Trellis coded modulation techniques

The subject of this thesis is an investigation of various trellis coded modulation (TCM) techniques that have potential for out-performing conventional methods. The primary advantage of TCM over modulation schemes employing traditional error-correction coding is the ability to achieve increased power efficiency without the normal expansion of bandwidth introduced by the coding process. Thus, channels that are power limited and bandwidth limited are an ideal application for TCM. In this thesis, four areas of interest are investigated. These include: signal constellation design, multilevel convolutional coding, adaptive TCM and finally low-complexity implementation of TCM. An investigation of the effect of signal constellation design on probability of error has led to the optimisation of constellation angles for a given channel signal to noise ratio and a given code. The use of multilevel convolutional codes based on rings of integers and multi-dimensional modulation is presented. The potential benefits of incorporating several modulation schemes with adaptive TCM which require a single decoder are also investigated. The final area of investigation has been the development of an algorithm for decoding of convolutional codes with a low complexity decoder. The research described in this thesis investigated the use of trellis coded modulation to develop various techniques applicable to digital data transmission systems. Throughout this work, emphasis has been placed on enhancing the performance or complexity of conventional communication systems by simple modifications to the existing structures

A variable-rate modulation and coding scheme for low earth orbit satellites

Low Earth Orbit (LEO) satellites are increasingly being used for a wide variety of communications applications. These satellites have to operate in widely varying channel conditions. These conditions are often significantly better than the 'worst case' situations that are experienced and thus a single rate transmission scheme is clearly suboptimal. The objective of the thesis is to suggest and test a method of modulation/coding that can take advantage of better signal strength conditions in order to improve data transmission rates. In order to provide the goal of approximately 50kbps transmission in a 10kHz Frequency Division Multiple Access (FDMA) channel it was necessary to consider spectrally efficient, rather than power efficient, modulations. The proposed modulation scheme makes use of an eight-dimensional trellis coded modulation system. Multiple signal constellation sets are used in conjunction with this coding in order to provide different transmission rates, depending on the signal to noise ratio and the channel state. To enhance the suitability of the modulation scheme for the channel, it was combined with Reed-Solomon Coding and interleaving in an inner/outer code arrangement. Various means of determining when to switch between coding rates were discussed briefly, but an in-depth treatment of the subject fell outside of the scope of the thesis. Various combinations of these codes were tested in gaussian noise conditions and various degrees of Rician and Rayleigh fading. In order to make use of the higher rate QAM constellations, it was necessary to provide the decoder with channel state information. The tested system achieved its purpose of providing a variable rate coding scheme resulting in good performance over a range of channel conditions. It is fairly flexible and can be adapted to specific channel requirements

On Optimal TCM Encoders

An asymptotically optimal trellis-coded modulation (TCM) encoder requires the joint design of the encoder and the binary labeling of the constellation. Since analytical approaches are unknown, the only available solution is to perform an exhaustive search over the encoder and the labeling. For large constellation sizes and/or many encoder states, however, an exhaustive search is unfeasible. Traditional TCM designs overcome this problem by using a labeling that follows the set-partitioning principle and by performing an exhaustive search over the encoders. In this paper we study binary labelings for TCM and show how they can be grouped into classes, which considerably reduces the search space in a joint design. For 8-ary constellations, the number of different binary labelings that must be tested is reduced from 8!=40320 to 240. For the particular case of an 8-ary pulse amplitude modulation constellation, this number is further reduced to 120 and for 8-ary phase shift keying to only 30. An algorithm to generate one labeling in each class is also introduced. Asymptotically optimal TCM encoders are tabulated which are up to 0.3 dB better than the previously best known encoders

Associative neural networks: properties, learning, and applications.

