This letter presents two new change detection (CD) methods for synthetic aperture radar (SAR) image stacks based on the Neyman–Pearson criterion. The first proposed method uses the data from wavelength–resolution images stack to obtain background statistics, which are used in a hypothesis test to detect changes in a surveillance image. The second method considersa prioriinformation about the targets to obtain the target statistics, which are used together with the previously obtained background statistics, to perform a hypothesis test to detect changes in a surveillance image. A straightforward processing scheme is presented to test the proposed CD methods. To assess the performance of both proposed methods, we considered the coherent all radio band sensing (CARABAS)-II SAR images. In particular, to obtain the temporal background statistics required by the derived methods, we used stacks with six images. The experimental results show that the proposed techniques provide a competitive performance in terms of probability of detection and false alarm rate compared with other CD methods.

Signal space diversity (SSD) introduced by Boutros and Viterbo tremendously improves the error performance over fading channels without any power or bandwidth sacrifice. Maximum benefit is obtained with full diversity (FD) multidimensional codebooks and the rather complex maximum likelihood (ML) detection. In the present work, we propose a generalized combinatorial representation and an associated low-complexity list-based detection algorithm that works for any non-full or full diversity multidimensional codebook. The algorithm includes three options of lists offering different complexity-performance trade-offs. One of the lists has random size and is guaranteed to contain the ML point, while the other two lists have fixed or limited size. Some analytical results are presented for the list sizes. The algorithm also includes a smart search to find the most probable codebook point in the list. Numerical results show that the proposed algorithm yields optimal or close-to-optimum performance with a noteworthy detection complexity reduction. Therefore, its adoption can be of practical interest, especially in applications where powerful error-correcting codes are not supported.

This letter presents a clutter statistical analysis for stacks of wavelength-resolution synthetic aperture radar (SAR) images. Each image stack consists of SAR images generated by the same sensor, using the same flight track illuminating the same scene but with a time separation between the illuminations. We test three candidate statistical distributions for time changes in the stack, namely, Rician, Rayleigh, and log-normal. The tests results reveal that the Rician distribution is a very good candidate for modeling stack of wavelength-resolution SAR images, where 98.59% of the tested samples passed the Anderson-Darling (AD) goodness-of-fit test. Also, it is observed that the presence of changes in the ground scene is related to the tested samples that have failed in the AD test for the Rician distribution hypothesis.

Previous transmission techniques for fading channels that exploit signal space diversity (SSD) are based on rotation or precoding of an original signal constellation. In this work, we follow a completely different approach to design full diversity multidimensional codebooks whose implementation has low complexity and requires little storage. The design consists of finding good permutations of the labels of points in a fixed grid. We consider both the uniform and the Gaussian-shaped grids. An ensemble average performance based on an enumerative analysis of the error events is presented, which brings some insight into the problem. Three low-complexity algorithms are then proposed to find good permutations sets. Both analytical and simulation results confirm the good performance of the proposed codebooks, which can be considered as good candidates for practical communications systems.

This paper investigates the performance of non-orthogonal multiple access (NOMA) in a 2-user uplink millimeter-wave (mmWave) network. In particular, we consider a scenario where the Base Station (BS) is equipped with an analog beamformer with a single radio-frequency chain and serves two single-antenna NOMA users, without knowledge of the channel state information (CSI) at the BS. As the power allocation inherently intertwines with Initial Access (IA), in this paper, a joint IA and power allocation problem is considered to optimize the achievable sum rate with minimum rate constraint for each user. To solve this non-convex problem, we first solve the IA problem to obtain a sub-optimal beamforming. Then, we achieve the sub-optimal power allocation for a 2-user uplink NOMA network. These optimization problems are solved using Particle Swarm Optimization (PSO). Extensive performance evaluations are conducted to compare the achievable sum rates of the NOMA and OMA systems. Results show that the performance of the NOMA system with the proposed sub-optimal solution is better than the OMA system and achieves near-ideal sum rate performance.

