A simple and effective precoding scheme for noise whitening onintersymbol interference channels

A precoding scheme for noise whitening on intersymbol interference (ISI) channels is presented. This scheme is compatible with trellis-coded modulation and, unlike Tomlinson precoding, allows constellation shaping. It can be used with almost any shaping scheme, including the optimal SVQ shaping, as opposed to trellis precoding, which can only be used with trellis shaping. The implementation complexity of this scheme is minimal-only three times that of the noise prediction filter, hence effective noise whitening can be achieved by using a high-order predictor     

Performance evaluation study of signal design and equalization options for high-bit-rate digital subscriber line transceivers

This paper analyses different equalization, coding and signal constellation alternatives for the proposed high-bit-rate (800 kb/s) digital subscriber loop transmission interface. The simulation results presented in the paper demonstrate that bit rates above 1000 kb/s at acceptably low bit-error rates (≤ 10^?7) are feasible, if baseband transceivers with appropriate equalization and simple trellis coding are used. It is also shown that baseband transmission and Tomlinson precoding provide a significant performance advantage over bandpass transmission and decision-feedback equalization, respectively.     

Adaptive coded modulation for fading channels

We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB     

Combined equalization and coding for high-density saturationrecording channels

Combined equalization and coding approaches which significantly outperform previous techniques are presented for the binary Lorentzian channel with additive Gaussian noise. The authors develop a technique based on the concatenation of standard trellis codes with an equalization code and a block decision feedback equalizer (BDFE). Signal sets for the trellis code are generated by partitioning BDFE output vectors according to four- and eight-dimensional lattices. They also investigate the combination of a decision feedback equalizer (DFE) and a convolutional code (CC) and find that this system provides theoretical coding gains from 1 to 3 dB in the high linear recording density range of 2⩽pw₅₀/T⩽3. Although the BDFE with the trellis code system does not perform as well as the DFE with CC system at high densities, it does produce substantial coding gains at low linear recording densities     

Combined trellis coding and DFE through Tomlinson precoding

The authors propose and evaluate a receiver architecture which combines the power of a decision feedback equalizer (DFE) with trellis coding, while allowing for minimal decoding delay in such a way that the total gain of the system is additive. The system is based on a structure that transposes the feedback filter of the DFE into the transmitter and, for high-order constellations, provides negligible increase in transmitter power. The first known hardware realization of a high bit rate digital subscriber line (HDSL) system that achieves the coding gain provided by a trellis code in addition to the equalization gain provided by the DFE is presented. A system whose complexity of implementation is comparable to that of a typical DFE and an independent Viterbi decoder is proposed     

Baseband trellis-coded modulation with combinedequalization/decoding for high bit rate digital subscriber loops

The authors present a simulation study evaluating the performance of trellis-coded modulation with combined code/ISI sequence estimation for high bit rate (800 kb/s) transmission on subscriber loops. The receiver contains a fractionally spaced forward filter of a decision feedback equalizer (DFE) as a front end. This is shown to suppress phase synchronized crosstalk very effectively. The performance is further enhanced by the use of trellis code with a large number of states received with an M algorithm sequence-estimating receiver with a smaller number of states     

Trellis-coded constant-envelope modulations with linear receivers

We present two multilevel constant-envelope continuous-phase modulation (CPM) schemes with four-dimensional (4-D) trellis coding. The receiver is composed of a simple quadrature demodulator, followed by a symbol-rate sampler and a Viterbi decoder matched to the code trellis. The first modulation is a quaternary CPM scheme whose phase transitions over a symbol interval are those of π/4-shift quaternary phase-shift keying (QPSK). The demodulator filter is optimized so as to minimize the combined effect of intersymbol interference (ISI) and noise at the decision instants. We use Wei's (1987) 16-state 4-D trellis code, and redefine the set partitioning tree so as to maintain the same minimum distance between parallel transitions as in quadrature amplitude modulation (QAM) signal sets. The resulting modulation outperforms minimum-shift keying (MSK) by as much as 3.5 dB, in addition to reducing the 30-dB signal bandwidth by 20%. Next, we introduce an octonary (8-level) CPM scheme whose phase transitions are those of π/8-shift 8PSK. The same trellis code and receive filter optimization are also applied to this modulation which is shown to achieve better error rate performance than MSK, while saving some 60% of the transmitted signal bandwidth     

