Computer vision for mobile systems is challenging. Video frame processing locally on mobile devices is impractical due to the device’s limited resources, whereas processing at remote cloud and edge servers is time-consuming due to the communication issues. In this paper, we propose an analytical approach to cope with the local and remote processing tradeoff in mobile computer vision systems. We devise a stochastic model for a mobile computer vision systems and derive closedform expressions for key performance metrics, namely, processing latency, offloading latency, and energy cost. We propose two heuristics to obtain useful insights regarding distributed computer vision in smart mobile systems. We illustrate the model’s application through a case study involving collaborative video analytics at mobile users and edge servers under different conditions. Numerical results show the distinctions in the processing and offloading energy costs at mobile devices and the high latency when a high offloading rate is used.

Internet of Things (IoT) has been used to empower smart environments and applications in different domains. In some IoT systems, IoT cameras live stream video frames to edge or cloud servers to be processed by machine learning (ML) models. The processing of the video frames will aim to detect and recognize objects or other entities of interest. However, the processing of IoT video frames at cloud servers often relies on high latency due to network congestion and high load at the cloud servers. In this paper, we proposed the SDNQ controller, a software-defined networking (SDN) controller that uses a reinforcement learning (RL) agent to decide how to route and where to process video frames from IoT flows. The proposed solution considers the network and servers' status, the latency experienced by admitted video flows, and the video flows' latency requirements when deciding the routing path and the destination edge or cloud server to process a newly admitted IoT video flow. Numerical results show that the proposed solution outperforms related works at the cost of blocking a low fraction of IoT flows.

Edge computing has been designed to deploy resources in the proximity of IoT devices, which reduces latency and network overhead. Nevertheless, resources on edge servers are limited and must efficiently be managed. In this paper, we propose a novel software-defined networking (SDN)-based scheme to balance the computation resource requests among a network of edge servers aimed at supporting IoT video analytics streaming applications. In the proposed solution, programmable switches periodically report the IoT video streaming workload forwarded to each edge server. This information is then used at the SDN controller to estimate the incoming and outgoing traffic load at edge servers and balance IoT video streaming among them, by updating routing tables at the programmable switches. The performance of the proposed solution is evaluated and compared to related schemes through extensive simulations using the Mininet emulator. Obtained results show that the proposed solution can reduce up to 21 % of average latency with 20 % load saving in each edge server, compared to deterministic and random-based related solutions.

Abstract This paper addresses the problem of minimum mean square error channel estimator for time division duplex massive multi‐user multi‐input multi‐output systems. It is noteworthy that, the minimum mean square error has been previously proposed for multi‐cell massive multi‐user multi‐input multi‐output channel estimation. However, the minimum mean square error estimator suffers from high computational complexity due to the large dimension of the covariance matrix inversion. In this study, low‐complexity channel estimator for time division duplex massive multi‐user multi‐input multi‐output networks is designed by using the low‐rank matrix approximation techniques. The proposed estimator is referred to as an approximate minimum mean square error estimator. Furthermore, the computational complexity of the proposed approximate minimum mean square error estimator is analysed and compared to the minimum mean square error and least square estimators. The normalised mean square error and the uplink achievable sum‐rate performance criteria are used to evaluate the performance of the proposed estimator. Finally, the simulation results show the effectiveness of the proposed estimator under two different scenarios: noise‐limited and pilot contamination. These simulation results are compared to the conventional minimum mean square error and least square estimators.

This paper investigates the application of multicast non-orthogonal multiple access (MC-NOMA) schemes to the forward link of a satellite communication system. In multicast transmission each frame contains information of multiple users. To benefit from the theory developed in NOMA, the proposed scheme creates two groups of users within each beam. The analysis conducted in this work reveals that the user grouping has an impact on the performance. In the light of this observation, power allocation and user clustering techniques have been derived to either maximize the sum-rate or achieve max-min fairness. The numerical simulation results show that MC-NOMA outperforms multicast orthogonal multiple access (MC-OMA) schemes, where different groups are served in orthogonal resources. Moreover, the gain of MC-NOMA over the MC-OMA becomes more prominent as number of users per group and the transmit power increases. The results show the minimum-rate and the sum-rate of MC-NOMA can be increased by a factor 2 and 1.45 with respect to MC-OMA, respectively.