In this paper, we propose a scheme that preserves the advantages of Windowed Cyclic Prefix FBMC/Circular Offset Quadrature Amplitude Modulation (WCP-COQAM) while guaranteeing the complex orthogonality. Indeed, WCP-COQAM is based on block processing and uses circular filtering in order to remove time overheads. However, like FBMC/OQAM scheme, WCP-COQAM suffers from the presence of intrinsic interference that prevents the combination with some Multiple Input Multiple Output (MIMO) techniques such as Alamouti Coding. This intrinsic interference results from the non-complex orthogonal property of WCP-COQAM and Filter Bank MultiCarrier (FBMC). In this work, we show that circular filtering makes the transmultiplexer impulse response circulant. Our proposed scheme, called COW-CFMC, exploits this circularity to restore the complex orthogonality by precoding the data symbols in each subcarrier. Thus, we show by simulation that our proposed scheme can enable Alamouti coding in a straightforward manner.

We propose a further generalization of spatial modulation (SM) in a downlink multiuser MIMO system with multicast in order to improve the system's spectral and energy efficiencies. A base station equipped with multiple antennas sends three types of information to several users who are also equipped with multiple antennas. The individual information to each user is conveyed in the form of receive SM as well as through conventional QAM modulation. On top of that, common transmit SM information is conveyed to all users. To this end, specific preprocessing and postprocessing are obtained based upon the singular value decomposition technique. A simple additional processing based on phase shifts is proposed to improve detectability. Computer simulation results reveal that the proposed scheme has improved average bit-error rate (BER) over a reference scheme under the same spectral efficiency.

This paper presents a new bit mapping strategy which aims to improve the performance of a LDPC-Coded QAM system such as the one specified in the G.hn standard. The proposed bit mapping is based on the assumption that bits transmitted in “good” sub-channels, with higher gains, help bits transmitted in “bad” sub-channels. This is possible by enforcing and prohibiting some connections between variable and check nodes in the Tanner graph, akin to Root-LDPC codes. The bit mapping is applied to G.hn, with QC-LDPC codes and QAM modulation. Simulation results show that the new bit mapping strategy improves performance for both single-carrier and OFDM-based systems.

In this paper, the use of network coding is exploited to improve the cooperative diversity order of multi-source multi-hop networks with line topology. We elaborate on a previous system model by allowing user nodes to be arbitrarily located along the line network, to have the ability to perform network decoding, and to be able to listen to upstream nodes. The recently introduced generalized dynamic-network codes (GDNC) are shown to be the best performing scheme under several distinct circumstances. Computer simulation results support the superiority of the GDNC scheme, and suggest that the connection between network coding and classical channel coding, initiated in a previous work, can once again be proved useful by reducing the design of network codes for arbitrarily located nodes to the design of classical block codes with unequal error/erasure protection.

In this paper, we apply nonbinary network coding to a multiple access cooperative vehicular ad hoc network (VANET), where the vehicles have independent information to transmit to a common destination. We consider that all the users in the network are provided with multiple antennas (MIMO), so that the benefits of both space-time codes and cooperative communication are used to increase the network diversity order and consequently provide more reliable communication. A Nakagami-m fading model is considered, aiming to evaluate the reliability of the proposed scheme mainly in scenarios where the channel condition is critical (sub-Rayleigh scenario with m<;1). The network outage probability is obtained analytically, and confirmed by numerical results.

In this letter, we evaluate the energy efficiency of a wireless network-coded cooperative system where multiple nodes cooperatively transmit their information to a common destination. The energy consumption of the transmission and reception circuits is taken into account. It is shown that network coding can provide significant energy savings compared to direct transmission and traditional cooperation techniques. We consider a Nakagami- m fading model, so that the influence of a line-of-sight is also investigated. The optimal number of users that minimizes the energy consumption is obtained analytically, and confirmed by numerical results. Using this number to organize the nodes in clusters can provide considerable energy savings and decrease the network encoding/decoding complexity.

