Coding for Relay Networks with Parallel Gaussian Channels

A wireless relay network consists of multiple source nodes, multiple destination nodes, and possibly many relay nodes in between to facilitate its transmission. It is clear that the performance of such networks highly depends on information for- warding strategies adopted at the relay nodes. This dissertation studies a particular information forwarding strategy called compute-and-forward. Compute-and-forward is a novel paradigm that tries to incorporate the idea of network coding within the physical layer and hence is often referred to as physical layer network coding. The main idea is to exploit the superposition nature of the wireless medium to directly compute or decode functions of transmitted signals at intermediate relays in a net- work. Thus, the coding performed at the physical layer serves the purpose of error correction as well as permits recovery of functions of transmitted signals. For the bidirectional relaying problem with Gaussian channels, it has been shown by Wilson et al. and Nam et al. that the compute-and-forward paradigm is asymptotically optimal and achieves the capacity region to within 1 bit; however, similar results beyond the memoryless case are still lacking. This is mainly because channels with memory would destroy the lattice structure that is most crucial for the compute-and-forward paradigm. Hence, how to extend compute-and-forward to such channels has been a challenging issue. This motivates this study of the extension of compute-and-forward to channels with memory, such as inter-symbol interference. The bidirectional relaying problem with parallel Gaussian channels is also studied, which is a relevant model for the Gaussian bidirectional channel with inter-symbol interference and that with multiple-input multiple-output channels. Motivated by the recent success of linear finite-field deterministic model, we first investigate the corresponding deterministic parallel bidirectional relay channel and fully characterize its capacity region. Two compute-and-forward schemes are then proposed for the Gaussian model and the capacity region is approximately characterized to within a constant gap. The design of coding schemes for the compute-and-forward paradigm with low decoding complexity is then considered. Based on the separation-based framework proposed previously by Tunali et al., this study proposes a family of constellations that are suitable for the compute-and-forward paradigm. Moreover, by using Chinese remainder theorem, it is shown that the proposed constellations are isomorphic to product fields and therefore can be put into a multilevel coding framework. This study then proposes multilevel coding for the proposed constellations and uses multistage decoding to further reduce decoding complexity

Successive Interference Cancellation for Bandlimited Channels with Direct Detection

Oversampling increases information rates for bandlimited channels with direct detection, but joint detection and decoding (JDD) is often too complex to implement. Two receiver structures are studied to reduce complexity: separate detection and decoding (SDD) and successive interference cancellation (SIC) with multi-level coding. For bipolar modulation, frequency-domain raised-cosine pulse shaping, and fiber-optic channels with chromatic dispersion, SIC achieves rates close to those of JDD, thereby attaining significant energy gains over SDD and classic intensity modulation. Gibbs sampling further reduces the detector complexity and achieves rates close to those of the forward-backward algorithm at low to intermediate signal-to-noise ratio (SNR) but stalls at high SNR. Simulations with polar codes and higher-order modulation confirm the predicted rate and energy gains.Comment: Submitted to IEEE Journal of Lightwave Technology on December 15, 2022; Resubmitted to IEEE Transactions on Communications on September 9, 2023

Write Channel Model for Bit-Patterned Media Recording

We propose a new write channel model for bit-patterned media recording that reflects the data dependence of write synchronization errors. It is shown that this model accommodates both substitution-like errors and insertion-deletion errors whose statistics are determined by an underlying channel state process. We study information theoretic properties of the write channel model, including the capacity, symmetric information rate, Markov-1 rate and the zero-error capacity.Comment: 11 pages, 12 figures, journa

A Framework for Low-Complexity Iterative Interference Cancellation in Communication Systems