An eight-dimensional 64-state trellis code for transmitting 4 bitsper 2-D symbol

An eight-dimensional, 64-state, 90° rotationally invariant trellis code for transmitting 4 bits/baud over a bandlimited channel is described. The 2-D constellation contains 20 points. The code achieves a 5.23-dB coding gain over the uncoded 4×4 QAM (quadrature amplitude modulation) constellation and a 1.23-dB gain over the standard CCITT V32 trellis code. Simulation results are presented that verify these coding gains. Simulation results showing symbol error probability versus signal/noise ratio and trellis depth are also presented     

Decoding of trellis-encoded signals in the presence of intersymbolinterference and noise

A novel receiver for data-transmission systems using trellis-coded modulation is investigated. It comprises a whitened-matched filter and a trellis decoder which combines the previously separated functions of equalization and trellis-coded modulation (TCM) decoding. TCM encoder, transmission channel, and whitened-matched filter are modeled by a single finite-state machine with combined intersymbol interference and code states. Using ISI-state truncation techniques and the set-partitioning principles inherent in TCM, a systematic method is then developed for reducing the state complexity of the corresponding ISI and code trellis. A modified branch metric is used for canceling those ISI terms which are not represented by the trellis states. The approach leads to a family of Viterbi decoders which offer a tradeoff between decoding complexity and performance. An adaptive version of the proposed receiver is discussed, and an efficient structure for reduced-state decoding is given. Simulation results are presented for channels with severe amplitude and phase distortion. It is shown that the proposed receiver achieves a significant gain in noise margin over a conventional receiver which uses separate linear equalization and TCM decoding     

Concatenated combined modulation and coding of frequency hoppingmultiaccess systems

A spread-spectrum system that does not have a separate state for initial code acquisition is presented. A uniform random variate selects one of several Gold codes for transmission, thus removing the notion of pseudorandom codes from spread-spectrum systems, making the effective code length infinite, and leading to acquisitionless systems. Because coding is critical to the proposed multiaccess frequency-hopping (FH) system, more powerful codes are needed. The performance of the proposed multiaccess system using the combined modulation and coding technique (trellis) concatenated with Reed-Solomon codes in partial-band jamming is investigated. The FH multiaccess performance of noncoherent soft detection of MFSK in association with trellis coding is introduced and the performance compared to that using RS outer/RS inner concatenated codes     

Filtered multitone modulation for very high-speed digitalsubscriber lines

A filter-bank modulation technique called filtered multitone (FMT) and its application to data transmission for very high-speed digital subscriber line technology are described. The proposed scheme leads to significantly lower spectral overlapping between adjacent subchannels than for known multicarrier techniques such as discrete multitone (DMT) or discrete wavelet multitone. FMT modulation mitigates interference due to echo and near-end crosstalk signals, and increases the system throughput and reach. Signal equalization in an FMT receiver is accomplished in the form of per-subchannel symbol-spaced or fractionally spaced linear or decision-feedback equalization. The problem of channel coding for this type of modulation is also addressed, and an approach that allows combined removal of intersymbol-interference via precoding and trellis coding is described. Furthermore, practical design aspects regarding filter-bank realization, initial transceiver training, adaptive equalization, and timing recovery are discussed. Finally, simulation results of the performance achieved by FMT modulation for very high-speed digital subscriber line systems, where upstream and downstream signals are separated by frequency-division duplexing, are presented and compared with DMT modulation     

Iterative packet combining schemes for intersymbol interferencechannels

We study packet combining techniques for retransmission schemes over intersymbol interference (ISI) channels. Two types of combining schemes are investigated, namely, maximum-likelihood combining (MLC) and iterative combining (IC). By first employing a precoding technique and then by interpreting the ISI channel as a trellis code, the transmissions of the same data packet at different times through the channel can be treated as the parallel concatenation of recursive trellis codes. If interleavers are used in between retransmissions, "turbo" coding gains can be achieved by iterative equalization. It is shown that IC provides excellent performance and outperforms other forms of combining in terms of frame error rate performance both analytically and through simulations     

