Reliability-Based Hybrid Automated Repeat reQuest (RB-HARQ) strongly improves the throughput of a communications system by identifying and retransmitting the symbols deemed most unreliable after decoding the initial transmission. Additional soft-value processing, large feedback messages and many retransmissions are required to achieve a high throughput. We compare a variant of RB-HARQ designed for limited feedback with a new low-overhead, clustered Parity-Based Partial-Retransmission (PBPR) HARQ scheme. The new scheme selects symbols connected to unsatisfied parity checks and intersects this set with a subset of all symbols consisting of uniformly distributed information or parity symbols to improve the throughput. Since clustered HARQ schemes work best with codes exhibiting high intra-codeword correlations, we use Spatially-Coupled Low-Density Parity-Check (SC-LDPC) codes for evaluation.

The iterative algorithms employed to decode Low-Density Parity-Check (LDPC) codes are not guaranteed to converge to a valid code word for every receive word. The goal of Early Termination (ET) is to prevent the waste of resources in such cases. In this paper, we conduct an analysis of the suitability of ET criteria by tracking the evolution of parameters available from decoder-internal states. We find that the commonly selected parameters, e.g., the mean Log-Likelihood Ratio (LLR) magnitude or the fraction of satisfied parity checks, result in similar probabilities of detecting non-converging receive words. We propose a novel criterion for Early Give-Up (EGU) and evaluate its performance using a cost metric based on the retransmission of individual code blocks initiated by higher-layer protocols.

We introduce π/2-shifted Phase Shift Keying on the Hypersphere (π/2-PSKH), a new modulation scheme for Multiple-Input Multiple-Output (mIMO) systems. π/2-PSKH is a multidimensional extension of shifted QAM which allows to use load-modulated MIMO transmitters with a highly efficient power amplifier with reduced backoff. We propose π/2-PSKH constellations and explain how a π/2-PSKH signal is generated. The signal point sequence for π/2-PSKH is time-varying and as such has an inherent code. For the receiver, three algorithms are introduced and numerical simulations are used to examine their performance. These algorithms are further modified in order to reduce their complexity. We discuss the effect of this complexity reduction and the trade-off between receiver complexity and performance. It is shown that due to its inherent code, π/2-PSKH shows excellent performance in terms of power efficiency even if used with conventional amplifiers.

We analyze the performance of Bit-Interleaved Coded Modulation (BICM) for MIMO systems employing Phase Shift Keying on the Hypersphere (PSKH), an extension of conventional PSK to higher dimensions. Because the quality of BICM relies on the bit-mapping between coded bits and signal points, PSKH constellations with superior distance properties and capacities might have poor power efficiency. In this paper, we analyze these losses in power efficiency and propose a new method to generate PSKH constellations, i.e., spherical codes, together with a BICM optimized bit-mapping. It turns out that for one bit per real dimension, individual QPSK per antenna is optimal, whereas for other constellation sizes notable gains can be achieved.

The performance of short block length low-density parity-check (LDPC) codes (both binary and nonbinary) and convolutional codes is compared under the constraint of tight structural delay constraints. Additionally, we use fundamental bounds on block codes and low rate turbo codes to evaluate our results in a broader context. It turns out that-depending on the code rate and given delay-convolutional codes are able to outperform fundamental lower bounds for block codes, yielding a definite result on the question, which codes are superior in this regime. From a break-even point onward, convolutional codes cannot compete with block codes anymore and nonbinary LDPC codes show the best performance. Turbo codes with a short interleaver length show competitive results.

A framework is proposed that allows for a joint description and optimization of both binary polar coding and the multilevel coding (MLC) approach for 2m-ary digital pulse-amplitude modulation (PAM). The conceptual equivalence of polar coding and multilevel coding is pointed out in detail. Based on a novel characterization of the channel polarization phenomenon, rules for the optimal choice of the bit labeling in this coded modulation scheme employing polar codes are developed. Simulation results for the AWGN channel are included.

A framework is proposed that allows for a joint description and optimization of both binary polar coding and 2m-ary digital pulse-amplitude modulation (PAM) schemes. For the latter, the multilevel coding (MLC) approach as well as bit-interleaved coded modulation (BICM) are considered. The conceptual equivalence of polar coding and multilevel coding is covered in detail. Based on an alternative characterization of the channel polarization phenomenon, rules for the optimum choice of the labeling in coded modulation schemes employing polar codes are developed. Simulation results regarding the error performance of the proposed schemes on the AWGN channel are included.

Information processing characteristics (IPC) provide a general framework for the analysis of a coding scheme. In this paper, we utilize IPCs to obtain performance estimates for the end-to-end coded channel for bit-interleaved coded modulation (BICM) using a given modulation format and coding scheme, i.e., its bit error rate and capacity. The proposed method enables to fully decouple the analysis of the coding scheme from the analysis of the higher-order modulation scheme and delivers very good performance estimates. Exemplarily, this is validated by means of numerical simulations for BICM using convolutional- and LDPC-coded amplitude-shift keying.

We consider the total capacity of a Gaussian multiple-access MIMO channel with a linear array of R receive antennas and T distributed transmit antennas. If the spatial distribution of transmit antennas weighed by their path loss and marginalized to a sphere around the receive array is proportional to the ratio of receive antenna directivity to transmit antenna directivity, the capacity is shown to approach Rlog(1 + SNR) as T → ∞, irrespective of the inter-element distance at the receiver.We further show that the capacity for other distributions of transmit antennas can be even greater, as the inter-element distance approaches zero.