Improving the performance of wireless networks to maintain good quality of service for all users is always an ultimate goal. To reach this goal, the performance should be evaluated accurately and then analysed. Geometric modelling of wireless networks is drawing significant attention with regard to analytically evaluating the performance. In this study, stochastic modelling of users is used to emulate their distribution in wireless networks, which is analysed when only one direct link is connecting the base station to each user over the cell. Hence, the final findings will be more universal and applicable for different types of mobile cellular networks. Probability density function (PDF) of signal‐to‐interference ratio, and signal‐to‐noise ratio are evaluated, and used to find the PDF of signal‐to‐interference‐plus‐noise ratio (SINR) in a uniform filed of interference. Then, the outage probability based on SINR is evaluated, since it is one of the important factors in studying the performance of wireless networks. Finally, simulations are performed in order to validate the analytical results.

In multi‐cell massive multiuser multi‐input multi‐output (MU‐MIMO) systems, the channel estimation performance is degraded by the pilot contamination problem. This effect occurs when non‐orthogonal pilot sequences are reused by other users in the adjacent cells. In this study, two channel estimation methods based on low‐rank matrix approximation technique are proposed to mitigate pilot contamination problem in time division duplex multi‐cell massive MU‐MIMO systems. In the first method, the massive MU‐MIMO channel estimation is formulated as the nuclear norm (NN) optimisation problem and solved by using a novel estimation algorithm proposed in this study. In the second method, the iterative weighted NN (IWNN) is proposed to improve the NN estimation performance. Consequently, the regularisation parameter of both optimisation methods is selected based on the cross‐validation curve method. The simulation results show that both proposed methods outperform the traditional least square method in terms of the normalised mean square error. Moreover, the IWNN estimation method demonstrates substantial improvement over the NN estimation method in the presence of strong pilot contamination problem.

The channel estimation problem for massive MIMO systems is a critical issue due to the large dimensions of channel matrix to be estimated within the limited coherence time interval. In this paper, iterative weighted nuclear norm minimization (IWNNM) method based on compressive sensing (CS) technique is proposed for massive multi-user (MU-MIMO) channel estimation problem. Consequently, the regularization parameter of this optimization problem is selected based on cross-validation (CV) curve method. The convergence time of the iterative algorithm is also studied. The simulation results show that the IWNNM estimation method outperforms the standard nuclear norm minimization (NNM) and conventional least square (LS) estimation.

Wireless communication is now accessible throughout the world, with an increasing number of users. Engineers are putting extra efforts to evaluate and improve the performance of wireless systems. Multi‐hop wireless systems have drawn significant attention as a cost‐effective solution to improve the performance of wireless systems. In these systems, a certain number of relays is deployed over the cell to help in the transmission of signals from the base station (BS) to the users. In a multi‐hop system, a low‐quality long‐distance link is broken into two or more better‐quality links, minimising the outage probability and enhancing the system performance. Interference is one of the fundamental elements affecting the quality of service in wireless networks. The probability density function (PDF) of the signal‐to‐interference ratio (SIR) is evaluated in a circular cell with uniformly distributed users around a BS located at the centre of the cell. Then, the PDF for outage probability is assessed, based on the evaluated SIR. After that, the minimum number of relays and their placement is found over the studied area, which can achieve the desirable performance of the wireless system. Finally, simulation is performed based on long‐term evolution parameters to validate the derived analytical solution.

Large-scale fading (LSF) between interacting nodes is a fundamental element in radio communications, responsible for weakening the propagation, and thus worsening the service quality. Given the importance of channel-losses in general, and the inevitability of random spatial geometry in real-life wireless networks, it was then natural to merge these two paradigms together in order to obtain an improved stochastical model for the LSF indicator. Therefore, in exact closed-form notation, we generically derived the LSF distribution between a prepositioned reference base-station and an arbitrary node for a multi-cellular random network model. In fact, we provided an explicit and definitive formulation that considered at once: the lattice profile, the users' random geometry, the effect of the far-field phenomenon, the path-loss behavior, and the stochastic impact of channel scatters. The veracity and accuracy of the theoretical analysis were also confirmed through Monte Carlo simulations.

In the literature, performance of a wireless system has been evaluated for uniformly distributed users. To efficiently evaluate the performance of a wireless system, we should emulate the distribution of users as the most likely occurring in real life. In many real-life cases, the distribution of users is considered to be Gaussian. In this work, we evaluate the probability density function (PDF) of outage probability based on signal to interference ratio (SIR) for Gaussian-distributed users around a centralized base station. Finally, simulations based on Long Term Evolution (LTE), are performed, which show good agreement with the analytical results.