by Chi-sing Leung.Thesis (Ph.D.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 236-244).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Background of Associative Neural Networks --- p.1Chapter 1.2 --- A Distributed Encoding Model: Bidirectional Associative Memory --- p.3Chapter 1.3 --- A Direct Encoding Model: Kohonen Map --- p.6Chapter 1.4 --- Scope and Organization --- p.9Chapter 1.5 --- Summary of Publications --- p.13Chapter I --- Bidirectional Associative Memory: Statistical Proper- ties and Learning --- p.17Chapter 2 --- Introduction to Bidirectional Associative Memory --- p.18Chapter 2.1 --- Bidirectional Associative Memory and its Encoding Method --- p.18Chapter 2.2 --- Recall Process of BAM --- p.20Chapter 2.3 --- Stability of BAM --- p.22Chapter 2.4 --- Memory Capacity of BAM --- p.24Chapter 2.5 --- Error Correction Capability of BAM --- p.28Chapter 2.6 --- Chapter Summary --- p.29Chapter 3 --- Memory Capacity and Statistical Dynamics of First Order BAM --- p.31Chapter 3.1 --- Introduction --- p.31Chapter 3.2 --- Existence of Energy Barrier --- p.34Chapter 3.3 --- Memory Capacity from Energy Barrier --- p.44Chapter 3.4 --- Confidence Dynamics --- p.49Chapter 3.5 --- Numerical Results from the Dynamics --- p.63Chapter 3.6 --- Chapter Summary --- p.68Chapter 4 --- Stability and Statistical Dynamics of Second order BAM --- p.70Chapter 4.1 --- Introduction --- p.70Chapter 4.2 --- Second order BAM and its Stability --- p.71Chapter 4.3 --- Confidence Dynamics of Second Order BAM --- p.75Chapter 4.4 --- Numerical Results --- p.82Chapter 4.5 --- Extension to higher order BAM --- p.90Chapter 4.6 --- Verification of the conditions of Newman's Lemma --- p.94Chapter 4.7 --- Chapter Summary --- p.95Chapter 5 --- Enhancement of BAM --- p.97Chapter 5.1 --- Background --- p.97Chapter 5.2 --- Review on Modifications of BAM --- p.101Chapter 5.2.1 --- Change of the encoding method --- p.101Chapter 5.2.2 --- Change of the topology --- p.105Chapter 5.3 --- Householder Encoding Algorithm --- p.107Chapter 5.3.1 --- Construction from Householder Transforms --- p.107Chapter 5.3.2 --- Construction from iterative method --- p.109Chapter 5.3.3 --- Remarks on HCA --- p.111Chapter 5.4 --- Enhanced Householder Encoding Algorithm --- p.112Chapter 5.4.1 --- Construction of EHCA --- p.112Chapter 5.4.2 --- Remarks on EHCA --- p.114Chapter 5.5 --- Bidirectional Learning --- p.115Chapter 5.5.1 --- Construction of BL --- p.115Chapter 5.5.2 --- The Convergence of BL and the memory capacity of BL --- p.116Chapter 5.5.3 --- Remarks on BL --- p.120Chapter 5.6 --- Adaptive Ho-Kashyap Bidirectional Learning --- p.121Chapter 5.6.1 --- Construction of AHKBL --- p.121Chapter 5.6.2 --- Convergent Conditions for AHKBL --- p.124Chapter 5.6.3 --- Remarks on AHKBL --- p.125Chapter 5.7 --- Computer Simulations --- p.126Chapter 5.7.1 --- Memory Capacity --- p.126Chapter 5.7.2 --- Error Correction Capability --- p.130Chapter 5.7.3 --- Learning Speed --- p.157Chapter 5.8 --- Chapter Summary --- p.158Chapter 6 --- BAM under Forgetting Learning --- p.160Chapter 6.1 --- Introduction --- p.160Chapter 6.2 --- Properties of Forgetting Learning --- p.162Chapter 6.3 --- Computer Simulations --- p.168Chapter 6.4 --- Chapter Summary --- p.168Chapter II --- Kohonen Map: Applications in Data compression and Communications --- p.170Chapter 7 --- Introduction to Vector Quantization and Kohonen Map --- p.171Chapter 7.1 --- Background on Vector quantization --- p.171Chapter 7.2 --- Introduction to LBG algorithm --- p.173Chapter 7.3 --- Introduction to Kohonen Map --- p.174Chapter 7.4 --- Chapter Summary --- p.179Chapter 8 --- Applications of Kohonen Map in Data Compression and Communi- cations --- p.181Chapter 8.1 --- Use Kohonen Map to design Trellis Coded Vector Quantizer --- p.182Chapter 8.1.1 --- Trellis Coded Vector Quantizer --- p.182Chapter 8.1.2 --- Trellis Coded Kohonen Map --- p.188Chapter 8.1.3 --- Computer Simulations --- p.191Chapter 8.2 --- Kohonen MapiCombined Vector Quantization and Modulation --- p.195Chapter 8.2.1 --- Impulsive Noise in the received data --- p.195Chapter 8.2.2 --- Combined Kohonen Map and Modulation --- p.198Chapter 8.2.3 --- Computer Simulations --- p.200Chapter 8.3 --- Error Control Scheme for the Transmission of Vector Quantized Data --- p.213Chapter 8.3.1 --- Motivation and Background --- p.214Chapter 8.3.2 --- Trellis Coded Modulation --- p.216Chapter 8.3.3 --- "Combined Vector Quantization, Error Control, and Modulation" --- p.220Chapter 8.3.4 --- Computer Simulations --- p.223Chapter 8.4 --- Chapter Summary --- p.226Chapter 9 --- Conclusion --- p.232Bibliography --- p.23