Unique word orthogonal frequency division multiplexing (UW-OFDM) inherently introduces a complex number Reed Solomon (RS) code. Originally, the code generator matrix of systematic coded UW-OFDM had been designed rather intuitively by minimizing the mean redundant energy. In this work we justify this approach by applying a cost function that incorporates the overall transceiver chain including a linear minimum mean square error (LMMSE) data estimator. In addition to the LMMSE estimator we investigate a nonlinear sphere detection (SD) receiver for both systematic and nonsystematic coded UW-OFDM. We study and interpret the estimators' performance and their diverse ability to exploit the redundant energy.

An alternative method for collaborative decoding of interleaved Reed-Solomon codes as well as Gabidulin codes for the case of high interleaving degree is proposed. As an example of application, simulation results are presented for a concatenated coding scheme using polar codes as inner codes.

Dynamic decode-and-forward (DDF) is a version of decode-and-forward relaying in which the duration of the listening phase at relays is not fixed. In this paper, we investigate half-duplex DDF relaying based on rateless codes. The use of rateless codes allows relays to autonomously switch from listening to the source node to transmitting to the destination node. We first revisit different signal combining strategies applied at the destination node, namely energy and information combining known from literature, and propose a new combining method which we refer to as mixed combining. The different combining methods give rise to different achievable rates, i.e., constrained channel capacities, for which we provide analytical expressions. The capacity analysis reveals the conditions under which mixed combining is superior and how it can be optimized. We then consider Raptor codes as a specific implementation of rateless codes and develop a density-evolution approximation to predict the data-rate performance of these codes in DDF relaying. Furthermore, we devise an optimization of the output symbol degree distribution of Raptor codes that is mainly used to benchmark the performance of Raptor codes with a fixed degree distribution. Numerical results for exemplary three-node and four-node relay networks show that the proposed mixed combining provides significant gains in achievable data rate and that Raptor codes with a fixed degree distribution are able to realize these gains and to approach closely the constrained-capacity limits.

Spherical logarithmic quantization (SLQ) is a vector quantization method for efficiently digitizing analog signals at a high dynamic range and with very low distortion while preserving the original waveform as closely as possible. SLQ is able to operate at a low data rate of, e.g., 2 bits per sample and at a very low signal delay of about ten samples, this corresponds to approximately 200 mus for high-quality audio signals. The technique of SLQ is universally applicable (i.e., not restricted to, e.g., audio signals) and achieves an efficient digital representation of waveforms with high longterm as well as high segmental signal-to-noise ratios. The aim of this paper is to give a detailed description of the SLQ algorithm and to present simulation results on the performance of this new quantization scheme that combines several advantages. After a review of some important basic principles concerning quantization, linear prediction and multidimensional spheres, the SLQ encoder is described. To short vectors of signal samples which are represented in sphere coordinates, logarithmic quantization is applied to the radius and uniform quantization is applied to the angles. This results in the advantage of a constant signal-to-noise ratio over a very high dynamic range at a small loss with respect to the rate-distortion theory. In order to increase the signal-to-noise ratio by exploitation of correlations within the source signal, a solution for the problem of combining this vector quantization scheme with scalar adaptive differential pulse code modulation (ADPCM), i.e., ADPCM with sample by sample backward recursion is presented. Furthermore, an indexing scheme for the quantization cells covering the surface of a multidimensional unit sphere is presented and simulation results using different source signals are given.

We introduce a new method for decoding short and moderate-length linear block codes with dense parity check matrix representations of cyclic form. This approach is termed multiple-bases belief-propagation. The proposed iterative scheme makes use of the fact that a code has many structurally diverse parity-check matrices, capable of detecting different error patterns. We show that this inherent code property leads to decoding algorithms with significantly better performance when compared to standard belief-propagation decoding. Furthermore, we describe how to choose sets of parity-check matrices of cyclic form amenable for multiple-bases decoding, based on analytical studies performed for the binary erasure channel. For several cyclic and extended cyclic codes, the multiple-bases belief propagation decoding performance can be shown to closely follow that of the maximum-likelihood decoder.

The invention of practical rate-less codes in the form of Luby transform and Raptor codes has facilitated the implementation of decode-and-forward relaying schemes which permit the relay to autonomously switch between listening and collaboration phase. Considering the classical three-node relay network employing such a flexible decode-and-forward mechanism, in this paper we investigate signal combining strategies for the destination node. In particular, we compare information and energy combining considered previously in the literature and introduce a new, so-called mixed combining scheme, which is a hybrid of the two former strategies. Assuming general finite-size signal constellations we show that mixed combining is advantageous over the pure combining schemes in terms of achievable rate given the same total transmit energy. A comparison of the associated constellation-constrained capacities with simulated rates achieved for relay transmission with moderate-length Raptor codes underscores (i) the relevance of the capacity-based analysis and (ii) the suitability of rate-less codes for relay transmission.

