We address the problem of minimax detecting and isolating abrupt changes in random signals. The criterion of optimality consists in minimizing the maximum mean detection/isolation delay for a given maximum probability of false isolation and mean time before a false alarm. It seems that such a criterion has many practical applications, especially for safety-critical applications, in monitoring dangerous industrial processes and also when the decision should be made in a hostile environment. The redundant strapdown inertial reference unit integrity monitoring problem is discussed. An asymptotic lower bound for the mean detection/isolation delay is given.
{"title":"A lower bound for the detection/isolation delay in a class of sequential tests","authors":"I. Nikiforov","doi":"10.1109/TIT.2003.818398","DOIUrl":"https://doi.org/10.1109/TIT.2003.818398","url":null,"abstract":"We address the problem of minimax detecting and isolating abrupt changes in random signals. The criterion of optimality consists in minimizing the maximum mean detection/isolation delay for a given maximum probability of false isolation and mean time before a false alarm. It seems that such a criterion has many practical applications, especially for safety-critical applications, in monitoring dangerous industrial processes and also when the decision should be made in a hostile environment. The redundant strapdown inertial reference unit integrity monitoring problem is discussed. An asymptotic lower bound for the mean detection/isolation delay is given.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"58 1","pages":"3037-3047"},"PeriodicalIF":0.0,"publicationDate":"2003-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80022933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a novel density evolution approach to analyze the iterative decoding algorithms of low-density parity-check (LDPC) codes and product codes, based on Gaussian densities. Namely, for these classes of codes we derive a one-dimensional (1D) map whose iterates directly represent the error probability both for the additive white Gaussian noise (AWGN) and the Rayleigh-fading channel. These simple models allow a qualitative analysis of the nonlinear dynamics of the decoding algorithm. As an application, we compute the decoding thresholds and show that they are consistent with the simulation results available in the literature.
{"title":"Analysis of the iterative decoding of LDPC and product codes using the Gaussian approximation","authors":"F. Lehmann, G. M. Maggio","doi":"10.1109/TIT.2003.819335","DOIUrl":"https://doi.org/10.1109/TIT.2003.819335","url":null,"abstract":"We propose a novel density evolution approach to analyze the iterative decoding algorithms of low-density parity-check (LDPC) codes and product codes, based on Gaussian densities. Namely, for these classes of codes we derive a one-dimensional (1D) map whose iterates directly represent the error probability both for the additive white Gaussian noise (AWGN) and the Rayleigh-fading channel. These simple models allow a qualitative analysis of the nonlinear dynamics of the decoding algorithm. As an application, we compute the decoding thresholds and show that they are consistent with the simulation results available in the literature.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"94 9 1","pages":"2993-3000"},"PeriodicalIF":0.0,"publicationDate":"2003-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87676451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Binary sequences of period 2/sup n/-1 generated by a linear feedback shift register (LFSR) whose stages are filtered by a nonlinear function, f, are studied. New iterative formulas are derived for the calculation of the linear complexity of the output sequences. It is shown that these tools provide an efficient mechanism for controlling the linear complexity of the nonlinearly filtered maximal-length sequences.
{"title":"On the linear complexity of nonlinearly filtered PN-sequences","authors":"N. Kolokotronis, N. Kalouptsidis","doi":"10.1109/TIT.2003.818400","DOIUrl":"https://doi.org/10.1109/TIT.2003.818400","url":null,"abstract":"Binary sequences of period 2/sup n/-1 generated by a linear feedback shift register (LFSR) whose stages are filtered by a nonlinear function, f, are studied. New iterative formulas are derived for the calculation of the linear complexity of the output sequences. It is shown that these tools provide an efficient mechanism for controlling the linear complexity of the nonlinearly filtered maximal-length sequences.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"30 1","pages":"3047-3059"},"PeriodicalIF":0.0,"publicationDate":"2003-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85966244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The primary contribution of this work lies in the derivation of the exact characteristic function (and hence, the mean and variance) of the capacity of multiple-input multiple-output (MIMO) systems for semicorrelated flat-fading channels. A Gaussian approximation to the exact capacity results is suggested and evaluated for its accuracy. We show that over a range of correlation levels this approximation is adequate even for moderate numbers of transmit and receive antennas.