Given that outage probability is one of the important factors to study the performance of a wireless system, we evaluate PDF for outage probability based on path-loss with uniformly distributed users in a circular cell. Also, we expand our method to enhance the performance of a wireless system by using multihop relaying system. In this solution, a certain number of relays are deployed over the cell to minimize outage probability and improve the performance of a wireless system. We investigate the optimal number of relays and their optimal location over the studied area to reach a specific outage probability. Finally, simulations are performed based on Long Term Evolution (LTE) parameters in order to validate the derived analytical solution.

We investigate the achievable performance gain that network coding (NC) when combined with successive interference cancellation (SIC) brings to a multihop wireless network. While SIC enables concurrent receptions from multiple transmitters, NC reduces the transmission time-slot overhead, and each of these techniques has shown independently great benefits in improving the network performance. We present a cross-layer formulation for the joint routing and scheduling problem in a wireless network with NC (with opportunistic listening) and SIC capabilities. We use the realistic signal-to-interference-plus-noise ratio (SINR) interference model. To solve this combinatorially complex nonlinear problem, we decompose it (using column generation) to two linear subproblems-namely opportunistic NC aware routing and scheduling subproblems. Our scheduling subproblem consists of activating noninterfering NC components, rather than links, which do not interfere with each other and will be used to route the traffic. We further extend our design to consider a multirate multihop wireless network with interference cancellation capabilities. We use numerical evaluation to present the achieved performance gain and compare our work to three other models: a base model with no NC and SIC, a model with only NC, and a model with only SIC capabilities. The numerical results show that our proposed method (both with and without variable transmission rate selection) achieves performance gains that range between moderate and significant for the various considered scenarios. Such improvements are attributed to the joint capabilities of SIC and NC in effectively controlling the interference and improving the spatial reuse.

In this paper, we study the performance of multi-hop wireless networks when both proper interference control and effective spatial reuse are jointly considered. For the former, we assume nodes endowed with Successive Interference Cancellation (SIC) capabilities at the physical layer and for the latter, we advocate joint link scheduling and power allocation. We study the achievable performance of such networks through a cross-layer design framework. We formulate the joint problem of routing, link scheduling and power allocation as a mixed integer non-linear program (MINLP) and we use column generation (CG) to decompose and linearize it, and hence, solve it. Our numerical results show that when SIC and power control are combined, around 75% performance improvement in dense networks may be achieved in comparison with a network that does not incorporate any advanced interference management techniques.

The emulation of wireless nodes spatial position is a practice used by deployment engineers and network planners to analyze the characteristics of a network. In particular, nodes geolocation will directly impact factors such as connectivity, signals fidelity, and service quality. In literature, in addition to typical homogenous scattering, normal distribution is frequently used to model mobiles concentration in a cellular system. Moreover, Gaussian dropping is often considered as an effective placement method for airborne sensor deployment. Despite the practicality of this model, getting the network channel loss distribution still relies on exhaustive Monte Carlo simulation. In this paper, we argue the need for this inefficient approach and hence derived a generic and exact closed-form expression for the path-loss distribution density between a base-station and a network of nodes. Simulation was used to reaffirm the validity of the theoretical analysis using values from the new IEEE 802.20 standard.

In this work a cross-layer optimization in centralized Wireless Mesh Networks equipped with multiple antennas is introduced. A scenario has been considered in which multiple antennas at each node are employed to suppress the interference through beam-forming. By integrating different constraints from MAC and Network layers, a mathematical LP formulation is presented to minimize the system activation time. Since the optimization problem is a complex combinatorial one, the optimal solution is approached by a Column Generation decomposition method. Numerical results indicating the theoretical capacity limit of the network are provided for different node densities, transmission ranges and number of antennas. It is shown that interference suppression increases the spectrum spatial reuse and enhances the throughput of the network by minimizing the operation time duration of the system. Moreover, depending on the density of the interference and traffic sessions, there is a saturation threshold on the number of antenna elements; beyond that, more antennas do not necessarily result in smaller system activation time. Furthermore, increasing the transmission range leads to decrease the system activation time of such networks.