We compare convolutional codes and LDPC codes with respect to their decoding performance and their structural delay, which is the inevitable delay solely depending on the structural properties of the coding scheme. Besides the decoding performance, the data delay caused by the channel code is of great importance as this is a crucial factor for many applications. Convolutional codes are known to show a good performance while imposing only a very low latency on the data. LDPC codes yield superior decoding performance but impose a larger delay due to the block structure. The results obtained by comparison will also be related to theoretical limits obtained from random coding and the sphere packing bound. It will be shown that convolutional codes are still the first choice for applications for which a very low data delay is required and the bit error rate is the considered performance criterion. However, if one focuses on a low signal-to-noise ratio or if the obtained frame error rate is the base for comparison, LDPC codes compare favorably.

We investigate properties of a channel coding scheme leading to the minimum-possible frame error ratio when transmitting over a memoryless channel with rate R > C. The results are compared to the well-known properties of a channel coding scheme leading to minimum bit error ratio. It is concluded that these two optimization requests are contradicting. A valuable application of the derived results is presented.

We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which quantifies the relationship between the number of redundant rows in any parity-check matrix of a given code and the size of its smallest trapping set. Trapping sets with certain parameter sizes are known to cause error-floors in the performance curves of iterative belief propagation (BP) decoders, and it is therefore important to identify decoding matrices that avoid such sets. Bounds on the trapping redundancy are obtained using probabilistic and constructive methods, and the analysis covers both general and elementary trapping sets. Numerical values for these bounds are computed for the [2640, 1320] Margulis code and the class of projective geometry codes, and compared with some new code-specific trapping set size estimates.

Bit interleaved coded space-time modulation (BIC- STM) is an attractive strategy to achieve high power- and bandwidth-efficiency over multiple-input and multiple-output (MIMO) fading channels due to coding and diversity gains promised by the serial concatenation of an outer convolutional code, a bitwise interleaver and an inner high order space-time modulation (STM). In this paper, BICSTM with iterative decoding (BICSTM-ID) including non-iterative decoding as a special case is considered. For designing the inner STM, two parameters based on bitwise pairwise error probabilities (b- PEP) for the cases with and without a-priori knowledge are proposed as new measures for designing labeling rules for the STM codewords set suited to iterative decoding. On the other hand, the BICSTM-ID scheme is analyzed from an information theoretical aspect, and Information Processing Characteristic (IPC) analysis is developed for MIMO systems in order to fully characterize the BICSTM-ID scheme based on a new equivalent model of combined binary input channels. The analysis results show that the IPC analysis offers a unified perspective for BICSTM and BICSTM-ID from an information theoretical point of view and provides a comprehensive insight into the whole BICSTM-ID scheme as well. Additionally, IPC based upper and lower bounds on bit error ratio (BER) performance are extended to BICSTM-ID, and are confirmed by simulations. These bounds are of significant practical interest for estimating the BER performance of the bit-interleaved concatenated schemes with general nonlinear inner systems.

We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the tradeoff between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for the stopping redundancy hierarchy via Lovasz's local lemma (LLL) and Bonferroni-type inequalities, and specialize them for codes with cyclic parity-check matrices. Based on the observed properties of parity-check matrices with good stopping redundancy characteristics, we develop a novel decoding technique, termed automorphism group decoding, that combines iterative message passing and permutation decoding. We also present bounds on the smallest number of permutations of an automorphism group decoder needed to correct any set of erasures up to a prescribed size. Simulation results demonstrate that for a large number of algebraic codes, the performance of the new decoding method is close to that of maximum-likelihood (ML) decoding.

In this paper differential space-frequency frequency division multiplexing (MIMO-OFDM) and multiple-symbol differential detection (MSDD) without channel state information (CSI) at the receiver is considered. Inspired by previous work presented in the literature, a novel DSFM scheme is devised, which makes use of spatial and/or spectral (multipath) diversity and is particularly suited for MIMO-OFDM and power-efficient, low-delay MSDD. Furthermore, the application of a two-dimensional (2D) observation window to MSDD (2D-MSDD) in order to exploit channel correlations in both time and frequency direction, is investigated and tree-search decoding is applied to solve the detection problem efficiently. An analytical approximation of the symbol-error rate of 2D-MSDD for MIMO-OFDM under spatially correlated fading is derived, which enables quick and accurate performance evaluations. Numerical and simulation results corroborate the efficacy of our approach and show that power efficiency close to that of coherent detection with perfect CSI is feasible in all standard fading scenarios at reasonable decoder complexity.

A novel soft-decoding method for algebraic block codes is presented. The algorithm is designed for soft-decision decoding and is based on belief-propagation (BP) decoding using multiple bases of the dual code. Compared to other approaches for high-performance BP decoding, this method is conceptually simple and does not change at each stage of the decoding process. With its multiple BP decoders the proposed scheme achieves the performance of a standard BP algorithm with a significantly lower number of iterations per decoder realization. By this means the data delay introduced by decoding is reduced. Moreover, a significant improvement in decoding performance is achieved while keeping the data delay small. It is shown that for selected codes the proposed scheme approaches near maximum likelihood (ML) performance for very small data processing delays.

We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly dependent rows in any parity-check matrix of a code that avoids stopping sets of up to a given size. Redundant parity-check equations can be shown to have a similar effect on decoding performance as permuting the coordinates of the received codeword according to a selected set of automorphisms of the code. Based on this finding we develop new decoding strategies for data transmission over the binary erasure channel that combine iterative message passing and permutation decoding in order to avoid errors confined to stopping sets. We also introduce the notion of s-SAD sets, containing the smallest number of automorphisms of a code with the property that they move any set of not more than s erasures into positions that do not correspond to stopping sets within a judiciously chosen parity-check matrix.

