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A fundamental component of spatial modulation (SM), termed generalized space shift keying (GSSK), is presented. GSSK modulation inherently exploits fading in wireless communication to provide better performance over conventional amplitude/phase modulation (APM) techniques. In GSSK, only the antenna indices, and not the symbols themselves (as in the case of SM and APM), relay information. We exploit GSSKpsilas degrees of freedom to achieve better performance, which is done by formulating its constellation in an optimal manner. To support our results, we also derive upper bounds on GSSKpsilas bit error probability, where the source of GSSKpsilas strength is made clear. Analytical and simulation results show performance gains (1.5-3 dB) over popular multiple antenna APM systems (including Bell Laboratories layered space time (BLAST) and maximum ratio combining (MRC) schemes), making GSSK an excellent candidate for future wireless applications.

In this paper, we propose a joint carrier frequency offset (CFO) and channel estimation scheme based on the well known variable projection (VP) method for the uplink channel of orthogonal frequency division multiplexing (OFDM) systems. The CFOs and channel coefficients are estimated by minimizing the least-squares (LS) cost function through a numerical optimization technique. In each iteration, the CFOs and channel coefficients are updated separately, which distinguishes the VP method from an existing method in which the CFOs and channel coefficients are treated together as a whole. We demonstrate through several numerical examples the superiority of the proposed scheme in terms of convergence speed, computational complexity and estimation performance with regard to CFO estimation. However, the proposed scheme does not provide reliable estimation for the channel coefficients. We will investigate this problem further in our future research work.

In this paper we construct a special type of cyclic codes called cyclic DNA codes over the ring R = {0, 1, u, u + 1} where u2 = 1. These codes are important in the subject of biomolecular computation and DNA computing. We apply a more suitable measure (the similarity measure) than the Hamming distance measure on the set of codewords. Our similarity measure depends on the number of hydrogen bonds between Watson Crick complement pairs.

This paper proposes an extended Kalman filter (EKF)-based and training symbol aided carrier frequency offset (CFO) estimation scheme for the uplink OFDM systems. Typically, in EKF-based estimation scheme, the measurement equation is a function of the CFO and channel coefficients. Therefore, a vector EKF has to be employed to estimate all the unknowns, which may sometime result in convergence problems. To avoid these problems, the proposed scheme uses a scalar EKF. The user signals are first separated by using multiple-access interference cancellation. Then, the unknown channel coefficients in the measurement equation are replaced with a non-linear function of the CFO so that the scalar EKF can be employed. The observation noise power is analyzed and its approximation is used in the EKF algorithm. Several numerical examples are presented to validate the efficacy of the proposed scheme. It is shown that the proposed scheme can achieve the Cramer-Rao lower bound (CRLB) when the number of users is small, whereas it degrades when the number of users increases. We also compare its computational complexity with several existing schemes.

We introduce coded cooperation diversity using relay nodes in the decode-and-forward (DF) mode, in which the codewords of the source node are partitioned and transmitted through independent fading channels to both relay and destination nodes, to achieve remarkable gains over a noncooperative system. The main difference between the distributed and the noncooperative space-time coding is that the link between the source and the relay node is not error-free in the distributed case, as opposed to the noncooperative case. In this work, we take into account the errors in the source-relay link and derive upper bounded expression for the symbol error rate on DF relaying in the case of M-ary phase shift keying (M-PSK) transmission. Our analytical results show that the maximum diversity order is achieved provided that the source-relay link is more reliable than the other links. Otherwise, the diversity degrades. This is unlike the case when the relay nodes operating in the DF mode are based on symbol-by-symbol decoding and forwarding. We present several numerical examples to support our analytical expression.

In this paper, we consider distributed coding for wireless cooperative networks with antenna/relay selection. The aim of this of work is to find ways to improve the reliability of the source-relay link in an effort to maintain the diversity order available in the system. To this end, we propose to use antenna selection at the relay node whereby the antenna with the best instantaneous received signal to noise ratio is selected. This assumes that the relay node is equipped with multiple antennas, but only one radio frequency (RF) chain is employed. The concept of antenna selection can be extended to relay selection. That is, among the available relay nodes, the one with the best source-relay link reliability is selected. Assuming decode-and-forward (DF) relaying, we analyze the antenna/relay selection in conjunction with a previously proposed distributed coded cooperation scheme based on convolutional codes. Specifically, we derive an upper bounded expression for the symbol error rate assuming M-ary phase shift keying (M-PSK) transmission. Our analytical results show that the maximum diversity order of the system is maintained for the entire range of bit error rate of interest, unlike the case without antenna selection. Several numerical and simulation results are presented to demonstrate the efficiency of the proposed scheme.