We present a cross-layer optimization framework for wireless mesh networks; we assume nodes are equipped with smart antenna and techniques such as beam-forming, spatial division multiple access and spatial division multiplexing are considered. These techniques provide interference suppression, capability to communicate with several nodes simultaneously and higher transmission data rates, respectively. By integrating different constraints from MAC and network layers, a mathematical formulation of the problem is presented. It is shown that the resulted directive, multiple access and multiplexing gain combined with optimal link scheduling effectively increase both the spectrum spatial reuse and the capacity of the links and thus, enhance the achievable system throughput. Since the optimization problem is a complex combinatorial one, the optimal LP solution is approached by a Column Generation decomposition method. The numerical results for different network topologies with various node densities, transmission ranges, traffics and number of antennas are provided, in which system activation time is reduced up to 86.9% by employing smart antenna techniques.

In this paper, we propose a scheme called "beam- nulling". In the beam-nulling scheme, the eigenvector of the weakest subchannel is fed back and then signals are sent over a generated subspace orthogonal to the weakest subchannel. Theoretical analysis and numerical results show that the capacity of beam-nulling is closed to the optimal water-filling at medium SNR. Additionally, signal-to-interference-plus-noise ratio (SINR) of MMSE receiver is derived for beam-nulling. Then the associated average bit-error rate (BER) of beam-nulling is given numerically and verified by simulation. Simulation results are provided to compare beam-nulling with beamforming. To improve performance further, beam-nulling is concatenated with linear dispersion code. Simulation results are also provided to evaluate the concatenated scheme beamforming at the same data rate.

The mapping of coded bits to constellation symbols plays an important role in determining the bit error rate performance of bit interleaved coded modulation systems. In this paper, we investigate the optimization of multi-dimensional mapping for bit interleaved coded modulation with iterative decoding over block fading MIMO channels. To introduce the optimized mappings, cost function is derived based on upper bound on the pairwise error probability. The optimized mappings perform better than the conventional mapping, and other proposed mappings.

In this paper, we present a study of error performance of linear dispersion codes. First, an upper bound of average error probability is derived for any signal-to-noise ratio. Based on this bound, a tight upper bound of average error probability at high signal-to-noise ratio is further derived to show the diversity advantage of linear dispersion codes. The tight bound demonstrates the relationship of error probability to constellation size and space-time symbol rate. The bound at high signal-to-noise ratio is verified by simulation results.

In this paper, the design of constellation mapping for bit interleaved coded modulation systems with iterative decoding (BICM-ID) for multiple input multiple output (MIMO) channel is studied. Based on minimizing pair-wise error probability, a design criterion is proposed to find the optimal constellation mapping for a MIMO-BICM-ID system. Using the design criterion and employing the binary switching algorithm, some optimal constellation mappings are found for 2-dimensional and 3-dimensional cases. It is shown that proposed mapping schemes outperform conventional ones significantly at high Signal to Noise Ratio (SNR) over fading channels.

In this paper, we propose a multiple input multiple output, orthogonal frequency division multiplexing, code-division multiple-access (MIMO OFDM-CDMA) scheme. The main objective is to provide extra flexibility in user multiplexing, and offer better diversity/multi-user-multiplexing tradeoff. This is done by spreading on all the signal domains; i.e, space-time-frequency spreading is employed to transmit users' signals. Our study and simulation results show that MIMO OFDM-CDMA is capable of flexible data rates and easy user multiplexing, while simultaneously suppressing the multi-user interfering signals. In addition, our scheme achieve a diversity gain significantly larger than that of the conventional 2-D CDMA OFDM scheme.

The authors investigate the design of linear dispersion (LD) codes, aiming at flexible encoding schemes that allow various rate–performance tradeoffs under a common coding structure. First, the capacity of LD codes is studied. It is shown that the maximum attainable multiplexing gain of a linear dispersion code is the number of symbols per channel use of the code (i.e. coding rate in symbols). In addition, conditions on the construction of linear dispersion matrices for various multiplexing gains are established. A general multilayered linear dispersion coding scheme that allows various multiplexing gains is then proposed. In the proposed scheme, coding rate can be adapted by employing different numbers of dispersion matrices. Furthermore, phase shifting among input symbols is applied to optimise the error performance without loss of multiplexing gain. The construction of dispersion matrices and the optimisation of the phase shifts together constitute a structured approach for the design of linear dispersion codes. Simulation results demonstrate that the new codes outperform conventional LD codes at various data rates.