We analyze the effect of redundant parity-check equations on the error-floor performance of low-density parity- check (LDPC) codes used over the additive white Gaussian noise (AWGN) channel. Our findings show that a large number of iterative decoding errors in the [2640,1320] Margulis code, confined to point trapping sets in the standard Tanner graph, can be corrected if only one redundant parity-check equation is added to the decoder's matrix. We also derive an analytic expression relating the number of rows in the parity-check matrix of a code and the parameters of trapping sets in the code's graph.

The concept of "information combing" is extended to multiple access schemes, where the receiver is equipped with multiple receive antennas. In particular, the connection of the respective rate region to that of the scalar MACs, which are present if the receive antennas are treated separately, is derived. This interpretation leads to new, expedient insights and the gains over "scalar combing", i.e., the synergy available in MIMO channels, are quantified from a new point of view. The theoretical results are illustrated by numerical examples

In the low signal-to-noise ratio regime, the performance of concatenated coding schemes is limited by the convergence properties of the iterative decoder. Idealizing the model of iterative decoding by an independence assumption, which represents the case in which the codeword length is infinitely large, leads to analyzable structures from which this performance limit can be predicted. Mutual information transfer characteristics of the constituent coding schemes comprising convolutional encoders and soft-in/soft-out decoders have been shown to be sufficient to characterize the components within this model. Analyzing serial and parallel concatenations is possible just by these characteristics. In this paper, we extend the method of extrinsic information transfer charts, that is limited to the case of a concatenation of two component codes, to the case of multiple turbo codes. Multiple turbo codes are parallel concatenations of three or more constituent codes, which, in general, may not be identical and may not have identical code rates. For the construction of low-rate codes, this concept seems to be very favorable, as power efficiencies close to the Shannon limit can be achieved with reasonable complexity

In mobile communications networks, system capacity is often limited by cochannel interference. Therefore, receiver algorithms for cancellation of cochannel interference have recently attracted much interest. At the mobile terminal, algorithms can usually rely only on one received signal delivered by a single receive antenna. In this letter, a low-complexity single antenna interference cancellation (SAIC) algorithm for real-valued modulation formats referred to as mono interference cancellation (MIC) is introduced which is well suited for practical applications. Field trials in commercial GSM networks using prototype terminals with the proposed MIC algorithm have demonstrated that the novel concept may yield capacity improvements of up to 80%. The underlying principle is also beneficial for adjacent channel interference and receivers with multiple antennas. Furthermore, in coverage-limited scenarios, there is no performance degradation compared with conventional receivers

Ideal coding schemes are defined as coding schemes that have the minimal symbol-error probability for a given code rate and a given communication channel. Ideal coding schemes with code-symbol decoding are analyzed with respect to their properties of processing mutual information. The wordwise mutual information, the symbol-wise mutual information and the extrinsic mutual information between code symbols and the corresponding decoder outputs are investigated. To analyze the extrinsic mutual information, the concept of information decomposition is introduced

When the same data sequence is transmitted over two independent channels, or when a data sequence is transmitted twice but independently over the same channel, the independent observations can be combined at the receiver side. From an information-theory point of view, the overall mutual information between the data sequence and the received sequences represents a combination of the mutual information of the two channels. This concept is termed information combining. A lower bound and an upper bound on the combined information is presented, and it is proved that these bounds are tight. Furthermore, this principle is extended to the computation of extrinsic information on single code bits for a repetition code and for a single parity-check code of length three, respectively. For illustration of the concept and the bounds on information combining, two applications are considered. First, bounds on the information processing characteristic (IPC) of a parallel concatenated code are derived from its extrinsic information transfer (EXIT) chart. Second, bounds on the EXIT chart for an outer repetition code and for an outer single parity-check code of a serially concatenated coding scheme are computed.

In this paper, a second stage for algorithms applying iterative soft decision interference cancellation (ISDIC) (R. R. Muller and J.B. Huber, 1998) (A. Lampe et. al., Jan., 2001) (J.F. Robler J. B. Huber Nov., 2002) and for multiuser detection is proposed performing error search and correction. Analysis by simulations shows for the considered downlink scenario that the bit error ratio of a matched filter (MF) ISDIC can he lowered by a factor of nearly 100 for high signal-to-noise ratios with the subsequent second stage approaching the performance of a more complex minimum mean-squared error (MMSE) ISDIC. Furthermore, the MMSE ISDIC can he improved by the proposed second stage by up to 0.5 dB. It is shown that the ISDIC scheme with additional second stage can approach the matched filter bound up to 1 dB for the analyzed channel and 4QAM transmission.

Bit interleaved coded space-time modulation with iterative decoding (BICSTM-ID) [1], [2] is an attractive strategy to achieve high power efficiency close to capacity limit by applying turbo principle to multiple-input and multiple-output (MIMO) channels. In this paper, Information Processing Characteristic (IPC) analysis [3] is extended to MIMO systems in order to fully characterize the BICSTM-ID scheme based on a new equivalent model of combined binary input channels. The analysis results show that the IPC analysis offers an unified aspect for BICSTM and BICSTM-ID from an information theoretical point of view and provides a valuable design guideline for BICSTM-ID as well. Moreover, IPC based upper and lower bounds on BER performance [4] are applied to BICSTM-ID, which are confirmed by simulations and seem to be very useful for performance estimation of coding schemes for space-time coded MIMO channels.