The performance and complexity of turbo decoding using rate k/n constituent codes are investigated. The conventional, minimal and sectionalized trellis modules of the constituent convolutional codes are utilized. The performance metric is the bit error rate (BER), while complexity is analyzed based on the number of multiplications, summations and comparisons required by the max-log-MAP decoding algorithm. Our results show that the performance depends on how the systematic bits are grouped in a trellis module. The best performance is achieved when the k systematic bits are grouped together in the same section of the module, so that the log-likelihood ratio (LLR) of the k-bit vector is calculated at once. This is a characteristic of the conventional trellis module and of some of the sectionalizations of the minimal trellis module. Moreover, we show that it is possible to considerably reduce the decoding complexity with respect to the conventional trellis if a particular sectionalization of the minimal trellis module is utilized. In some cases, this sectionalization is found within the best performing group, while in some other cases a small performance loss can be traded off for a large complexity reduction.

This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The model considered here assumes that all transfer matrices with the same rank are equiprobable, so that the channel is completely characterized by the rank distribution of the transfer matrix. This model is seen to be more flexible than previously proposed ones in describing random linear network coding systems subject to link erasures, while still being sufficiently simple to allow tractability. The model is also conservative in the sense that its capacity provides a lower bound on the capacity of any channel with the same rank distribution. A main contribution is to express the channel capacity as the solution of a convex optimization problem which can be easily solved by numerical computation. For the special case of constant-rank input, a closed-form expression for the capacity is obtained. The behavior of the channel for asymptotically large field size or packet length is studied, and it is shown that constant-rank input suffices in this case. Finally, it is proved that the well-known approach of treating inputs and outputs as subspaces is information-lossless even in this more general model.

We present an improved decoding algorithm for joint turbo decoding and physical-layer network coding. Instead of decoding the individual (binary) messages separately at the relay, the proposed algorithm, from the superimposed faded signals, yields an XOR estimate of the sent messages. Moreover, we introduce a softening of the XOR values to improve the overall performance. Simulation results show that this simple idea yields gains up to 4.5 dB in a Rayleigh fading channel model when compared to a similar scheme.

In this work, we propose an adaptive distributed network-channel coding for a cooperative multiple access channel where M users cooperatively communicate with a common base station. The scheme is based on the recently proposed generalized dynamic-network codes (GDNC), in which the network code design that maximizes the diversity order was recognized as equivalent to the design of linear block codes over a nonbinary finite field under the Hamming metric. The aim here is to increase the system average code rate without reducing its diversity order, making use of a small quantity of feedback. The average rate and the diversity order are obtained analytically, and computer simulations are shown to agree with the analytical results.

This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. Our model allows this transfer matrix to have any rank, while assuming that all transfer matrices with the same rank are equiprobable. While in general the capacity cannot be obtained in closed form, we provide a simplification of the problem (from qnmto O(n) variables) which allows for easy numerical computation. A tight upper bound on the capacity is also derived, and for the special case of constant-rank input, we obtain an exact formula. Several existing results can be obtained as special cases of our approach. In addition, we prove that the well-known approach of treating inputs and outputs as subspaces is information-lossless even in this more general case.

We consider high-rate systematic recursive convolutional encoders to be adopted as constituent encoders in turbo schemes. It has been shown by Douillard and Berrou that the construction of high-rate turbo codes by means of high-rate constituent encoders offers several advantages over the typical construction based on the puncturing of rate-1/2 constituent encoders. To reduce the decoding complexity associated with high-rate codes, we adopt the “minimal” trellis representation of convolutional codes introduced by McEliece and Lin. While in the literature this trellis has been obtained for nonrecursive nonsystematic generator matrices, we herein introduce the construction of the “minimal” trellis for a systematic recursive convolutional encoding matrix. We also derive expressions for the arithmetic decoding complexity when the max-log-MAP algorithm is applied over the conventional and the “minimal” trellises. Examples are provided, which show that significant savings in decoding complexity are obtained, while keeping the same error performance of conventional schemes, when the minimal trellis is used. Finally, a code search is conducted and examples are provided which indicate that a refinement in terms of decoding complexity-error performance trade-off is obtained.

In this work, network coding is employed to obtain maximum diversity order in a network where the users have independent information to transmit to a common base station. We elaborate on the recently proposed generalized dynamic network codes (GDNC), which can only achieve part of the maximum diversity order when the inter-user channels are subject to outages. In particular, by allowing the users to perform network decoding, in this paper we show that maximum diversity order can be achieved. Results are restricted to the 2-user case, although some discussion regarding the general case is provided.