In this paper, we present a new adaptation scheme for MIMO systems using linear dispersion code. The statistics of signal-to-interference-noise for a MIMO transceiver using linear dispersion code and linear minimum-mean-square-error (MMSE) receiver over a Rayleigh fading channel is studied. The associated probability density function of the signal-to interference-noise is derived and verified. The average BER over MIMO fading channel for a given constellation using the MMSE receiver is calculated numerically. The numerical and simulation results match very well. With the statistics as a guideline, we study new design of selection-mode adaptation using a linear dispersion code. A new adaptive parameter, called space-time symbol rate, can be applied due to the use of linear dispersion code. An adaptive algorithm for the selection-mode adaptation is proposed. Based on the proposed algorithm, two adaptive techniques using constellation and space-time symbol rate are studied, respectively. If constellation and space-time symbol rate are considered jointly, more selection modes can be available. Theoretical analysis demonstrates that the average transmission rate of selection-mode adaptation can be improved in this case. Simulation results are provided to show the benefits of our new design.

In this paper, we analyze the convergence speed of the iterative multi-user detection turbo-coded CDMA system. The convergence speed is measured in terms of iterations. We are mainly interested in the influence of the system parameters on the convergence speed to the single-user performance. We use the variance exchange graph (VEG) to predict and visualize the convergence speed of the proposed system. The variance exchange graph provides us a detailed description of the iterative process, and enables us to investigate the convergence speed of the system from two angles: first, the influence of multiple access interference (MAI) and channel noise on the convergence speed of the system is studied; second, the convergence speed of the system with different turbo decoding iterations is investigated. Some design guidelines are obtained to choose an efficient iteration pattern for the system.

In this paper, a new approach to improving reliability and bandwidth efficiency in communications over frequency-selective channels using multiple antennas is proposed. In the heart of the new approach is a novel space-time orthogonal frequency division multiplexing (OFDM) scheme. The proposed space-time OFDM modulator translates a multiple-input multiple-output (MIMO) channel into a single-input multiple-output (SIMO) channel without the loss of system freedom (the available diversity gain). This translation simplifies code design as compared to that in the conventional MIMO OFDM approach. Instead of more complicated space-time codes, codes that are designed for single-input fading channels can be used with the proposed space-time modulation. For bandwidth-efficient applications, a channel multiplexing scheme is developed to work with the space-time modulator. Unlike the conventional spatial multiplexing schemes, an arbitrary number of data streams can be created and each layer occupies all the transmit antennas all the time. As a result, all the available degrees of freedom are preserved for each layer and a full range of optimal tradeoffs between data rate and reliability is possible. Several examples are given to demonstrate the advantages of the proposed approach over the conventional MIMO OFDM approach

In this paper, a prototype design for a wireless modem suitable for digital satellite news gathering is presented. The implementation aspects of a two-stage Pragmatic TCM codec into a Xilinx Virtex-II FPGA are addressed. The main design challenge is to implement the algorithm from a high abstract-level down to an actual circuitry, using the Xilinx system generator for DSP. This tool provides high-level abstractions that are automatically compiled into an FPGA, with no loss in performance over designs implemented in lower-level languages [7]. The system includes concatenated FEC codes, interleaver/de- interleaver and SQRC digital filters. The design flow demonstrates an approach to implement and prototype real-time base band modem into a programmable chip. The modem is efficiently implemented into 0.15 mum/0.12 mum CMOS 8-layer metal process Virtex II FPGA. Finally, the resulting circuitry is simulated and confirmed to transmit/receive digital audio and video signals up to 27.778 Mbit/s.

This paper examines the performance of space- time trellis codes (STTCs) over block Rayleigh fading channels with receive antenna selection. Antenna selection is performed based on maximizing the instantaneous received signal-to-noise ratio (SNR). We derive explicit upper bounds on the pairwise error probability and show that the resulting diversity order deteriorates with antenna selection and becomes a function of the number of selected antennas. We provide numerical examples and simulation results that validate these theoretical findings. We remark that the same result holds for fast fading channels, as well as for quasi-static fading channels when the underlying STTC is rank deficient. However, when the channel is quasi-static fading and the STTC is full rank, the diversity order is maintained with antenna selection. In contrast, when the underlying code is an orthogonal space-time block code (OSTBC), the diversity order is always maintained with antenna selection regardless of the type of fading involved. The same results hold when the OSTBC is concatenated with an outer channel code. These findings render STTCs when antenna selection is employed unattractive.