In this paper, we consider a coded cooperation diversity scheme suitable for relay channels. The proposed scheme is based on convolutional coding, where each codeword of the source node is partitioned into two parts. The first part is transmitted from the source to the relays and destination. The second part is transmitted simultaneously from the source and relay nodes to the destination. All the relay nodes are assumed to be operating in the decode-and-forward (DF) mode. At the destination, the two replicas of the second sub-codeword are combined using maximum ratio combining (MRC). The entire codeword is decoded via the Viterbi algorithm. We analyze the proposed scheme for L-relay channels in terms of its probability of symbol error and outage probability. In that, explicit upper bounds are obtained assuming M-ray phase shift keying (M-PSK) transmission. Our analytical results show that the maximum diversity order is achieved provided that the source-relay link is more reliable than the other links. Otherwise, the diversity degrades. However, in both cases, it is shown that substantial performance improvements are possible to achieve over noncooperative coded systems. Several numerical and simulation results are presented to demonstrate the efficiency of the proposed scheme.

In this paper, we introduce a novel approach to interference cancellation for code division multiple access (CDMA) uplink transmission. Several models combining principles of serial (SIC) and parallel (PIC) interference cancellation are discussed. The proposed scheme is derived from the analysis of these hybrid models and applies a user configuration algorithm (termed "trickle") in order to provide improved bit-error-rate (BER) performance. The algorithm utilizes an adaptive matrix to compute the required configuration to be used for the subsequent interference cancellation stage. Bit-streaming, pipelined multiuser detection is employed and channel estimates are obtained using sample pilot data known at the receiver. We demonstrate that significant performance improvements can by achieved over various hybrid schemes. An improvement over the previous trickle model is also demonstrated where processing delay is greatly reduced while maintaining similar performance.

In this paper, we propose a new transceiver architecture for multiple-input multiple-output (MIMO) systems. The proposed scheme borrows ideas from the multilayered space-time coding (MLSTC) and threaded space-time coding (TSTC) schemes in an effort to maximize the diversity order while maintaining a low complexity detection. Specifically, the proposed scheme has a structure similar to that of the MLSTC while it employs a spatial interleaver (SI) in front of the MLSTC encoder. We also consider a low-complexity decoder that is based on the minimum mean squared error (MMSE) criterion and the QR decomposition (QRD). We provide analytical and simulation results through which we demonstrate that the proposed scheme provides improved diversity-multiplexing gain trade-off, as well as improved performance, all relative to the MLSTC scheme. In addition, with the proposed scheme, all layers achieve the same performance, which makes it attractive in multiuser environments.

This chapter contains sections titled: Capacity and Information Rates of Noisy Channels Capacity and Information Rates of AWGN and Fading Channels Capacity of MIMO Channels Constrained Signaling for MIMO Communications Discussion: Why Use MIMO Systems? Chapter Summary and Further Reading Problems

This chapter contains sections titled: MIMO Frequency Selective Channels Capacity and Information Rates of MIMO Frequency Selective Fading Channels Space‐Time Coding for MIMO FS Channels Channel Detection for MIMO FS Channels MIMO OFDM Systems Chapter Summary and Further Reading Problems

This chapter contains sections titled: Transmit Diversity with Two Antennas: The Alamouti Scheme Orthogonal Space‐Time Block Codes Quasi‐Orthogonal Space‐Time Block Codes Linear Dispersion Codes Chapter Summary and Further Reading Problems

In this paper, we investigate the performance of a coded cooperation diversity using relay nodes in the decode-and-forward (DF) mode, in which the codewords of the source node are partitioned and transmitted through independent fading channels to both the relay and destination nodes. The application of such a cooperative coding scheme is shown to offer remarkable gains over a noncooperative system. Unlike noncooperative space-time coding, in distributed cooperative coding, the link between the source and the relay node is not error-free. In this work, we take into account the errors in the source-relay link and derive the outage probability of DF relaying for binary phase shift keying (BPSK) transmission. Our analytical results show that the proposed scheme achieves full diversity. This is different from conventional relay systems where the relay nodes operating in the DF mode are based on symbol-by-symbol decoding and forwarding. Numerical results are shown to support our analytical expression.