Diagonal block space-time code design for diversity and coding advantage over flat fading channels

The potential promised by multiple transmit antennas has raised considerable interest in space-time coding for wireless communications. In this paper, we propose a systematic approach for designing space-time trellis codes over flat fading channels with full antenna diversity and good coding advantage. It is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations. The key to this approach is to separate the traditional space-time trellis code design into two parts. It first encodes the information symbols using a one-dimensional (M,1) nonbinary block code, with M being the number of transmit antennas, and then transmits the coded symbols diagonally across the space-time grid. We show that regardless of channel time-selectivity, this new class of space-time codes always achieves a transmit diversity of order M with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code. Traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed. To maximize the coding advantage, we introduce an optimal construction of the nonbinary block code for a given modulation scheme. In particular, an efficient suboptimal solution for multilevel phase-shift-keying (PSK) modulation is proposed. Some code examples with 2-6 bits/s/Hz and two to six transmit antennas are provided, and they demonstrate excellent performance via computer simulations. Although it is proposed for flat fading channels, this coding scheme can be easily extended to frequency-selective fading channels.     

Performance evaluation of super-orthogonal space-time trellis codes using a moment generating function-based approach

A new class of space-time codes called super-orthogonal trellis codes was introduced that combine set-partitioning with a super set of orthogonal space-time block codes in such a way as to provide full diversity with increased rate and improved coding gain over previous space-time trellis code (STTC) constructions. Here, we extend the moment generating function-based method, which was previously applied to analyzing the performance of space-time block orthogonal and trellis codes, to the above-mentioned super-orthogonal codes. It is shown that the maximum-likelihood metric and expressions for the pairwise error probability previously developed for the Alamouti (1998) space-time block code combined with multidimensional trellis-coded modulation can be readily extended to the super-orthogonal case. As such, the evaluation of the pairwise error probability for the latter can be performed in a similar manner to that previously described with the specific results depending on the particular trellis code design.     

Analysis of the pairwise error probability of noninterleaved codeson the Rayleigh-fading channel

The majority of previous analytical studies of signal-space coding techniques (includes trellis and block codes) on the Rayleigh-fading channel have assumed ideal interleaving. The effect of finite interleaving on the performance of different coding schemes has been studied only by simulation In this paper we first derive a maximum likelihood (ML) decoder for codewords transmitted over a noninterleaved Rayleigh flat fading channel, followed by an exact expression for the pairwise error event probability of such a decoder. It includes phase shift keying (PSK), quadrature amplitude modulation (QAM) signal sets, trellis coded modulation (TCM) and block coded modulation (BCM) schemes, as well as coherent (ideal channel state information) and partially coherent (e.g., differential, pilot tone, etc.) detection. We derive an exact expression for the pairwise event probability in the case of very slow fading-i.e., the fading experienced by all the symbols of the codeword is highly correlated. We also show that the interleaving depth required to optimize code performance for a particular minimum fading bandwidth can be approximated by the first zero of the fading channel's auto-correlation function     

Coding for intersymbol interference channels-combined coding andprecoding

This paper describes a new coding scheme for transmission over intersymbol interference (ISI) channels. This scheme, called ISI coding, combines trellis coding with precoding (used to combat ISI). Like the recently introduced precoding scheme of Laroia, Tretter, and Farvardin (LTF), the ISI coder makes it possible to achieve both shaping and coding gains over ISI channels. By combining coding and precoding, however, the ISI coder makes the “precoding loss” independent of the number of coset partitions used to generate the trellis code. At high rates (large signal-to-noise ratio (SNR)), this makes it possible to approach the Shannon capacity of an ISI channel. The V.34 (formerly V.fast) international modem standard for high-speed (up to 28.8 kb/s) communication over voice-band telephone lines uses the version of the ISI coder described in Section IV of this paper     

On the Performance of Combined Quadrature Amplitude Modulation and Convolutional Codes for Cross-Coupled Multidimensional Channels

