Reduced-state Sequence Detection Research Articles

Generalized Reduced-State Vector Sequence Detection

A multi-dimensional set-partitioning scheme is proposed for joint reduced-state sequence detection (JRSSD) of vector sequences corrupted by intersymbol interference (ISI) and additive white Gaussian noise (AWGN). The existing multi-dimensional set-partitioning schemes result in complexity exponential in the dimensionality of the vectors in the vector sequence. The proposed set-partitioning scheme allows the construction of reduced-state trellises with very few states even when the vectors are of high dimensionality. One of the key requirements of the JRSSD algorithm is an efficient algorithm for spatial multi-symbol detection, for which we propose the reduced-state tree (RST) detection algorithm. In addition to performance improvement, the inclusion of RST algorithm for spatial multi-symbol detection provides a common framework for designing receivers for both flat-fading and frequency-selective fading MIMO channels.

State-Complexity Reduction in MLSD Receivers for Optical Communications With Direct Photodetection

We investigate the impact of state-complexity reduction on the performance of maximum likelihood sequence detection (MLSD) receivers for direct-photodetection long-haul optical communication systems affected by uncompensated chromatic dispersion (CD). We directly compare two possible approaches: (i) detection through a simple ldquobrute-forcerdquo state-complexity reduction strategy and (ii) a more structured reduced-state sequence detection (RSSD) strategy. The performance of both state-complexity reduction techniques is evaluated considering two realistic optical transmission schemes, based on on-off keying (OOK) and optical duobinary modulation (ODBM), respectively. The detection algorithms are characterized considering the impact of the timing offset, the quantization scheme, and the amount of uncompensated CD. As one would expect, for a given number of states in MLSD receivers, the schemes based on RSSD exhibit better performance with respect to those based on simple brute-force state-complexity reduction. However, we show that MLSD schemes based on the use of brute-force state-complexity reduction are characterized by a better complexity/performance trade-off for low/medium CD values, whereas RSSD is the best choice for high CD values.

A reduced state SISO iterative decoding algorithm for serially concatenated continuous phase modulation

In this paper, serially concatenated continuous phase modulation (SCCPM) system is analyzed and a reduced state soft input soft output (SISO) a posteriori probability algorithm is proposed. Based on the reduced state sequence detection (RSSD), it has the more general form compared with other reduced state SISO algorithms. The proposed algorithm can greatly reduce the state number, thus leads to the computation complexity reduction. It also minimizes the degradation in Euclidean distance with decision feedback in the reduced state trellis. Analysis and simulation results show that the performance degradation is little with proper reduction scheme.

Serially concatenated continuous phase modulation with reduced iterative demodulation and detection

A reduced state Soft Input Soft Output (SISO) a posteriori probability algorithm for Serially Concatenated Continuous Phase Modulation (SCCPM) is proposed in this paper. Based on the Reduced State Sequence Detection (RSSD), it has more general form compared with other reduced state SISO algorithms. The proposed algorithm can greatly reduce the state number, thus leads to the computation complexity reduction. It also minimizes the degradation in Euclidean distance with decision feedback in the reduced state trellis. Analysis and simulation results show that the performance degradation is little with proper reduction scheme.

Coset detection in MIMO systems based on spatial multiplexing

For multiple-input multiple-output (MIMO) spatial multiplexing systems the complexity of the maximum likelihood detector (MLD) can be prohibitively large when the number of transmitting antennas and constellation points is high. To simplify the MLD many linear and nonlinear techniques have been proposed. In this letter the principle of reduced state sequence detection, based on mapping by set partitioning, is applied to perform detection in spatial multiplexing MIMO systems based on non-binary constellations. Simulation results are presented to show the benefits of our proposal. An upper bound to the symbol error probability is also derived.

Noncoherent sequence detection of differential space-time modulation

Approximate maximum-likelihood noncoherent sequence detection (NSD) for differential space-time modulation (DSTM) in time-selective fading channels is proposed. The starting point is the optimum multiple-symbol differential detection for DSTM that is characterized by exponential complexity. By truncating the memory of the incremental metric, a finite-state trellis is obtained so that a Viterbi algorithm can be implemented to perform sequence detection. Compared to existing linear predictive receivers, a distinguished feature of NSD is that it can accommodate nondiagonal constellations in continuous fading. Error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers. By incorporating the reduced-state sequence detection techniques, performance and complexity tradeoffs can be controlled by the branch memory and trellis size. Numerical results show that most of the performance gain can be achieved by using an L-state trellis, where L is the size of the DSTM constellation.