Merging layered space-time (LST) coding, which provides high data rate transmission, with space-time block coding (STBC) provides a tradeoff between transmit diversity and bandwidth efficiency in multiple-input multiple-output (MIMO) systems. This architecture is known as multilayered space time coding (MLSTC). In this paper, we propose a reduced complexity MMSE detector based on the Sorted QR decomposition, intended for MLSTC systems. The proposed decoder has reduced computational complexity in comparison to the group interference cancellation scheme. Our proposed decoder allows for the number of receive antennas to be less than the number of transmit antennas. Since we are dealing with a multiuser system, we wish all users to benefit from the same performance. We therefore use power allocation techniques to amplify users to the highest level of performance available and thus improving the performance.

This paper proposes a hybrid interference cancellation scheme for wideband code division multiple access (WCDMA) uplink transmission. Principles of serial (SIC) and parallel (PIC) interference cancellation are combined with a novel user configuration algorithm (termed "trickle") in order to provide improved bit-error-rate (BER) performance while maintaining overall processing delay as compared to previous hybrid schemes. The proposed scheme utilizes an adaptive matrix to compute the required number of interference cancellation iterations for each user prior to the detection process. The total number of iterations is determined based on the number of users and is set to match that of previously designed interference cancellation models. Bit-streaming, pipelined multiuser detection is employed and channel estimates are obtained using sample pilot data known at the receiver. The trickle algorithm is applied to conventional SIC as well as previous hybrid models. Results show an improvement of 1 dB over group-wise SIC and similar performance to hybrid IC with reduced processing delay at the cost of complexity.

Taking into consideration the dominance of the multiple access interference (MAI) in spread spectrum based CDMA systems, power control plays a vital role in reducing the system interference and helps in increasing the capacity of the system while maintaining the quality of the received signal. Closed loop power control is mainly used to mitigate the near-far effect in the uplink direction. In this paper, we propose a bit error rate (BER)-based first order distributed power control algorithm. Being distributed, the proposed algorithm has the flexibility of using the benefits of fast closed loop power control and thus can be used to update the transmit power of a single user at a time. Signal-to-interference ratio (SIR) based algorithms are in extensive use. But considering that the SIR is time variant, the BER would be a better quality of service (QoS) parameter because it can be easily measured using already known pilot bits. We analyze the convergence performance of the proposed algorithm and show that its convergence is always guaranteed. We demonstrate that a considerable improvement in the convergence speed along with the required average signal-to-noise ratio (SNR) is achieved as compared with other BER-based algorithms under comparison. We also show that the proposed algorithm performs well at different mobile speeds.

Cooperative diversity provides reliable communications between nodes in a network through relay nodes. In this paper, we introduce a new transmission protocol for relay fading channels. We examine the performance of the proposed protocol using both the amplify-and-forward (AF) and decode-and-forward (DF) modes. Our results prove that using this protocol, one can achieve full spatial diversity at full rate. We also show that our protocol with M relays is equivalent to a delay diversity scheme with M + 1 transmit antennas. At the receiver side, a maximum likelihood sequence detector is used to recover the transmitted symbols. Comparing our protocol with existing ones, we noted large performance degradations in all protocols when the relay is operating in the DF mode where detection errors exist. This is different from the AF mode, where diversity is always maintained and only a SNR loss is incurred (relative to the ideal case of error-free relay transmission). This, in turn, suggests that even with the large cost/complexity involved in the DF mode, the ensuing performance may be poor compared to the AF mode. Motivated by this fact, we obtain a bit-error rate upper bound for a multi-relay configuration where all relay nodes operate in the AF mode. At high signal-to-noise ratio (SNRs), this error bound is shown to be tight when compared to simulation results.

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.

Power control has been an important issue in multiple access systems allowing more users to share the system resources. The capacity of the WCDMA system is limited by the total interference, called multiple access interference (MAI). An efficient power control algorithm is always required to improve the system performance. In this paper, we propose a distributed, first order power control algorithm. The proposed algorithm uses an exponential function with a modified form of the LMS algorithm in order to achieve a better speed of convergence. We examine the proposed algorithm for time varying multipath Rayleigh fading environment. We compare the performance of the proposed algorithm and the 3GPP standard algorithm. We demonstrate that the proposed algorithm achieves better convergence and saves on the signal-to-noise ratio (SNR) required to achieve a certain performance. We also demonstrate that the proposed algorithm works well for different mobile speeds with a continuously changing channel.