In this paper, we study the performance of space-time trellis codes (STTCs) with receive antenna selection over fast fading channels. Specifically, we derive upper bounds on the pairwise-error probability (PEP) with antenna selection. In performing the selection, we adopt a criterion that is based on using L out of the available M receive antennas that result in maximizing the instantaneous signal-to-noise ratio (SNR) at the receiver, where L les M. We show that the diversity order resulting from antenna selection deteriorates significantly and is actually dictated by the number of selected antennas. The implication of this result is that adding more receive antennas, while maintaining the same number of selected ones, will have no impact on the diversity order, but it does, however, provide some additional coding gain. This is unlike the case for quasi-static fading channels in which the diversity order is always preserved with antenna selection when the underlying STTC is full-rank. We present numerical examples that support our analysis

In this paper, a new layered space-time coding scheme for flat fading MIMO channels is presented. Based on linear dispersive coding that preserves the channel capacity, the proposed scheme employs phase shifts among input symbols to maximize both diversity and coding gains without loss of mutual information. In addition, this coding scheme provides simple spatial multiplexing (channel layering) through antenna weighting. As a result, a class of linear block space-time codes can be designed to achieve various tradeoffs between performance and spectral efficiency. Simulation results are provided to show the merits of the proposed scheme compared to conventional schemes.

We derive explicit upper bounds on the pairwise-error probability (PEP) for space-time trellis codes (STTCs) with receive antenna selection over fast fading channels. In performing antenna selection, we adopt a selection criterion that is based on selecting L out of the available M receive antennas that result in maximizing the instantaneous signal-to-noise ratio (SNR) at the receiver, where L/spl les/M. We show that the resulting diversity order deteriorates significantly and becomes a function of the number of selected antennas. The implication of this result is that adding more receive antennas, while maintaining the same number of selected ones, will have no impact on the diversity order, but it does, however, provide some additional coding gain. This is unlike the case for quasistatic fading channels in which the diversity order is always preserved with antenna selection when the underlying space-time code is full-rank. We also present simulation results that support our analysis.

This paper presents a new diversity scheme for quasi-static wireless MIMO channels. In the proposed scheme, an innovative pre-coding/framing mechanism is employed to translate a multiple-input multiple-output (MlMO) frequency-selective channel into a mathematically equivalent single-input multiple-output (SIMO) channel. Consequently, the conventional trellis codes designed for fast fading channels can be used to exploit diversity in both spatial and frequency domains. It was shown that the diversity gain of the proposed scheme equals the effective length of the conventional trellis codes used. This is in contrary to the case of space-time coded OFDM (STC-OFDM) where no systematic methods exist for the design of space-time trellis codes with a given target of diversity gain. Simulations have been carried out and results are given to show the merits of the proposed scheme.

A new cellular structure for a versatile Reed-Solomon (RS) decoder is introduced based on time domain decoding algorithm. The time domain decoding algorithm is restructured to be suitable for introducing the cellular structure. The main advantages of this structure are its versatility and very simple cellular structure. By versatile decoder we mean a decoder that can be programmed to decode any (n, k) RS code defined in Galois field 2/sup m/ with a fixed block length n and a fixed symbol size m. This decoder can correct both errors and erasures for any message length k. The introduced decoder is cellular and has a very simple structure and hence it is suitable for VLSI designs.

A technique for reducing the number of inversions in the time-domain decoding algorithm based on an algebraic decoder (Blahut's decoder) is introduced. It is proved that the modified algorithm is equivalent to the original one. The modified algorithm can be used in the universal Reed-Solomon decoder to decrease complexity.>

A versatile Reed-Solomon (RS) decoder structure based on the time-domain decoding algorithm (transform decoding without transforms) is developed. The algorithm is restructured, and a method is given to decode any RS code generated by any generator polynomial. The main advantage of the decoder structure is its versatility, that is, it can be programmed to decode any Reed-Solomon code defined in Galois field (GF) 2/sup m/ with a fixed symbol size m. This decoder can correct errors and erasures for any RS code, including shortened and singly extended codes. It is shown that the decoder has a very simple structure and can be used to design high-speed single-chip VLSI decoders. As an example, a gate-array-based programmable RS decoder is implemented on a single chip. This decoder chip can decode any RS code defined in GF (2/sup 5/) with any code word length and any number of information symbols. The decoder chip is fabricated using low-power 1.5- mu , two-layer-metal, HCMOS technology.>