A precoding scheme for multiuser broadcast communications is described, which fills the gap between the low-complexity Tomlinson-Harashima precoding and the sphere decoder-based system of Peel et al. Simulation results show that, replacing the closest-point search with the Babai approximation, the full diversity order supported by the channel is available to each user, as in the system of Peel et al., and unlike Tomlinson-Harashima precoding, which suffers some diversity penalty. The complexity of the scheme is similar to that of Tomlinson-Harashima precoding.

In this paper, Tomlinson-Harashima Precoding for multiple-input/multiple-output systems including multiple-antenna and multiuser systems is studied. It is shown that nonlinear preequalization offers significant advantages over linear preequalization which increases average transmit power. Moreover, it outperforms decision-feedback equalization at the receiver side which is applicable if joint processing at the receiver side is possible, and which suffers from error propagation. A number of aspects of practical importance are studied. Loading, i.e., the optimum distribution of transmit power and rate is discussed in detail. It is shown that the capacity of the underlying MIMO channel can be utilized asymptotically by means of nonlinear precoding.

The combination of continuous phase modulation (CPM) with direct-sequence code-division multiple access (DS-CDMA) for multiuser transmission over the additive white Gaussian noise channel is discussed. Concentrating on the important special case of generalized minimum-shift keying, particularly simple receiver structures are obtained. To emphasize on low complexity, noncoherent reception is proposed and appropriate transmitter and receiver designs are provided. The application of reduced-state noncoherent sequence detection and noncoherent filter adaptation ensures high power efficiency and robustness against channel phase variations. Simulation results confirm that the chosen approach of CPM for DS-CDMA achieves high performance with very moderate complexity.

In this paper, an equalization algorithm employing soft-decision feedback, designed for transmission with general square QAM constellations is introduced like e.g. 16QAM or 64QAM allowing high data rates. It is derived from [J.F. Robler, W.H. Gerstacker, A. Lampe, and J.B.Huder, 2002] where it was originally developed for 4QAM transmission. The algorithm employs a minimum mean-square error (MMSE) filter in each iteration in order to refine the data estimates. The rule for generating soft decisions is adapted continuously to the current state of the algorithm. It can be shown by simulations for a 16QAM transmission, that a linear finite length MMSE channel equalizer according to [J.G. Proakis, 1995] is clearly outperformed. In addition to [J.F. Robler, W.H. Gerstacker, A. Lampe, and J.B. Huder, 2002], we compare our new generalized scheme for different MMSE filter lengths and show the achievable extra gain.

Asymptotical analysis of concatenated codes with EXIT charts (ten Brink, S., 1999) or the AMCA (Huettinger, S. and Huber, J., 2002) has proven to be a powerful tool for the design of power-efficient communication systems. However, the result of the asymptotical analysis is usually a binary decision, whether convergence of iterative decoding is possible at the chosen signal-to-noise ratio, or not. We show how to obtain the information processing characteristic (IPC) introduced by Huettinger et al. for concatenated coding schemes (see Proc. 39th Allerton Conf. on Commun., Control and Computing, 2001). If asymptotical analysis is performed under the assumption of infinite interleaving and infinitely many iterations, this IPC is a lower bound. Furthermore, it is also possible to estimate the performance of realistic coding schemes by restricting the number of iterations. Finally, the IPC can be used to estimate the resulting bit error ratio for the concatenated coding scheme. As an upper and a lower bound on the bit error ratio for a given IPC exist, we are able to lower bound the performance of any concatenated coding scheme and give an achievability bound, i.e. it is possible to determine a performance that can surely be achieved if sufficiently many iterations are performed and a large interleaver is used.

A bit-interleaved concatenated coding scheme consisting of an outer convolutional code and an inner space-time modulation together with an iterative decoding-demapping method is analyzed. As a result, two parameters based on bitwise pairwise error probabilities (b-PEP) for the cases with and without a-priori knowledge are proposed as new measures for a labeling of signal points suited to iterative decoding-demapping. In particular, we demonstrate that the two parameters are closely related to the transfer characteristic (TC) of the demapper and accordingly lead to the same design guideline as a TC analysis. By optimizing these two analytical parameters for an orthogonal space-time block code (oSTBC) employing 16QAM constituent symbols w.r.t. an outer simple 4-states rate 1/2 convolutional code, a highly power efficient concatenated scheme with rate of 2 bits per channel use is proposed, which offers an excellent trade off between power efficiency and complexity.

Abstract For the narrow band Wireless Code Division Multiple Access (WCDMA) system, there are some channel coding schemes proposed and applied like Turbo code and convolutional codes. But for the 4G Code Division Multiple Access (CDMA) wideband systems, we have to use new channel coding schemes with high bandwidth efficiency. In this case, multilevel coding (MLC) scheme is easy to map to Multiple Quardrature Amplitude Modulation (MQAM) modulation strategy to be used for 4G, and MLC+MQAM will be a potential channel coding scheme for the error correcting of next generation of mobile systems. A novel criterion, that is ‘capacity rule’ plus ‘mapping rule’, for the design of the optimum MLC scheme for radio systems over Rayleigh fading channels is proposed in this paper. Based on this theory, a few of key issues related to design an optimum MLC system are investigated. These include a novel optimum design criterion proposed, different mapping strategies, different decoding methods of MLC/MSD and MLC/Parallel Decoding on Levels (PDL) and their performance comparison over Additive White Gaussian Noise (AWGN) and Rayleigh fading channels respectively. Copyright © 2003 John Wiley & Sons, Ltd.