In this work, we propose and analyze a construction of adaptive network codes for a multiple access network under independent block-fading assumption. We aim to increase the system average transmission rate of the recently proposed generalized dynamic-network codes (GDNC) without reducing its diversity order, making use of a small amount of information fed back by the base station. The average rate and the diversity order are obtained analytically, and computer simulations of the diversity order are shown to agree with the analytical results.

In this work, we propose and analyze a generalized construction of distributed network codes for a network consisting of M users sending different information to a common base station through independent block fading channels. The aim is to increase the diversity order of the system without reducing its code rate. The proposed scheme, called generalized dynamic-network codes (GDNC), is a generalization of the dynamic-network codes (DNC) recently proposed by Xiao and Skoglund. The design of the network codes that maximizes the diversity order is recognized as equivalent to the design of linear block codes over a nonbinary finite field under the Hamming metric. The proposed scheme offers a much better tradeoff between rate and diversity order. An outage probability analysis showing the improved performance is carried out, and computer simulations results are shown to agree with the analytical results.

The process of adding high-density information onto printed material enables and improves interesting hardcopy document applications, such as: security, authentication, physical-electronic round tripping, item-level tagging as well as consumer/product interaction. This investigation on robust and high capacity print codes aims to maximize information payload in a given printed page area, subject to robustness to distortions originated by printing and scanning processes and also to degradations introduced by user manipulation of printed documents. The novel approach includes statistical print-and-scan channel characterization, designing of robust segmentation, unsupervised Bayesian color classification with expectation-maximization algorithm for parameters estimation of a mixture of Gaussians model and design of error correction codes. Results illustrate the performance evaluated under real channel and distortions conditions. High payload is achieved with sufficient robustness to distortions resulting of regular office hardcopy document handling: print-and-scan channel and user manipulation.

The subspace channel was introduced by Koetter and Kschischang as an adequate model for the communication channel from the source node to a sink node of a multicast network that performs random linear network coding. So far, attention has been given to one-shot subspace codes, that is, codes that use the subspace channel only once. In contrast, this paper explores the idea of using the subspace channel more than once and investigates the so called multishot subspace codes. We present definitions for the problem, a motivating example, lower and upper bounds for the size of codes, and a multilevel construction of codes based on block-coded modulation.

Adding high-density information to printed materials enables and improves interesting hardcopy document applications involving security, authentication, physical-electronic round tripping, item-level tagging, and consumer/product interaction. This investigation of robust and high capacity print codes aims to maximize information payload in a given printed page area, subject to robustness to channel errors including distortions introduced by the printing and scanning processes and also due to the usual degradations introduced by user manipulation of printed documents. The novel approach includes statistical print-and-scan channel characterization, designing of robust segmentation using visual cues, unsupervised Bayesian color classification with expectation-maximization algorithm for parameters estimation of a mixture of Gaussians model and design of error correction codes. Results illustrate the performance evaluated under real channel and distortions conditions. High payload is achieved with sufficient robustness to distortions resulting of regular office hardcopy document handling: print-and-scan channel and user manipulation.

We conduct a code search, restricted to the recently introduced class of generalized punctured convolutional codes, under the minimal trellis complexity measure defined by McEliece and Lin. For the same decoding complexity and the same code rate, new codes are compared to well-known existing classes of convolutional codes. Some of the best convolutional codes (in a distance spectrum sense) of existing and new trellis complexities are tabulated.

In this paper, we propose an LDPC coding scheme based on repeat-accumulate (RA) codes for partial-response (PR) channels. We modify the original RA encoder in such a way that there exists a one-to-one relationship between a sequence called the D-codeword (which is not the transmitted codeword but contains the information bits) and the noiseless received sequence at the output of the PR channel. A consequence of this is that the graph used for decoding the D-codeword, which is different from the encoder graph, is of low complexity. Moreover, with the appropriate modification of the RA encoder, the graph used for decoding is the same of any PR channel, which makes sense calling these codes graph-matched. The simplicity of the decoder, resulting from the "binary" interference removal (precoding) and the linear, as opposed to quadratic, complexity of the encoder make the proposed scheme attractive. For a code rate R = 3641/4096 = 0.89 and for the PR4 channel, an LDPC code has been designed and a simulated coding gain of about 5 dB for a bit error rate less than 10-5was obtained.