On Bit-interleaved Coded Modulation with QAM Constellations

Bit-interleaved coded modulation (BICM) is a flexible modulation/coding scheme which allows the designer to choose a modulation constellation independently of the coding rate. This is because the output of the channel encoder and the input to the modulator are separated by a bit-level interleaver. In order to increase spectral efficiency, BICM can be combined with high-order modulation schemes such as quadrature amplitude modulation (QAM) or phase shift keying. BICM is particularly well suited for fading channels, and it only introduces a small penalty in terms of channel capacity when compared to the coded modulation capacity for both additive white Gaussian noise (AWGN) and fading channels. Additionally, if the so-called BICM with iterative decoding (BICM-ID) is used, the demapper and decoder iteratively exchange information, improving the system performance. <p>At the receiver's side of BICM, the reliability metrics are calculated for the coded bits under the form of logarithmic likelihood ratios, or simply L-values. These metrics are then deinterleaved and further used by the soft-input channel decoder. This thesis deals with the probabilistic characterization of the L-values calculated by the demapper when BICM is used in conjunction with high order QAM schemes. Three contributions are included in this thesis.</p> <p>In <b>Paper A</b> the issue of the probabilistic modelling of the extrinsic L-values for BICM-ID is addressed. Starting with a simple piece-wise linear model of the L-values obtained via the max-log approximation, expressions for the probability density functions (PDFs) for Gray-mapped 16-QAM are found. The developed analytical expressions are then used to efficiently compute the so-called extrinsic information transfer functions of the demapper, and they are also compared with the histograms of the L-values obtained through numerical simulations.</p> <p>In <b>Paper B</b> closed-form expressions for the PDFs of the L-values in BICM with Gray mapped QAM constellations are developed. Based on these expressions, two simple Gaussian mixture approximations that are analytically tractable are also proposed. The developments are used to efficiently calculate the BICM channel capacity and to develop bounds on the coded bit-error rate when a convolutional code is used. The coded performance of an hybrid automatic repeat request based on constellation rearrangement is also evaluated.</p> <p>In <b>Paper C</b> closed-form expressions for the PDFs of the L-values in BICM transmissions with Gray-mapped QAM constellations over fully-interleaved fading channels are derived. The results are particularized for a Rayleigh fading channel, however, developments for the general case of a Nakagami-$m$ case are also included. Using the developed expressions, the performance of BICM transmissions using convolutional and turbo codes is efficiently evaluated. The BICM channel capacity for different fading channels and constellation sizes is also calculated.</p