{"title":"Capacity of MIMO systems with semicorrelated flat fading","authors":"Peter J. Smith, Sumit Roy, M. Shafi","doi":"10.1109/TIT.2003.817472","DOIUrl":"https://doi.org/10.1109/TIT.2003.817472","url":null,"abstract":"The primary contribution of this work lies in the derivation of the exact characteristic function (and hence, the mean and variance) of the capacity of multiple-input multiple-output (MIMO) systems for semicorrelated flat-fading channels. A Gaussian approximation to the exact capacity results is suggested and evaluated for its accuracy. We show that over a range of correlation levels this approximation is adequate even for moderate numbers of transmit and receive antennas.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"29 1","pages":"2781-2788"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84949835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Approximate maximum-likelihood noncoherent sequence detection (NSD) for differential space-time modulation (DSTM) in time-selective fading channels is proposed. The starting point is the optimum multiple-symbol differential detection for DSTM that is characterized by exponential complexity. By truncating the memory of the incremental metric, a finite-state trellis is obtained so that a Viterbi algorithm can be implemented to perform sequence detection. Compared to existing linear predictive receivers, a distinguished feature of NSD is that it can accommodate nondiagonal constellations in continuous fading. Error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers. By incorporating the reduced-state sequence detection techniques, performance and complexity tradeoffs can be controlled by the branch memory and trellis size. Numerical results show that most of the performance gain can be achieved by using an L-state trellis, where L is the size of the DSTM constellation.
{"title":"Noncoherent sequence detection of differential space-time modulatio","authors":"Cong Ling, K. H. Li, A. Kot","doi":"10.1109/TIT.2003.817452","DOIUrl":"https://doi.org/10.1109/TIT.2003.817452","url":null,"abstract":"Approximate maximum-likelihood noncoherent sequence detection (NSD) for differential space-time modulation (DSTM) in time-selective fading channels is proposed. The starting point is the optimum multiple-symbol differential detection for DSTM that is characterized by exponential complexity. By truncating the memory of the incremental metric, a finite-state trellis is obtained so that a Viterbi algorithm can be implemented to perform sequence detection. Compared to existing linear predictive receivers, a distinguished feature of NSD is that it can accommodate nondiagonal constellations in continuous fading. Error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers. By incorporating the reduced-state sequence detection techniques, performance and complexity tradeoffs can be controlled by the branch memory and trellis size. Numerical results show that most of the performance gain can be achieved by using an L-state trellis, where L is the size of the DSTM constellation.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"29 1","pages":"2727-2734"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74926827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We derive some upper bounds of the rates of (generalized) complex orthogonal space-time block codes. We first present some new properties of complex orthogonal designs and then show that the rates of complex orthogonal space-time block codes for more than two transmit antennas are upper-bounded by 3/4. We show that the rates of generalized complex orthogonal space-time block codes for more than two transmit antennas are upper-bounded by 4/5, where the norms of column vectors may not be necessarily the same. We also present another upper bound under a certain condition. For a (generalized) complex orthogonal design, its variables are not restricted to any alphabet sets but are on the whole complex plane. A (generalized) complex orthogonal design with variables over some alphabet sets on the complex plane is also considered. We obtain a condition on the alphabet sets such that a (generalized) complex orthogonal design with variables over these alphabet sets is also a conventional (generalized) complex orthogonal design and, therefore, the above upper bounds on its rate also hold. We show that commonly used quadrature amplitude modulation (QAM) constellations of sizes above 4 satisfy this condition.