We propose a simple cooperative diversity scheme for a communication system consisting of two cooperating nodes that receive a single channel state information (CSI) bit from the destination node. Essentially, the feedback bit tells which cooperating node has the strongest channel, and this information is used appropriately to obtain cooperative diversity. A simple linear receiver is proposed and its performance is shown to be very close to the maximum-likelihood performance. An upper bound on the average error probability is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels under the assumption of ideal inter-user channel. In addition, through computer simulations, it is verified that the proposed scheme presents a good error performance when the inter-user channel signal-to-noise ratio is high or when the inter-user channel has a well-defined line-of-sight component. In other words, the new scheme becomes interesting when the cooperating nodes are close to each other. Comparisons with a cooperative scheme based on the Alamouti code are provided.

In this paper, we propose linear dispersion codes (LDCs) for multiple-input multiple-output (MIMO) channels with a prescribed amount of feedback. The proposed scheme selects the LDC from a set of LDCs that minimizes the error probability based on the instantaneous channel conditions. The determination of the best set of LDCs, i.e., the one that minimizes the average error probability, is described as a constrained optimization problem. While this problem appears to be intractable in general, for certain parameters we present good sets of LDCs, obtained from an iterative optimization algorithm. Results are given for rate-one LDCs only, but this restriction can be removed. Computer simulations show that the proposed schemes outperform previously reported comparable schemes for the same number of feedback bits.

We present new space-time trellis codes for two transmit antennas and p-PSK modulations, where p=3. 5. 7.11. 13.17, satisfying the rank and the determinant or the trace criteria. The system utilizes a rate 1/2 convolutional encoder over GF(p), p a prime. Some encoder properties are presented that simplify the code search.

We propose an enhancement of opportunistic beamforming (OBF) to improve the system's overall throughput over time-correlated fading channels. By saving at the base station (BS) the sequence of antenna gains and corresponding SNRs for each user, the proposed system can adopt for the selected user the most appropriate antenna gain from the memory, rather than the current gain, as in the original OBF approach. Computer simulation results for the Jakes-correlated fading channels indicate a favorable throughput performance. Moreover, the proposed scheme can be easily combined with previous enhancements of OBF, yielding further performance improvements.

In this paper, we investigate the behavior of the distance spectrum of convolutional codes when the decoding complexity is measured by the total number of edge symbols per information bit in the minimal trellis module representing the code. We conduct a code search restricted to the recently introduced class of generalized punctured convolutional codes, which is broad enough to contain good codes and yet has structural properties that facilitate the code search. New good convolutional codes are tabulated. For the same decoding complexity and the same code rate, the new codes have slightly better distance spectrum than the best known punctured convolutional codes. When compared to the best known unit-memory convolutional codes of the same rate, the new codes typically have improved free distance for a given decoding complexity, or about the same distance spectrum is achieved with much lower decoding complexity. Under this decoding complexity measure, the behaviour that higher decoding complexity implies better distance spectrum remains valid.

Opportunistic beamforming has been proposed to exploit multiuser diversity in slow fading channels. The benefit of multiuser diversity is obtained using the proportional fair scheduling algorithm in combination with multiple transmit antennas. The antenna gains (power and phase) are randomly varied to induce fast fluctuation in slow fading channels. In this paper, we present an enhancement of this technique, named time coherent-opportunist beamforming, which exploits the time coherence existing in the slow fading channels to yield improved throughput. The proposed scheme is compared to opportunistic beamforming. Computer simulation results indicate a favorable throughput performance. Analysis in terms of scheduling jitter and frame size is also carried out. The average throughput of the proposed scheme approaches the average throughput of the optimal beamforming independently of the number of users. For a fixed number of users, the proposed scheme converges to the optimal beamforming as either the frame size or the scheduling jitter goes to infinity. Furthermore, the implementation requires only base station updates, facilitating the adoption of the proposed scheme

In this correspondence, it is shown that some convolutional codes with distinct memory sizes of minimal encoders are equivalent in the sense that the minimal trellises of these codes are the shifted versions of one another. For an$(n,k)$binary convolutional code, the weight spectrum obtained from the minimal trellis may be slightly different from that obtained from the conventional code trellis with$n$-bit branches. Code search is conducted to find some good$(n,n-1)$binary convolutional codes. Bounds on the trellis complexity, measured by the number of states and the number of branches in the minimal trellis module, of any convolutional code and its equivalent codes are also derived.

