sequential decoding algorithms is investigated. Both the stack and the Fano algorithms have been thoroughly tested through computer simulation with coding rates ranging from R=2/spl sol/3 to R=/spl frac78/. Error and overflow probabilities and variability of decoding effort are similar for both algorithms. With hard quantization, plateaus appear in the cumulatives of decoding effort for both algorithms. Comparing the punctured approach of decoding to the more traditional technique for high-rate codes, it is found that punctured decoders perform a larger number of simpler computations, so that the overall decoding effort is on the average more important for the usual decoder than it is for its punctured counterpart. Finally, computational variability, error and overflow probabilities are no worse for punctured decoders than they are for normal decoders.>

The Zigangirov-Jelinek (stack) algorithm allows decoding convolutional codes with a small computational effort compared to the optimum Viterbi algorithm. However, it suffers from a variability of that computational effort that is highly undesirable. The paper describes an architecture that implements a multiple-path-like stack algorithm for reducing this variability. This architecture is organized as a linear structure comprising special processors for extending tree nodes, called extenders, and priority stacks for storing nodes in sorted metric order. The architecture is shown to have a good potential for reducing the computational variability without adding much overhead to the system. Simulations have shown that this architecture effectively reduces computational variability as the number of processors increases, even for a relatively large number of extenders. Simulations run for up to 16 extenders have also shown that using 4 to 16 extenders is a good choice. The architecture is also shown to reduce computational variability like the multiple path algorithm does, while having a better time performance.>

The troublesome operation of reordering the stack in stack sequential decoders is alleviated by storing the nodes in a systolic priority queue that delivers the true top node in a short and constant amount of time. A new systolic priority queue is described that allows each decoding step, including retrieval, reordering and storage of the nodes, to take place in a single clock period. A complete decoder architecture designed around this queue is compared to a conventional stack-bucket architecture from both speed and cost points of view. The proposed decoder architecture appears to be faster, affordable, and compatible with convolutional codes having long memory and high coding rate.>

Bidirectional multiple-path tree searching algorithms for the decoding of convolutional codes are presented. These suboptimal coding algorithms use a multiple-path breadth-first bidirectional tree exploration procedure and long-memory convolution codes. It is shown that, compared to the usual M-algorithm, the bidirectional exploration considerably reduces the bit error propagation due to correct path loss. Computer simulations using rate-1/2 codes over binary symmetric channels are used to analyze the effect of the number of path extensions, code memory, and frame length on the bit error probability. The results show that with a bit error probability of 10/sup -5/, coding gains on the order of 2 dB over the M-algorithm and 1 dB over a Viterbi decoder of equivalent complexity can be achieved.>

Bidirectional suboptimal breadth-first decoding of convolutional codes is an attractive technique for slowly-varying and quasistatic fading channels as it restricts the extent of decoding errors due to correct path loss to very heavy noise or interference regions. The paper compares the performance of such a decoding scheme to the Viterbi algorithm over wideband TDMA indoor radio links where equalization and space diversity are also used to combat dispersive fading and cochannel interference. It is shown that, with dual space diversity, Viterbi decoding and bidirectional decoding of convolutional codes are both attractive alternatives, in terms of outage rate, to increasing the space diversity order from two to three. On the basis of equal computational complexity, bidirectional decoding is also shown to be superior to Viterbi decoding. Furthermore, this advantage increases as the bit error rate performance criterion becomes more stringent which makes bidirectional decoding particularly attractive for data applications.>

New upper bounds on the error performance of coded systems for Rician channels are presented. The fading channels need not be fully interleaved to obtain meaningful performance results. These bounds hold for coherent, differentially coherent and noncoherent demodulation of binary signals. They provide a useful analytical approach to the evaluation of the error performance of convolutional or block coding and they may be generalized to M-ary signals and trellis modulation. The approach allows for complex bounds using the fine structure of the code, for simpler bounds similar to those on memoryless channels and finally for a random coding bound using the cutoff rate of the channel. The analysis thus permits a step by step evaluation of coded error performances for Rician-fading channels.>

A branching process analysis in a random environment is presented for bounding the average number of computations of sequential decoding over a finite state channel. Closed-form expressions applicable to specific cases are derived and evaluated. These unique bounds substantially reduce the need for lengthy simulations.>

The authors present and analyze an efficient partial retransmission automatic repeat request (ARQ) strategy using convolutional coding and sequential decoding in conjunction with code combining. In the proposed ARQ scheme, whenever a packet of data needs to be retransmitted that packet is not repeated entirely as in the case of conventional full retransmission ARQ strategies. Instead, symbols of that packet are repeated a few at a time, sequentially, as needed, hence making a more effective use of the channel. It is shown that partial repetitions and code combining still yields an increase of the apparent Pareto exponent of sequential decoding, as in the case of full repetition-code combining. A throughput analysis shows that the partial retransmission ARQ strategy yields a substantial throughput improvement over the full retransmission-code combining ARQ strategies.>

New VLSI architectures for fast convolutional threshold decoders that process soft-quantized channel symbols are presented. The new architectures feature pipelining and parallelism and make it possible to fabricate decoders for data rates up to hundreds of Mbits per second. With these architectures, the data rate is shown to be independent of the memory of the code, implying that fast AAPP (approximate a posteriori probability) decoders can be built for long powerful codes. Furthermore, the architectures are convenient to use with low and high coding rates. Using a typical example it is shown that a soft-decision threshold decoder can provide a substantial coding gain while being less costly to implement than the hard-decision threshold decoder.>