Noise can highly impact the performance of video processing algorithms. This paper proposes a new real-time spatio-temporal method for estimating the noise variance in video signals. The proposed algorithm selects 3D regions or cubes in the video signal with high intensity uniformity. The noise variance is estimated from the selected set of spatially, temporally and spatio-temporally intensity-uniform cubes using local variances calculated along homogeneous plains. The proposed algorithm works well for sequences with high structure and motion activity and outperforms other methods with a worst-case estimation error of 2 dB. It works well for highly noisy and non-noisy sequences.

This paper proposes a method for the reduction of white Gaussian video noise. The method achieves a maximum gain of 5.6 dB and is capable of preserving image content. It adapts window size, weighting and behavior to both image content and noise level in order to optimize the filtering. It starts by detecting the intensity-homogeneous direction from 8 different candidates. A variant of the Wiener filter is then applied directionally. The filtering is performed along homogeneous areas and not across edges. For noisy images, the filtering is increased automatically by using a larger kernel size. The proposed filter achieves better image preservation by turning off gradually for less noisy images. It works well for both highly noisy and good-quality images.

In this paper, we present a comprehensive analysis of the outage probability for multiple-input multiple-output (MIMO) systems over spatially correlated Rayleigh fading chan-nels. In our analysis, we assume that 1) the channel state information (CSI) is perfectly known at the receiver but not at the transmitter, 2) the spatial correlation is present at both ends of the wireless communications link, 3) the transmit and receive correlation matrices may or may not be full rank, and 4) the underlying channel is quasi-static fading. With these assumptions, we derive explicit bounds for the outage probability and show that the diversity order is simply the product of the rank of the transmit correlation matrix and the rank of the receive correlation matrix. We also derive an expression that accurately quantifies the degradation in the signal-to-noise ratio (SNR) due to the presence of correlation. We present several numerical examples that validate our analysis.

In this paper, we study a special class of nonbinary additive cyclic codes over GF(4) which we call reversible complement cyclic codes. Such codes are suitable for constructing codewords for DNA computing. We develop the theory behind constructing the set of generator polynomials for these codes. We study, as an example, all length—7 codes over GF(4) and list those that have the largest minimum Hamming distance and largest number of codewords.

The asymptotic behavior of the outage probability has been studied recently with the assumption that the receiver is equipped with a single antenna. In this paper, we extend this study to an arbitrary number of receive antennas. We use the Gaussian approximation for the distribution of the random mutual information to derive a threshold for the outage probability. We extend our results to the case when the receiver selects a subset of the available antennas where selection is based on maximizing capacity. We derive the pdf of the mutual information with antenna selection, and show that it can be approximated well with a Gaussian distribution. Based on this pdf, we derive a threshold for the outage probability with antenna selection. We also present several numerical examples that validate our analysis.

In this paper, we present a comprehensive performance analysis of combined convolutional coding and space-time block coding with receive antenna selection. In our analysis we assume that the receiver uses only L out of the available M receive antennas, where, typically, L /spl les/ M. The selected antennas are those that maximize the instantaneous received signal-to-noise ratio (SNR). We derive explicit upper bounds on the bit error rate (BER) performance of the above concatenation scheme for any N, M and L, where N denotes the number of transmit antennas. We show that the diversity order, with antenna selection, is maintained as the same as that of the full complexity system, whereas the deterioration in SNR is upper bounded by 10log/sub 10/(M/L) dB. We also derive two tighter upper bound on the BER for generalized orthogonal STBC and the Alamouti scheme when L = 1. Finally, we present simulation results that validate our analysis.

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.

We analyzed the performance of the serial concatenation of convolutional coding with space-time block coding. We obtained an error bound for the space-time coded system with ideal channel interleaving. Our results indicated that these error bounds are in a good agreement with the exact BER performance especially at low BER levels where error bounds become more significant. We have also shown that the use of antenna selection at the receiver side only effects the SNR coding gain, but not the overall diversity order. This phenomena was evident for both the fast and block flat fading channel models. Moreover, we have shown that the receiver performance is affected significantly by channel interleaving. In that, a comparison between the quasi-static and fast fading channels was conducted where it was shown that the time diversity order dominates the overall system diversity. Furthermore, we have noted that the use of antenna selection results in almost the same SNR reduction regardless of the channel model used.