Assuming that a feedback channel is available and the fading coefficients are known at the transmitter, Gore and Paulraj (2002) have proposed a transmit antenna selection scheme that uses the Alamouti code with the best pair of antennas, selected from m /spl ges/ 3 transmit antennas available, where the selection criterion is to minimize the instantaneous probability of error. They have showed that a diversity order of m is achieved, as if all the m antennas were used. The advantage is that only two RF chains are required, reducing the transmitter cost. In this paper, full-rate, non-orthogonal space-time block codes are produced by repeating and permuting columns of the Alamouti code matrix. These codes need only two RF chains, have decoding delay equal to two, and their maximum likelihood decoders based on linear processing are essentially the same as that of the Alamouti code. Based on the instantaneous fading coefficients, the transmitter selects either one of the proposed codes with three antennas or the Alamouti code with two antennas. Simulations results for a simple case indicate that full diversity is achieved in spite of using non-orthogonal codes, and a coding gain of up to 1 dB over Gore and Paulraj's scheme is observed.

In this paper, we consider a space-time coded system composed of an encoder over GF(p), where p can be any prime number, followed by a serial-to-parallel converter, n mappers from GF(p) into a p-PSK signal constellation, and a transmitter with n antennas. The codes are designed to provide the best error performance in the quasi-static, flat Rayleigh fading channel, according to the rank and the determinant criteria derived by Tarokh et al. We present two theorems by which we can simplify the design of full diversity space-time trellis codes (STTCs), for any number of transmit antennas. A spectral efficiency of Iog/sub 2/(p) b/s/Hz is achieved. Such non-integral rates can be useful to serve a wider range of multimedia applications. New STTCs with n = 2, 3, and 4 transmit antennas are presented for the 5-PSK, 7-PSK, and 11-PSK modulations.

Complex orthogonal space-time block codes for more than two transmit antennas cannot achieve full rate over the fading channel. By relaxing the orthogonality constraint, however, it is possible to achieve full rate or even rates higher than one for any number of transmit antennas at the expenses of loosing some degree of diversity advantage. On the other hand, if a feedback channel is available and the fading coefficients are known at the transmitter, then maximum diversity advantage can be achieved with transmit antenna selection. In this paper, a new full-rate nonorthogonal space-time block code for three transmit antennas is proposed that needs only two RF chains, has decoding delay equal to two, and whose maximum likelihood decoder based on linear processing is the same as that of the Alamouti code. We then introduce hybrid transmit antenna/code selection. Based on the instantaneous fading coefficients, the transmitter selects either the proposed code with the best three antennas or the Alamouti code with the best pair of antennas. Simulations results for up to six transmit antennas and one receive antenna indicate that full diversity is achieved in spite of using a nonorthogonal code. With this simple example, coding gains of up to 0.4 dB over the pure antenna selection with Alamouti, proposed by Gore and Paulraj (2002), is also observed.

We consider a design procedure for achieving full 2-level diversity and coding advantage for space-time convolutional codes over GF(p), where p can be any prime number. Using a p-ary constellation (not necessarily PSK), the spectral efficiency is log/sub 2/(p) b/s/Hz. Simple conditions on the generator matrices of a rate R = 1/2 convolutional code are given so that maximum diversity is guaranteed, while reducing the computer search effort. New 2-space-time codes are presented for the 5-PSK and 7-PSK modulations. Simulation results validate the presented code design procedure.