The weight spectra of high-rate lpunctured convolutional codes are evaluated under the hypothesis of a low-rate structure. This interpretation yields results slightly different from those obtained when weight spectra are evaluated assuming a true high-rate structure for punctured codes. The search for long memory punctured codes is extended by providing new punctured codes of rates 4/5, 5/6, 6/7, and 7/8 with memories ranging from 9 to 19.>

A method is presented to construct rate-compatible convolutional (RCC) codes from known high-rate punctured convolutional codes, obtained from best-rate 1/2 codes. The construction method is rather simple and straightforward, and still yields good codes. Moreover, low-rate codes can be obtained without any limit on the lowest achievable code rate. Based on the RCC codes, a generalized type-II hybrid ARQ scheme, which combines the benefits of the modified type-II hybrid ARQ strategy of J. Hagenauer (1988) with the code-combining ARQ strategy of D. Chase (1985), is proposed and analyzed. With the proposed generalized type-II hybrid ARQ strategy, the throughput increases as the starting coding rage increases, and as the channel degrades, it tends to merge with the throughput of rate 1/2 type-II hybrid ARQ schemes with code combining, thus allowing the system to be flexible and adaptive to channel conditions, even under wide noise variations and severe degradations.>

The authors present some properties of punctured convolutional codes, providing a construction method and a list of new, good, high-rate, long-memory punctured codes. The structure of punctured codes is examined and an upper bound on the free distance of punctured codes is derived, indicating that punctured codes are good codes. A construction method that generates the low-rate original codes which duplicate given known high-rate codes through perforation is proposed. Tables of punctured codes that duplicate the best known nonsystematic codes of rates 2/3 and 3/4 with memory lengths ranging from 3 to 23 and from 3 to 9, respectively, are given, together with the best known systematic codes for rates ranging from 2/3 to 7/8 with very long memory, M=44 through 48.>

An investigation is conducted of the high-rate punctured convolutional codes suitable for Viterbi and sequential decoding. Results on known short-memory codes M>

Several new architectures for high-speed convolution encoders and threshold decoders are developed. In particular, it is shown that new architectures featuring both parallelism and pipelining are promising from a speed point of view. These architectures are practical for a wide range of coding rates and constant lengths. Two integrated circuits featuring these architectures have been designed and fabricated in a CMOS 3- mu m technology. The two circuits have been tested and can be used to build convolutional encoders and definite threshold decoders operating at data rates above 100 Mb/s. It is shown that with these architectures, encoders and threshold decoders could easily be designed to operate at data rates above 1 Gb/s.>

Sequential decoding with ARQ (automatic-repeat-request) and code combining under the timeout condition is considered. That is, whenever the decoding time of a given packet exceeds some predetermined duration, decoding is stopped and retransmission of the packet is requested. However, the unsuccessful packets are not discarded, but are combined with their retransmitted copies. It is shown that the use of code combining allows sequential decoding to operate efficiently even when the coding rate R exceeds the computational cutoff rate R/sub comp/. Furthermore, an analysis of the selective-repeat ARQ scheme shows that the use of code combining yields a significant throughput even at very high channel error rates, thus making the system very robust under severe degradations of the channel.>

This paper discusses a number of coding techniques for future satellite communication; they include Reed-Solomon error decoding for message blocks, probabilistic decoding techniques for punctured convolutional codes, and planar Euclidean geometry difference set codes for random multiple access applications. The provision of code concatenation, helical interleaving, and simulation results of new punctured convolutional codes are included. A number of coded satellite systems that demonstrate the usefulness of coding in satellite communications are described.

A new analysis for bounding the average computational effort of sequential decoding is presented. It is based on a branching process model of the subset of incorrect paths explored by the decoder. Closed-form expressions formulated in terms of the set of branch metrics and their probability assignments as actually used by the decoder are derived. Code characteristics in the form of Hamming weights of the 'incorrect paths or column distance function are incorporated, making the analysis directly applicable to specific cases. Evaluation of the bounds is not difficult. Results are in good agreement with those obtained by lengthy computer simulations.

Using Massey's Markov chain model of the correct path metric, closed-form expressions are derived for the average separation between nonsearch nodes for the single path and the multiple path sequential decoder. An exact expression for the cumulative distribution of the correct path metric dips is also derived. All expressions are given in matrix form in terms of the correct path branch metric values and their probability assignments.

A new class of generalized stack algorithms for decoding convolutional codes is presented. It is based on the Zigangirov-Jelinek (Z-J) algorithm but, instead of extending just the top node of the stack at all times, a number of the most likely paths are simultaneously extended. This number of paths may be constant or may be varied to match the current decoding effort with the prevalent noise conditions of the channel. Moreover, the trellis structure of the convolutional code is used by recognizing and exploiting the reconvergence of the paths. As a result the variability of the computation can be reduced up to a limit set by the "ideal" stack algorithm. Although the tail of the computational distribution is still Pareto, it is shown and verified from simulation with short constraint length codes(K \leq 9)of rate\frac{1}{2}that, compared to sequential decoding, the variability of the number of computations per decoded bit and the maximum computational effort are both reduced at the cost of a modest increase in the average decoding effort. Moreover, some of the error events of sequential decoding are corrected. These algorithms fill the gap between the one-path sequential decoding nad the all-path Viterbi decoding.