The performance of cross-coupled,M-ary quadrature amplitude modulation (QAM) systems is determined when bandwidth efficient trellis codes are used to combat interference. Performance with and without compensation for cross-coupled interference is presented. It is found that simple trellis codes can maintain the error probability at an acceptable level for cross-coupling parameters that render uncoded systems unusable. Up to two-dimensional trellis codes are considered for four-dimensional QAM signals, and possibilities of obtaining diversity advantages in the form of higher total system throughput by prolonged availability of the two signals are explored. This is accomplished through joint coding over two different constellations. The probability of the most likely error events is calculated by using the method of moments. The results are applicable to any digital communication system using multidimensional quadrature amplitude modulation, e.g., voiceband modems, cross-polarized radio systems and, to some extent, optical systems. In the paper the analysis is restricted to nondispersive cross-coupling models. In most cases the coding gain is larger than in the absence of cross-coupling interference. Specifically, it is found that simple codes have coding gains increased by at least 2 dB with cross-coupling interference relative to that obtained on the additive white Gaussian noise channel.     

Practical coding for QAM transmission of HDTV

It is demonstrated how modulation schemes based on QPSK can be directly incorporated into QAM-based systems. It is argued that this leads directly to an easily implementable structure that is both efficient in bandwidth and data reliability. It is contended that the correct solution to the concatenated coding problem for HDTV transmission is to simply extend the modulation codes developed for QPSK-to-QAM modulation. In nonconcatenated situations, a trellis code based on a binary code at rate 2/3 is usually best. However, this is not the case for higher error rates at the output of the trellis decoder (e.g., when a symbol error correcting decoder follows as a concatenated code). The reason for this follows from an analysis of the effect of the number of nearest neighbors on the error rate. A four-way partition of QAM is a natural extension of QPSK modulation; it is a simple matter to incorporate any good QPSK code into a trellis coding scheme for QAM modulation. A concatenated coding scheme based on QPSK trellis codes and symbol error correcting coding is proposed. An example is presented to show the advantages of this approach     

Space-time codes and concatenated channel codes for wirelesscommunications

Following a brief historical perspective on channel coding, an introduction to space-time block codes is given. The various space-time codes considered are then concatenated with a range of channel codecs, such as convolutional and block-based turbo codes as well as conventional and turbo trellis codes. The associated estimated complexity issues and memory requirements are also considered. These discussions are followed by a performance study of various space-time and channel-coded transceivers. Our aim is first to identify a space-time code/channel code combination constituting a good engineering tradeoff in terms of its effective throughput, bit-error-rate performance, and estimated complexity. Specifically, the issue of bit-to-symbol mapping is addressed in the context of convolutional codes (CCs) and convolutional coding as well as Bose-Chaudhuri-Hocquenghem coding-based turbo codes in conjunction with an attractive unity-rate space-time code and multilevel modulation is detailed. It is concluded that over the nondispersive or narrow-band fading channels, the best performance versus complexity tradeoff is constituted by Alamouti's twin-antenna block space-time code concatenated with turbo convolutional codes. Further comparisons with space-time trellis codes result in similar conclusions     

Trellis-coded differential unitary space-time modulation over flat fading channels

Coding and modulation for multiple-antenna systems have gained much attention in wireless communications. This paper investigates a noncoherent trellis-coded scheme based on differential unitary space-time modulation when neither the transmitter nor the receiver know the channel. In a time-varying flat Rayleigh fading environment, we derive differentially noncoherent decision metrics and obtain performance measures for systems with either an ideal interleaver or no interleaver. We demonstrate that with an ideal interleaver, the system performance is dominated by the minimum Hamming distance of the trellis code, while without an interleaver, the performance is dominated by the minimum free squared determinant distance (a novel generalization of the Euclidean distance) of the code. For both cases, code construction is described for Ungerboeck-type codes. Several examples that are based on diagonal cyclic group constellations and offer a good tradeoff between the coding advantage and trellis complexity are provided. Simulation results show that, by applying the soft-decision Viterbi decoder, the proposed scheme can achieve very good performance even with few receive antennas. Extensions to trellis-coded differential space-time block codes are also discussed.