Sequence detection in nonlinear channels: a convenient alternative to analog predistortion

A new maximum-likelihood sequence detection receiver for spectrally efficient linear modulations on bandlimited bandpass nonlinear channels is proposed. The receiver is based on oversampling the received signal corrupted by noise and nonlinear distortion. Contrary to other solutions in the literature, in the proposed technique there is no need for a bank of matched filters, and the receiver front end reduces to a single lowpass filter. For a given peak power level, a performance gain can be achieved over more traditional approaches to transmission on nonlinear channels, such as those based on predistortion, if a moderate spectral expansion is allowed. To analyze the receiver performance, the concept of distance spectrum is employed, since the minimum distance alone cannot account for a reliable performance evaluation. Both analysis and simulation are carried out for realistic narrowband nonlinear channels, possibly employing reduced-state sequence detection. Appreciable gain margins are confirmed to be possible in these realistic cases.

Reduced-state BCJR-type algorithms

We propose a technique to reduce the number of trellis states in BCJR-type algorithms, i.e., algorithms. with a structure similar to that of the well-known algorithm by Bahl, Cocke, Jelinek, and Raviv (1974). This work is inspired by reduced-state sequence detection (RSSD). The key idea is the construction, during one of the recursions in the reduced-state trellis, of a map to be used in the other recursion. In a more general setting, two distinct survivor maps could be determined in the two recursions and used jointly to approximate the a posteriori probabilities. Three examples of application to iterative decoding are shown: (1) coherent detection for intersymbol interference (ISI) channels; (2) noncoherent detection based on an algorithm previously proposed by the authors; and (3) detection based on linear prediction for Rayleigh fading channels. As in classical RSSD, the proposed algorithm allows significant state-complexity reduction with limited performance degradation.

Codes preventing quasi-catastrophic error propagation in partial-response systems

The problem of preventing quasi-catastrophic error propagation in maximum-likelihood and reduced-state sequence detection for multilevel partial-response channels with transfer functions (1-D/sup P/) and (1+D/sup P/) is studied. M-ary channel input sequences that limit the length of minimum distance error events to L symbols are exhaustively characterized by finite-state transition diagrams. An efficient procedure for computing the capacity associated with these transition diagrams is given. Efficient constrained codes that can be readily implemented by finite-state encoders and block decoders with small error propagation are constructed. >

Reduced-state sequence detection with convolutional codes

Reduced-state sequence detection (RSSD) reduces the state trellis of a channel code by forming the states into classes. States within a class are such that paths into the states lie further than a distance parameter d from each other. An RSSD decoder retains only one survivor per class at each trellis level. The authors apply RSSD to ordinary binary convolutional codes. They first give a class-forming algorithm that finds the greatest reduction. It turns out that no commonly tabulated good code benefits from RSSD. However, RSSD is an effective way to repair weaker codes, such as quick look-in and RCPC codes. Finally, the authors show that RSSD cannot be more efficient than the M-algorithm. >

Reduced-state sequence detection of multilevel partial-response signals

This work is concerned with the problem of designing reduced-complexity Viterbi decoders for the transmission of digital data over intersymbol interference channels. First, optimal state-grouping for constructing reduced-state trellises is presented and illustrative examples are given for multilevel transmission over partial-response channels of the type 1+or-D/sup n/, (1+D)/sup 2/, (1+D)/sup 2/(1-D), and (1+D)/sup 3/(1-D). Then, the quaternary 1-D type partial-response channel is considered in more detail and a difference-matric algorithm employing state-reduction is derived and shown to result in a simple decoding scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reduced state sequence detection of partial response continuous phase modulation

A reduced state sequence detector (RSSD) which combines decision feedback with Viterbi decoding is proposed for partial response continuous phase modulation (CPM). This detector can successfully be used for both binary and high-level partial response CPM schemes. This detector is analysed by means of minimum Euclidean distance and by simulations of the symbol error probability. It is shown that the phase states in the receiver trellis of the maximum likelihood detector for partial response CPM can be exchanged by decision feedback in the metric calculations. This can be achieved without sacrificing minimum Euclidean distance of the first error event or symbol error probability. This RSSD is most attractive for narrow-band CPM schemes and at most about 2 dB in increased energy efficiency as compared with MSK is possible. Further reductions in number of states is possible, especially for high-level CPM schemes, by reducing the number of correlative states. For the most frequently used CPM schemes this can be done with a very small degradation in error performance. In this class of schemes, a complexity reduction of at least a factor five to ten is possible.

Reduced state sequence detection of full response continuous phase modulation

A reduced state sequence detector (RSSD) which combines decision feedback with Viterbi decoding is proposed for M-ary full response continuous phase modulation. The detector is analysed with minimum Euclidean distances and by simulations of the symbol error probability. It is shown that M-ary full response CPM schemes can be optimally decoded by a decoder with only two states when the modulation index is relatively small ( >