Irregular Variable Length Coding

In this thesis, we introduce Irregular Variable Length Coding (IrVLC) and investigate its applications, characteristics and performance in the context of digital multimedia broadcast telecommunications. During IrVLC encoding, the multimedia signal is represented using a sequence of concatenated binary codewords. These are selected from a codebook, comprising a number of codewords, which, in turn, comprise various numbers of bits. However, during IrVLC encoding, the multimedia signal is decomposed into particular fractions, each of which is represented using a different codebook. This is in contrast to regular Variable Length Coding (VLC), in which the entire multimedia signal is encoded using the same codebook. The application of IrVLCs to joint source and channel coding is investigated in the context of a video transmission scheme. Our novel video codec represents the video signal using tessellations of Variable-Dimension Vector Quantisation (VDVQ) tiles. These are selected from a codebook, comprising a number of tiles having various dimensions. The selected tessellation of VDVQ tiles is signalled using a corresponding sequence of concatenated codewords from a Variable Length Error Correction (VLEC) codebook. This VLEC codebook represents a specific joint source and channel coding case of VLCs, which facilitates both compression and error correction. However, during video encoding, only particular combinations of the VDVQ tiles will perfectly tessellate, owing to their various dimensions. As a result, only particular sub-sets of the VDVQ codebook and, hence, of the VLEC codebook may be employed to convey particular fractions of the video signal. Therefore, our novel video codec can be said to employ IrVLCs. The employment of IrVLCs to facilitate Unequal Error Protection (UEP) is also demonstrated. This may be applied when various fractions of the source signal have different error sensitivities, as is typical in audio, speech, image and video signals, for example. Here, different VLEC codebooks having appropriately selected error correction capabilities may be employed to encode the particular fractions of the source signal. This approach may be expected to yield a higher reconstruction quality than equal protection in cases where the various fractions of the source signal have different error sensitivities. Finally, this thesis investigates the application of IrVLCs to near-capacity operation using EXtrinsic Information Transfer (EXIT) chart analysis. Here, a number of component VLEC codebooks having different inverted EXIT functions are employed to encode particular fractions of the source symbol frame. We show that the composite inverted IrVLC EXIT function may be obtained as a weighted average of the inverted component VLC EXIT functions. Additionally, EXIT chart matching is employed to shape the inverted IrVLC EXIT function to match the EXIT function of a serially concatenated inner channel code, creating a narrow but still open EXIT chart tunnel. In this way, iterative decoding convergence to an infinitesimally low probability of error is facilitated at near-capacity channel SNRs

Performance evaluation of communication systems with transmit diversity

Transmit diversity is a key technique to combat fading with multiple transmit antennae for next-generation wireless communication systems. Space-time block code (STBC) is a main component of this technique. This dissertation consists of four parts: the first three discuss performance evaluation of STBCs in various circumstances, the fourth outlines a novel differential scheme with full transmit diversity. In the first part, closed-form expressions for the bit error rate (BER) are derived for STBC based on Alamouti\u27s scheme and utilizing M-ary phase shift keying (MPSK) modulation. The analysis is carried out for a slow, flat Rayleigh fading channel with coherent detection and with non-coherent differential encoding/decoding. The BER expression for coherent detection is exact. But for differential detection it is an approximation appropriate for a high signal-to-noise ratio. Numerical results are provided for analysis and simulations for BPSK and QPSK modulations. A signal-to-noise ratio loss of approximately 3 dB always occurs with conventional differential detection for STBC compared to coherent detection. In the second part of this dissertation, a multiple-symbol differential detection (MSDD) technique is proposed for MPSK STBCs, which greatly reduces this performance loss by extending the observation interval for decoding. The technique uses maximum likelihood block sequence detection instead of traditional block-by-block detection and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric for an observation interval of N blocks is derived. It is shown that for a moderate number of blocks, MSDD provides more than 1.0 dB performance improvement corresponding to conventional differential detection. In addition, a closed-form pairwise error probability for differential BPSI( STBC is derived for an observation interval of N blocks, and an approximate BER is obtained to evaluate the performance. In the third part, the BER performance of STBC over a spatio-temporal correlated channel with coherent and noncoherent detection is illustrated, where a general space-time correlation model is utilized. The simulation results demonstrate that spatial correlation negatively effects the performance of the STBC scheme with differential detection but temporal correlation positively impacts it. However, with coherent detection, spatial correlation still has negative effect on the performance but temporal correlation has no impact on it. In the final part of this dissertation, a differential detection scheme for DS/CDMA MIMO link is presented. The transmission provides for full transmit and receive diversity gain using a simple detection scheme, which is a natural extension of differential detection combined with an orthogonal transmit diversity (OTD) approach. A capacity analysis for this scheme is illustrated