{"title":"Upper bounds of rates of complex orthogonal space-time block code","authors":"Haiquan Wang, X. Xia","doi":"10.1109/TIT.2003.817830","DOIUrl":"https://doi.org/10.1109/TIT.2003.817830","url":null,"abstract":"We derive some upper bounds of the rates of (generalized) complex orthogonal space-time block codes. We first present some new properties of complex orthogonal designs and then show that the rates of complex orthogonal space-time block codes for more than two transmit antennas are upper-bounded by 3/4. We show that the rates of generalized complex orthogonal space-time block codes for more than two transmit antennas are upper-bounded by 4/5, where the norms of column vectors may not be necessarily the same. We also present another upper bound under a certain condition. For a (generalized) complex orthogonal design, its variables are not restricted to any alphabet sets but are on the whole complex plane. A (generalized) complex orthogonal design with variables over some alphabet sets on the complex plane is also considered. We obtain a condition on the alphabet sets such that a (generalized) complex orthogonal design with variables over these alphabet sets is also a conventional (generalized) complex orthogonal design and, therefore, the above upper bounds on its rate also hold. We show that commonly used quadrature amplitude modulation (QAM) constellations of sizes above 4 satisfy this condition.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"41 1","pages":"2788-2796"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76425931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a narrow-band point-to-point communication system with many (input) transmitters and a single (output) receiver (i.e., a multiple-input single output (MISO) system). We assume the receiver has perfect knowledge of the channel but the transmitter only knows the channel distribution. We focus on two canonical classes of Gaussian channel models: (a) the channel has zero mean with a fixed covariance matrix and (b) the channel has nonzero mean with covariance matrix proportional to the identity. In both cases, we are able to derive simple analytic expressions for the ergodic average and the cumulative distribution function (c.d.f.) of the mutual information for arbitrary input (transmission) signal covariance. With minimal numerical effort, we then determine the ergodic and outage capacities and the corresponding capacity-achieving input signal covariances. Interestingly, we find that the optimal signal covariances for the ergodic and outage cases have very different behavior. In particular, under certain conditions, the outage capacity optimal covariance is a discontinuous function of the parameters describing the channel (such as strength of the correlations or the nonzero mean of the channel).
{"title":"Optimizing multiple-input single-output (MISO) communication systems with general Gaussian channels: nontrivial covariance and nonzero mean","authors":"A. L. Moustakas, S. Simon","doi":"10.1109/TIT.2003.817464","DOIUrl":"https://doi.org/10.1109/TIT.2003.817464","url":null,"abstract":"We consider a narrow-band point-to-point communication system with many (input) transmitters and a single (output) receiver (i.e., a multiple-input single output (MISO) system). We assume the receiver has perfect knowledge of the channel but the transmitter only knows the channel distribution. We focus on two canonical classes of Gaussian channel models: (a) the channel has zero mean with a fixed covariance matrix and (b) the channel has nonzero mean with covariance matrix proportional to the identity. In both cases, we are able to derive simple analytic expressions for the ergodic average and the cumulative distribution function (c.d.f.) of the mutual information for arbitrary input (transmission) signal covariance. With minimal numerical effort, we then determine the ergodic and outage capacities and the corresponding capacity-achieving input signal covariances. Interestingly, we find that the optimal signal covariances for the ergodic and outage cases have very different behavior. In particular, under certain conditions, the outage capacity optimal covariance is a discontinuous function of the parameters describing the channel (such as strength of the correlations or the nonzero mean of the channel).","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"21 11 1","pages":"2770-2780"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77296204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The critical design criterion for space-time codes in asymptotically good channels is the minimum rank between codeword pairs. Rank codes are a two-dimensional matrix code construction where by the rank is the metric of merit. We look at the application of rank codes to space-time code design. In particular, we provide construction methods of full-rank codes over different complex signal constellations, for arbitrary numbers of antennas, and codeword periods. We also derive a Singleton-type bound on the rate of a code for the rank metric, and we show that rank codes satisfy this bound with equality.
{"title":"Maximum rank distance codes as space-time codes","authors":"P. Lusina, E. Gabidulin, M. Bossert","doi":"10.1109/TIT.2003.818023","DOIUrl":"https://doi.org/10.1109/TIT.2003.818023","url":null,"abstract":"The critical design criterion for space-time codes in asymptotically good channels is the minimum rank between codeword pairs. Rank codes are a two-dimensional matrix code construction where by the rank is the metric of merit. We look at the application of rank codes to space-time code design. In particular, we provide construction methods of full-rank codes over different complex signal constellations, for arbitrary numbers of antennas, and codeword periods. We also derive a Singleton-type bound on the rate of a code for the rank metric, and we show that rank codes satisfy this bound with equality.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"38 1","pages":"2757-2760"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80981962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that for any (Q/spl times/M) space-time code S having a fixed, finite signal constellation, there is a tradeoff between the transmission rate R and the transmit diversity gain /spl nu/ achieved by the code. The tradeoff is characterized by R/spl les/Q-/spl nu/+1, where Q is the number of transmit antennas. When either binary phase-shift keying (BPSK) or quaternary phase-shift keying (QPSK) is used as the signal constellation, a systematic construction is presented to achieve the maximum possible rate for every possible value of transmit diversity gain.