We propose a simple remedy for the exaggerated extrinsic information produced by the soft-output Viterbi algorithm (SOVA). We argue that what leads to these optimistic extrinsic values is the inherent strong correlation between the intrinsic information (input to the SOVA) and extrinsic information (output of the SOVA). The proposed remedy involves employing two attenuators, one applied to the immediate output of the SOVA and another applied to the extrinsic information before it is passed to the other decoder (assuming iterative decoding). We examine the modified SOVA (MSOVA) on additive white Gaussian noise (AWGN) and fading channels for serial concatenated codes (SCCs). We show that the MSOVA provides substantial performance improvements over both channels. For example, it provides improvements of about 0.8 to 1.0 dB at P/sub b/ = 10/sup -5/ in AWGN, and about 1.4 to 2.0 dB at P/sub b/ = 10/sup -5/ in fading channels, all relative to the SOVA. We extend the proposed modifications to the a posteriori probability (APP) algorithm with favorable results. We demonstrate that the modified APP (MAPP) provides performance improvements between 0.3 to 0.6 dB at P/sub b/ = 10/sup -5/ relative to the APP.

We present a modified soft-output Viterbi algorithm (MSOVA) that performs as good as the a posteriori probability (APP) algorithm with a complexity similar to that of the conventional SOVA algorithm. The idea behind the MSOVA centers around reducing the inherent correlation between the intrinsic information (input to the SOVA) and extrinsic information (output of the SOVA), where the latter is typically much higher than its APP counterpart. The proposed algorithm employs two attenuators, one applied directly to the output of the SOVA and another applied to the extrinsic information before it is passed to the other decoder (assuming iterative decoding). We examine the MSOVA on additive white Gaussian noise (AWGN) and fading channels. We show that the MSOVA provides improvements of about 0.8 to 1.0 dB at P/sub b/ = 10/sup -5/ in AWGN over the conventional SOVA, and is only about 0.1 dB away from the APP. It also provides improvements of 1.4 to 2.0 dB at P/sub b/ = /sup -5/ on fading channels.

In this paper, we present a comprehensive analysis of the outage probability for multiple-input multiple-output (MIMO) systems with receive antenna selection over spatially correlated fading channels. In our analysis, we assume that 1) the channel state information (CSI) is perfectly known at the receiver but not at the transmitter, 2) antenna selection is based on maximizing the channel capacity, 3) the spatial correlation is present at both ends of the wireless communications link, 4) the transmit and receive correlation matrices may or may not be full rank, and 5) the underlying channel is quasi-static fading. With these assumptions, we derive explicit bounds for the outage probability and show that the diversity order is the same as that of the full complexity system. We also derive an expression that quantifies the loss in signal-to-noise ratio (SNR) due to antenna selection We also present several numerical examples that validate our analysis

This paper proposes a real-time method for the reduction of white Gaussian video noise. The method achieves a maximum gain of 4.8 dB and is capable of preserving image content. It adapts window size, weighting and behavior to both image content and noise level in order to optimize the filtering. It starts by detecting the intensity-homogeneous direction from 8 different candidates. A variant of the sigma filter is then applied directionally. The filtering is performed along homogeneous areas and not across edges. For noisy images, the filtering is increased automatically by using the two most homogeneous directions with a larger kernel size. The proposed filter achieves better image preservation by turning off gradually for less noisy images. It works well for both highly noisy and good-quality images without the introduction of speed or hardware implementation challenges.

In this paper, we study cyclic codes of length n= 2/sup e/ over the ring R/sub 4/= /spl Zopf//sub 4/[x]/(x/sup n/-1). In particular, we derive a mass formula of these codes for a given length n. We also give an example in which we study codes of length 8.