We propose a novel design method, which is an extension to the EXIT charts introduced by ten Brink (see IEE Electronics Letters, vol.35, no.10, p. 806-808, 1999), for low-rate power-efficient codes. An exemplary design of a rate -1/4 code shows more than 1 dB more coding gain than the original turbo-code of rate -1/2. Using this code in a CDMA scheme while reducing the spreading by a factor of 2 helps improving the overall performance of the multi-user scheme significantly.

A well-known receiver strategy for a linearly modulated signal transmitted over a frequency-selective channel is channel equalization. Recently it was proposed to employ a minimum mean-squared error (MMSE) channel equalizer for the downlink of CDMA. In this paper, we introduce a new receiver concept using MMSE channel equalization as a first stage and MMSE decision-feedback equalization (DFE) utilizing soft feedback from the decoding unit as a second stage. Both schemes are compared for the downlink of CDMA. It turns out, that after channel decoding we gain about 1 dB compared to conventional MMSE channel equalization.

A novel multiuser detector for direct sequence code division multiple access is proposed. The receiver performs iterated soft decision interference cancellation (ISDIC) based on multiuser interference suppression filters designed for minimization of the mean-square error. Assuming a complex modulation format, we show that the multiuser interference becomes rotationally variant in the course of the iterations. Regarding this rotational variance in the design of the multiuser interference suppression filter, the presented iterative multiuser detector achieves significant performance gains compared with conventional ISDIC employing a standard minimum mean-squared error filter which is optimum only for rotationally invariant multiuser interference.

Precoding, i.e., nonlinear pre-equalization, at the transmitter side has been proved to be a very efficient strategy for channel equalization in single-carrier digital transmission schemes. It enables the application of coded modulation in a seamless fashion. A drawback of precoding is that the signal at the input of the decision device exhibits a huge dynamic range. Based on dynamics shaping, a combined precoding/shaping technique introduced in the paper by Fischer et al. (1995), a new shaping strategy is developed in this paper. This technique enables a flexible tradeoff among: (1) reduction of the average transmit power; (2) avoidance of peaks in the transmit signal in order to facilitate line driver implementation; and (3) restriction of the maximum amplitude at the receiver side to a prescribed value. Over a wide range, all three demands can be met simultaneously. As the scheme is fully compatible with Tomlinson-Harashima (1971, 1972) precoding, it can replace the precoder even in existing and standardized schemes. Simulation results for a typical digital subscriber line scenario show the achievable gains.

Coded continuous phase modulation based on a feedback-free modulator with noncoherent detection is discussed. Low-complexity receiver processing is achieved by using only two or three linear filters for demodulation and applying noncoherent sequence estimation with reduced-state Viterbi decoding and simple branch metric calculation. Overall, the proposed noncoherent receiver provides significant advantages over previously presented approaches.

In advanced time-division multiple-access (TDMA) mobile communications systems, reduced-state equalization algorithms have to be employed because high-level modulation is used in order to improve spectral efficiency. Reduced-state equalizers yield only high performance, if the overall discrete-time system to be equalized is minimum-phase. Therefore, in general, a discrete-time prefilter has to be inserted in front of equalization. For prefilter computation, several approaches are investigated in this paper. For the finite impulse response (FIR) prefilter case, which seems to be more relevant for practical applications than the in finite impulse response case, we discuss a method based on minimum mean-squared error decision-feedback equalization and a novel approach based on linear prediction (LP). The LP method seems to be very robust and requires an only moderate amount of computational complexity. Here, the prefilter consists of the cascade of a channel-matched filter and a prediction-error filter, which may be viewed as a finite-length approximation to the noise whitening part of the ideal prefilter transfer function. A key observation of the paper is that the proposed cascaded structure enables a very efficient prefilter computation because a prediction-error filter can be calculated via the Levinson-Durbin algorithm. Simulation results are given, which demonstrate that the performance of reduced-state equalization with proper FIR prefiltering is close to that of equalization combined with ideal all-pass prefiltering. Furthermore, it is shown that high performance can be obtained for TDMA mobile communications systems, if the LP scheme is employed for prefiltering.

Precoding at the transmitter side has been proved to be a very efficient strategy for channel equalization in single-carrier digital transmission schemes. It enables the application of coded modulation in a seamless fashion. A drawback of precoding is that the signal at the input of the decision device exhibits a huge dynamic range. Based on dynamics shaping, a combined precoding/shaping technique introduced previously (see Fischer, R. et al., IEEE JSAC, p.1622-33, 1995), a new shaping strategy is developed. This technique enables a flexible trade-off between (i) reduction of the average transmit power, (ii) avoidance of peaks in the transmit signal in order to facilitate a line driver implementation, and (iii) restriction of the maximum amplitude at the receiver side to a prescribed value. Over a wide range, all three demands can be met simultaneously. As the scheme is fully compatible with Tomlinson-Harashima precoding, it can replace the precoder even in existing and standardized schemes. Simulation results for a typical DSL scenario show the achievable gains.