{"title":"Rate-diversity tradeoff of space-time codes with fixed alphabet and optimal constructions for PSK modulation","authors":"Hsiao-feng Lu, P. V. Kumar","doi":"10.1109/TIT.2003.817469","DOIUrl":"https://doi.org/10.1109/TIT.2003.817469","url":null,"abstract":"We show that for any (Q/spl times/M) space-time code S having a fixed, finite signal constellation, there is a tradeoff between the transmission rate R and the transmit diversity gain /spl nu/ achieved by the code. The tradeoff is characterized by R/spl les/Q-/spl nu/+1, where Q is the number of transmit antennas. When either binary phase-shift keying (BPSK) or quaternary phase-shift keying (QPSK) is used as the signal constellation, a systematic construction is presented to achieve the maximum possible rate for every possible value of transmit diversity gain.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"49 1","pages":"2747-2751"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75833040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The pseudo-Wishart distribution arises when a Hermitian matrix generated from a complex Gaussian ensemble is not full-rank. It plays an important role in the analysis of communication systems using diversity in Rayleigh fading. However, it has not been extensively studied like the Wishart distribution. Here, we derive some key aspects of the complex pseudo-Wishart distribution. Pseudo-Wishart and Wishart distributions are treated as special forms of a Wishart-type distribution of a random Hermitian matrix generated from independent zero-mean complex Gaussian vectors with arbitrary covariance matrices. Using a linear algebraic technique, we derive an expression for the probability density function (p.d.f.) of a complex pseudo-Wishart distributed matrix, both for the independent and identically distributed (i.i.d.) and non-i.i.d. Gaussian ensembles. We then analyze the pseudo-Wishart distribution of a rank-one Hermitian matrix. The distribution of eigenvalues of Wishart and pseudo-Wishart matrices is next considered. For a matrix generated from an i.i.d. Gaussian ensemble, we obtain an expression for the characteristic function (cf) of eigenvalues in terms of a sum of determinants. We present applications of these results to the analysis of multiple-input multiple-output (MIMO) systems. The purpose of this work is to make researchers aware of the pseudo-Wishart distribution and its implication in the case of MIMO systems in Rayleigh fading, where the transmitted signals are independent but the received signals are correlated. The results obtained provide a powerful analytical tool for the study of MIMO systems with correlated received signals, like systems using diversity and optimum combining, space-time systems, and multiple-antenna systems.
{"title":"The pseudo-Wishart distribution and its application to MIMO systems","authors":"R. Mallik","doi":"10.1109/TIT.2003.817465","DOIUrl":"https://doi.org/10.1109/TIT.2003.817465","url":null,"abstract":"The pseudo-Wishart distribution arises when a Hermitian matrix generated from a complex Gaussian ensemble is not full-rank. It plays an important role in the analysis of communication systems using diversity in Rayleigh fading. However, it has not been extensively studied like the Wishart distribution. Here, we derive some key aspects of the complex pseudo-Wishart distribution. Pseudo-Wishart and Wishart distributions are treated as special forms of a Wishart-type distribution of a random Hermitian matrix generated from independent zero-mean complex Gaussian vectors with arbitrary covariance matrices. Using a linear algebraic technique, we derive an expression for the probability density function (p.d.f.) of a complex pseudo-Wishart distributed matrix, both for the independent and identically distributed (i.i.d.) and non-i.i.d. Gaussian ensembles. We then analyze the pseudo-Wishart distribution of a rank-one Hermitian matrix. The distribution of eigenvalues of Wishart and pseudo-Wishart matrices is next considered. For a matrix generated from an i.i.d. Gaussian ensemble, we obtain an expression for the characteristic function (cf) of eigenvalues in terms of a sum of determinants. We present applications of these results to the analysis of multiple-input multiple-output (MIMO) systems. The purpose of this work is to make researchers aware of the pseudo-Wishart distribution and its implication in the case of MIMO systems in Rayleigh fading, where the transmitted signals are independent but the received signals are correlated. The results obtained provide a powerful analytical tool for the study of MIMO systems with correlated received signals, like systems using diversity and optimum combining, space-time systems, and multiple-antenna systems.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"66 1","pages":"2761-2769"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83253465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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