Shannon defined the capacity of the discrete noiseless channel (DNC) and considered a finite-state model from which the capacity can be calculated. Alternatively, the DNC may be (and often is) represented by a finite list of forbidden strings. In this correspondence, we demonstrate the application of combinatorial techniques to finding the Shannon capacity of the DNC directly from the forbidden list. In our derivations, the case of noninteger symbol durations, as introduced by Csiszar, is considered.

We investigate a method of communicating with chaos described by Hayes, Grebogi, and Ott (19913), which uses the idea of controlling chaos by small perturbations. Although allowing the electronics controlling the output signal to remain at the low-power level, this method unavoidably incurs a capacity loss, which we calculate for a chaotic CO/sub 2/ laser model. We first determine an approximation to the laser language, by means of a forbidden set representation, and then find its Shannon (1963) capacity. The results indicate that, since the capacity loss is not significant, the tradeoff is worthwhile. Finally, we point to simple finite-state encoders that satisfy the constraints imposed by the language.

This paper is concerned with the well-known coding technique that uses cosets of convolutional codes along with precoding to increase the free squared Euclidean distance at the output of a partial-response channel. The focus is on totally trellis-matched codes, for which the decoding trellis has the fewest number of states. Codes totally trellis-matched to the extended partial-response class 4 (EPR4) and the doubly extended partial-response class 4 (E/sup 2/PR4) channels for a variety of code rates and overall constraint lengths are sought for with respect to the squared Euclidean distance spectrum criterion. Furthermore, some previously published codes are shown to contain flawed codewords and are replaced with new ones.

The performance of maximum-likelihood decoding of trellis codes for moderate-to-high SNR is dictated by their distance spectrum. An improved version of a bidirectional algorithm is used to find cosets of convolutional codes for the EPR4 and EEPR4 channels with best (squared Euclidean) distance spectrum. Results are restricted to the class of totally trellis-matched codes. Distance spectra results for these new optimized codes as well as for some related previously published codes are tabulated. Moreover, we call attention to some codes that were erroneously tabulated in a previous paper.

The multilevel coding approach of Imai and Hirakawa (1977) is used to construct trellis-matched codes for binary-input partial-response channels. For the codes to be trellis matched, the signal constellations are selected according to certain constraints, but no conditions are imposed on the component codes. New codes for the (1-D)(1+D)/sup n/ channel compare favorably to existing codes.

We extend the coding technique for the 1-D channel, due to Wolf and Ungerboeck, to the case of the (1-D)(1+D)/sup n/ channel. The technique employs a convolutional encoder, a precoder, and the channel in cascade. A computer-aided search for channel codes with large minimum free squared Euclidean distance, d/sub free//sup 2/, is introduced. The search is limited to a class of convolutional encoders for which an encoder with constraint length /spl nu/ generates a decoder trellis with 2/sup /spl nu// states only, as opposed to 2/sup /spl nu/+n+1/ states obtained when a general convolutional encoder is used. These channel codes are said to be totally trellis-matched (TTM) to the (1-D)(1+D)/sup n/ channel. A limitation on the maximum zero-run length, L/sub MAX/ is attained by choosing a nontrivial coset of the convolutional code. A class of coset representatives from which the resulting run-length-limited channel codes are TTM is determined. While minimal encoders generate channel codes containing no flawed codewords, it is shown that some nonminimal encoders do the same while achieving larger dg/sub free//sup 2/. Both types of encoders are considered in the search. Many new channel codes for the (1-D)(1+D)/sup 2/ and the (1-D)(1+D)/sup 3/ channels, with diverse rates and decoding complexities, are tabulated. The codes have relatively low decoding complexity for rates up to 0.8. Two of the new channel codes are compared to a matched spectral null (MSN) code. With the same decoding complexity and code rate, one of these two new channel codes has a smaller d/sub free//sup 2/ and larger L/sub MAX/ than the MSN code. However, with slightly higher decoding complexity, the second new channel code outperforms the MSN code.

The authors propose a decoding strategy based on the multistage decoding method of Imai and Hirakawa (1977). This scheme is shown to be a generalization of the conventional multistage decoders. A general procedure to derive an upper bound on the bit error probability, which takes into account wrong side information effects, is stated. Finally. a comparison with conventional multistage decoders is presented to show that the proposed decoding strategy outperforms the previous ones.>