A hierarchically designed channel coding scheme protects a few number of input data streams, so-called layers, with a decreasing amount of redundancy from layer 0 to layer L. Such a code design clearly leads to unequal error protection, but as shown by Huettinger and Huber (see Winter School on Coding and Information Theory, Reisensburg, December 2000) it can be superior in the average bit error rate compared to an equal error protection (EEP) design, if the protection of layers is not too different. This is due to the fact, that a near-EEP hierarchical design can match the properties of the iterative decoder. We extend the result to woven convolutional codes (WCC). Based on asymptotical analysis of the convergence of iterative decoding by means of EXIT charts we show that for an infinite interleaver size the hierarchical structure is superior. Furthermore, we show that even for practical block sizes used in modern communication systems a significant improvement is possible by the hierarchical design.

Continuous phase modulation (CPM) systems for noncoherent coded transmission are proposed and analyzed. Specifically, the application of a feedback-free modulator is regarded. For demodulation, a receiver structure which requires only two or three linear filters is considered. For decoding, noncoherent sequence estimation (NSE) with Viterbi decoding and per-survivor processing is applied. Noteworthy, in our approach the problems of low-complexity filtering and reduced-state decoding can be treated separately. Since we give a recursive formula for the phase reference symbol necessary for NSE metric calculation, computational effort is further decreased. Overall, in terms of complexity, the proposed noncoherent receiver provides significant advantages over approaches in the literature. The high performance of the novel noncoherent CPM system is confirmed by simulation results.

An upper bound on the minimum distance of turbo codes is derived, which depends only on the interleaver length and the component scramblers employed. The derivation of this bound considers exclusively turbo encoder input words of weight 2. The bound does not only hold for a particular interleaver but for all possible interleavers including the best. It is shown that in contrast to general linear binary codes the minimum distance of turbo codes cannot grow stronger than the square root of the block length. This implies that turbo codes are asymptotically bad. A rigorous proof for the bound is provided, which is based on a geometric approach.

In this article, prediction-based decision-feedback differential detection (DF-DD) for 16-level differentially encoded amplitude/phase-shift keying is proposed. Unlike previously reported DF-DD schemes, this scheme provides a performance gain over conventional differential detection under general Ricean fading conditions. A further important advantage of the novel scheme is that it is able to compensate a small carrier frequency offset. The linear predictor coefficients may be updated using the recursive least-squares algorithm, which can start blind, i.e., without a priori knowledge about the channel statistics and without a training sequence. This makes the scheme attractive for application in mobile communications since the statistics of a nonstationary mobile channel can be tracked.

In this paper, new upper bounds on the maximum attainable minimum Hamming distance of turbo codes with arbitrary-including the best-interleavers are established using a combinatorial approach. These upper bounds depend on the interleaver length, the code rate, and the scramblers employed in the encoder. Examples of the new bounds for particular turbo codes are given and discussed. The new bounds are tighter than all existing ones and prove that the minimum Hamming distance of turbo codes cannot asymptotically grow at a rate more than the third root of the codeword length.

Selected mapping (SLM) peak power reduction is distortionless as it selects the actual transmit signal from a set of alternative signals, which all represent the same information. Usually, the specific signal generation information needs to be transmitted and carefully protected against bit errors. Here, we propose an extension of SLM, which employs scrambling and refrains from transmitting explicit side information. Some additional complexity and nearly vanishing redundancy is introduced to achieve markedly improved transmit signal statistics. Even though SLM is applicable with any modulation, we concentrate on orthogonal frequency-division multiplexing (OFDM).

Conventional orthogonal frequency-division multiplexing (OFDM) receivers disregard oversized guard intervals. An (adaptive) Nyquist-shaped receive window could exploit signal samples in its unconsumed portion to improve demodulation. The OFDM transmitter is not modified, subcarrier orthogonality is preserved, and the DFT size may be retained. In this paper, we optimize the window shape by considering additive noise and intercarrier interference due to carrier frequency offsets, jointly.

A novel noncoherent linear equalization scheme is introduced and analyzed. The proposed scheme is not only applicable for M-ary differential phase-shift keying (MDPSK) but also for M-ary differential amplitude/phase-shift keying (MDAPSK) and minimizes the variance of intersymbol interference (ISI) in the equalizer output signal. The optimum equalizer coefficients may be calculated directly from an eigenvalue problem. For an efficient recursive adaptation of the equalizer coefficients, a modified least-mean-square (LMS) algorithm is proposed. Simulations confirm the good performance of the considered noncoherent equalization scheme and its robustness against frequency offset.

In advanced TDMA mobile communications systems, reduced-state equalization algorithms have to be employed because a high-level modulation is used in order to improve the spectral efficiency. Such equalizers only have a high performance, if the overall discrete-time system to be equalized is minimum-phase. Therefore, in general, a discrete-time prefilter has to be inserted in front of equalization. In the literature, several approaches have been proposed for computation of a suitable FIR or IIR prefilter. We present an approach for FIR prefilter computation, which is quite robust and requires an only moderate computational complexity. The prefilter consists of the cascade of a channel-matched filter and a prediction-error filter, which can be calculated via the Levinson-Durbin algorithm. Simulation results are given, which demonstrate that the performance of the proposed approach is essentially equivalent to the case of reduced-state equalization combined with ideal allpass prefiltering.

In this letter, a novel equalization algorithm applying soft-decision feedback and designed for binary transmission is introduced. In contrast to conventional decision-feedback equalization (DFE), iterations are necessary, because a simple matched filter serves as feedforward filter, which collects signal energy, but creates noncausal intersymbol interference. The rule for generating soft decisions is adapted continuously to the current state of the algorithm. In most cases, standard DFE methods are clearly outperformed. For a class of certain channel impulse responses, performance of maximum-likelihood sequence estimation is attained, in principle. The high performance of the scheme is explained using results from neural network theory.