In this paper, we derive upper bounds on the bit error rate performance of orthogonal space-time block codes (STBCs) with receive antenna selection. We show that the diversity order is maintained as that of the full complexity system, whereas the deterioration in SNR is upper bounded by 10 log10(M/L) dB where M is the number of available receive antennas and L is the number of selected antennas

The paper is focused on estimating the signal-to-interference ratio (SIR) per multipath component in CDMA systems operating over frequency selective Rayleigh fading channels. A per-path SIR estimator is proposed and its performance is compared to the Cramer-Rao bound (CRB) derived for this problem. To account for the hardware limitations of portable mobile terminals, a low complexity version of the estimator is introduced and incorporated in the receiver structure. Based on the per-path SIR estimates, a new finger assignment algorithm (FAA) is proposed and compared to the conventional energy-based FAA. We show that the proposed FAA exhibits an improved multipath detection capability. Hence, more sophisticated multipath acquisition circuits can be realized based on the per-path SIR estimates.

In this paper we derive upper bounds on the bit error rate (BER) performance of orthogonal space-time block codes (STBC) with receive antenna selection. In our analysis, we assume that the receiver uses only L out of the available M receive antennas, where, typically, L /spl les/ M. The selected antennas are those that maximize the instantaneous received signal-to-noise ratio (SNR). We show that the diversity order with antenna selection is maintained as that of the full complexity system, whereas the deterioration in SNR is upper bounded by 10log/sub 10/(M/L) dB. Furthermore, we derive an expression for the exact BER performance for the Alamouti (1998) scheme when L = 1. Finally, we present simulation results that validate our analysis.

We deal with antenna selection at the receiver side for space-time coded systems over frequency-selective fading channels. We reveal that introducing antenna selection based on the signal-to-noise-ratio (SNR) observed can still achieve the full diversity available, if the underlying space-time code (STC) is full-rank (i.e., if it achieves full diversity without antenna selection over the frequency-selective fading channel). We also argue that if the code is not full-rank, antenna selection results in a loss in the diversity of the system.

In this paper, we discuss an approach for analyzing the serial concatenation of a high rate convolutional code and a preceded intersymbol interference (ISl) channel. The proposed approach is simple and can be used to identify the preceder that results in the lowest error rate floor analytically without resorting to simulations. Also, the proposed approach can be used to enhance the interleaver design to achieve further performance improvement. We extend the proposed technique to fading ISI channels using statistical models of these channels. Simulation results suggest that the optimal preceder, when selected based on the statistical model of the channel, is optimal or somewhat optimal for the time varying channel. We finally remark that the proposed analytical approach is not limited to high rate convolutional codes, but it also applies to arbitrary high rate linear outer codes.

In this paper, we study cyclic codes of length n = 2/sub e/ over the ring R/sub 4/ = /spl Zopf/[x]/(x/sup n/ - 1). In particular, we study the rank of these codes and derive a closed-form expression for that. Finally, we give an example in which we study all codes of length 8 and classify them according to their type.

We examine the performance of the iterative soft-output Viterbi algorithm (SOVA) for high rate turbo codes on an additive white Gaussian noise (AWGN) channel and compare its performance to that of the a posteriori probability (APP) algorithm. Code rates of the form k/sub 0//k/sub 0/+1 (k/sub 0/=4, 8, 16, 92, and 64) are considered. In our simulations, we show that the SOVA algorithm yields a bit error probability (P/sub b/) performance that is only about 0.7 dB inferior to the performance of the APP algorithm and about 1.7 dB from the capacity limit at P/sub b/=10/sup -5/. We also examine SOVA performance as a function of the number of iterations and a parameter we call the reliability depth.

We consider an improved S-random interleaver design for the serial concatenation of a high rate punctured convolutional code and a precoded intersymbol interference (ISI) channel separated by an interleaver. We first identify the error patterns that dominate the performance in the floor region. We then modify the S-random interleaver design such that the dominant weight-2 error patterns are eliminated. Simulation results indicate that a performance improvement of about 0.4 dB at a probability of error of about 10/sup -6/ is possible. More investigation, however, is still required in order to understand the effect of the new design on the distance spectrum corresponding to higher weight patterns.

We discuss two algorithms for mitigating the deleterious effects of nonlinear intersymbol interference (ISI) in PR4- and EPR4-equalized magnetic recording channels. We call them RAM-search algorithms as they borrow the idea of employing a RAM (random access memory) from the RAM-DFE, and because they involve a search. The algorithms have been devised to circumvent the error propagation problem that arises in making tentative decisions in ISI cancellers used together with partial response signaling. Adopting a simple partial erasure model for the magneto-inductive head and a third-order polynomial model for the magneto-resistive head to represent the nonlinear distortion, we show that improvements of about 3 dB are possible.