A novel noncoherent receiver for M-ary differential phase-shift keying signals transmitted over intersymbol interference channels is presented. The noncoherent receiver consists of a linear equalizer and a decision-feedback differential detector. A significant performance gain over a previously proposed noncoherent receiver can be observed. For an infinite number of feedback symbols, the optimum equalizer coefficients can be calculated analytically, and the performance of the proposed receiver approaches that of a coherent linear minimum mean-squared-error equalizer. Moreover, a modified least mean square and a modified recursive least squares algorithm for adaptation of the equalizer coefficients are discussed.

In this paper, decision-feedback differential detection (DF-DD) of M-ary differential phase-shift keying (MDPSK) signals, which has been introduced previously for the additive white Gaussian noise (AWGN) channel by Leib et al. (1988) and Edbauer (1992), is extended to flat Rayleigh fading channels. The corresponding DF-DD metric is derived from the multiple-symbol detection (MSD) metric and for genie-aided DF-DD, an exact expression for the bit-error rate (BER) of QDPSK (M=4) is calculated. Furthermore, the dependence of BER on the power spectrum of the fading process is investigated for feedback filters of infinite order. It is shown that in this case, for ideally bandlimited fading processes, the error floor of conventional differential detection (DD) can be removed entirely. Simulation results confirm that both MSD and DF-DD with feedback filters of finite order can reduce the error floor of conventional DD significantly. DF-DD thereby causes considerably less computational load.

A new technique is proposed to improve the performance of differential detection (DD) of M-ary differential phase-shift keying (MDPSK) significantly, applying sequence estimation. In order to obtain an appropriate representation of the received signal, a nonlinear time-variant finite impulse response or infinite impulse response prediction-error filter is used. For both filter structures the optimum coefficients are derived, assuming transmission over an additive white Gaussian noise (AWGN) channel. Delayed decision-feedback sequence estimation (DDFSE) is employed to estimate the transmitted symbol sequence. It is shown by simulations that even for decision-feedback equalization, which is a simple special case of DDFSE, a significant performance improvement of conventional DD under AWGN conditions results. In contrast to other noncoherent low-complexity receivers proposed in literature, this receiver is very robust under flat fading (Rayleigh and Ricean) conditions.

This paper deals with 2/sup l/-ary transmission using multilevel coding (MLC) and multistage decoding (MSD). The known result that MLC and MSD suffice to approach capacity if the rates at each level are appropriately chosen is reviewed. Using multiuser information theory, it is shown that there is a large space of rate combinations such that MLC and full maximum-likelihood decoding (MLD) can approach capacity. It is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and, therefore, require the huge complexity of MLD. The capacity rule, the balanced distances rules, and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design. Simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies. Moreover, topics relevant in practical applications such as signal set labeling, dimensionality of the constituent constellation, and hard-decision decoding are emphasized. Bit interleaved coded modulation, proposed by Caire et al. (see ibid., vol.44, p.927-46, 1998), is reviewed in the context of MLC. Finally, the combination of signal shaping and coding is discussed. Significant shaping gains are achievable in practice only if these design rules are taken into account.

An efficient and distortionless scheme for peak power reduction in orthogonal frequency division multiplexing (OFDM) is proposed, which introduces some additional complexity but nearly vanishing redundancy. The approach is very flexible and works with arbitrary numbers of subcarriers and without restriction on the type of modulation applied in them. The core of the approach is the coordination of appropriately phase rotated signal parts to minimize the peak power of the multiplex signal. The improved statistics of peak power in the optimized transmit signal are demonstrated by simulation results. Finally, it is shown that this scheme is close to the theoretical limit curve of redundancy versus minimum peak-to-average power ratio (PAR).

Precoding at the transmitter side is a practicable method for transmission over intersymbol interference channels. In contrast to decision-feedback equalization no error propagation occurs and coded modulation can be applied as for the intersymbol interference free channel. Tomlinson-Harashima (1971, 1972) precoding and flexible precoding are analyzed and compared. The dualities and differences are discussed. The focus of interest is the application of precoding to fast digital transmission over twisted pair lines, such as high-rate or asymmetric digital subscriber lines. It turns out that flexibility-which is not necessary in the specific application, digital subscriber lines-of flexible precoding is paid with a performance loss compared to Tomlinson-Harashima precoding.

A new combined precoding/shaping technique for fast digital transmission over twisted pair lines is proposed. Major advantages of this "dynamics shaping" are: Dynamics of the signal at the input of the decision device are reduced by a great amount. Thereby, A/D-conversion, adaptive equalization, and symbol timing are rather facilitated. A trade-off between signal dynamics at the transmitter output, decision device input and SNR-gain by noise whitening is offered. For dynamics limitation relevant in practice, gains up to 6 dB are achieved. Additionally, the transmitter can be fixed to a typical application because, in contrast to Tomlinson-Harashima or other precoding techniques, blind adaptive equalization is practicable to remove residual intersymbol interference in the case of a mismatch of precoding and actual cable characteristics. The residual SNR-loss is negligible in most applications. SNR-gains due to noise prediction, channel coding and signal shaping simply can be combined us...