Thesis Supervisor: Gregory W. Wornell Title: ProfessorCommunication over interference channels poses challenges not present for the more traditional additive white Gaussian noise (AWGN) channels. In order to approach the information limits of an interference channel, interference mitigation techniques need to be integrated with channel coding and decoding techniques. This thesis develops such practical schemes when the transmitter has no knowledge of the channel. The interference channel model we use is described by r = Hx + w, where r is the received vector, H is an interference matrix, x is the transmitted vector of data symbols chosen from a finite set, and w is a noise vector. The objective at the receiver is to detect the most likely vector x that was transmitted based on knowledge of r, H, and the statistics of w. Communication contexts in which this general integer programming problem appears include the equalization of intersymbol interference (ISI) channels, the cancellation of multiple-access interference (MAI) in code-division multiple-access (CDMA) systems, and the decoding of multiple-input multiple-output (MIMO) systems in fading environments. We begin by introducing mode-interleaved precoding, a transmitter precoding technique that conditions an interference channel so that the pairwise error probability of any two transmit vectors becomes asymptotically equal to the pairwise error probability of the same vectors over an AWGN channel at the same signal-to-noise ratio (SNR). While mode-interleaved precoding dramatically increases the complexity of exact ML detection, we develop iterated-decision detection to mitigate this complexity problem. Iterateddecision detectors use optimized multipass algorithms to successively cancel interference from r and generate symbol decisions whose reliability increases monotonically with each iteration. When used in uncoded systems with mode-interleaved precoding, iterated-decision detectors asymptotically achieve the performance ofML detection (and thus the interferencefree lower bound) with considerably lower complexity. We interpret these detectors as low-complexity approximations to message-passing algorithms. The integration of iterated-decision detectors into communication systems with coding is also developed to approach information rates close to theoretical limits. We present joint detection and decoding algorithms based on the iterated-decision detector with modeinterleaved precoding, and also develop analytic tools to predict the behavior of such systems. We discuss the use of binary codes for channels that support low information rates, and multilevel codes and lattice codes for channels that support higher information ratesHewlett-Packard under the MIT/HPAlliance, the National Science Foundation, the Semiconductor Research Corporation, Texas Instruments through the Leadership Universities Program, and the Natural Sciences and Engineering Research Council of Canada (NSERC) Postgraduate Scholarship Program

A framework for low-complexity iterative interference cancellation in communication systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 211-215).Communication over interference channels poses challenges not present for the more traditional additive white Gaussian noise (AWGN) channels. In order to approach the information limits of an interference channel, interference mitigation techniques need to be integrated with channel coding and decoding techniques. This thesis develops such practical schemes when the transmitter has no knowledge of the channel. The interference channel model we use is described by r = Hx + w, where r is the received vector, H is an interference matrix, x is the transmitted vector of data symbols chosen from a finite set, and w is a noise vector. The objective at the receiver is to detect the most likely vector x that was transmitted based on knowledge of r, H, and the statistics of w. Communication contexts in which this general integer programming problem appears include the equalization of intersymbol interference (ISI) channels, the cancellation of multiple-access interference (MAI) in code-division multiple-access (CDMA) systems, and the decoding of multiple-input multiple-output (MIMO) systems in fading environments. We begin by introducing mode-interleaved precoding, a transmitter preceding technique that conditions an interference channel so that the pairwise error probability of any two transmit vectors becomes asymptotically equal to the pairwise error probability of the same vectors over an AWGN channel at the same signal-to-noise ratio (SNR). While mode-interleaved precoding dramatically increases the complexity of exact ML detection, we develop iterated-decision detection to mitigate this complexity problem. Iterated-decision detectors use optimized multipass algorithms to successively cancel interference from r and generate symbol(cont.) decisions whose reliability increases monotonically with each iteration. When used in uncoded systems with mode-interleaved preceding, iterated-decision detectors asyrmptotically achieve the performance of ML detection (and thus the interference-free lower bound) with considerably lower complexity. We interpret these detectors as low-complexity approximations to message-passing algorithms. The integration of iterated-decision detectors into communication systems with coding is also developed to approach information rates close to theoretical limits. We present joint detection and decoding algorithms based on the iterated-decision detector with mode-interleaved precoding, and also develop analytic tools to predict the behavior of such systems. We discuss the use of binary codes for channels that support low information rates, and multilevel codes and lattice codes for channels that support higher information rates.by Albert M. Chan.Ph.D

Optimal transmit filters for constrained complexity channel shortening detectors

We consider intersymbol interference channels with reduced-complexity, mutual information optimized, channel shortening detectors. For a given channel and receiver complexity, we optimize the transmit filter to use. The cost function we consider is the (Shannon) achievable information rate of the entire transceiver system. By functional analysis, we can establish a general form of the optimal transmit filter, which can then be optimized by standard numerical methods. As a side result, we also obtain an insight of the behaviour of the standard waterfilling algorithm for intersymbol interference channels

Turbo Decoding and Detection for Wireless Applications

A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon’s visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon’s capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted

Coding for Relay Networks with Parallel Gaussian Channels

A wireless relay network consists of multiple source nodes, multiple destination nodes, and possibly many relay nodes in between to facilitate its transmission. It is clear that the performance of such networks highly depends on information for- warding strategies adopted at the relay nodes. This dissertation studies a particular information forwarding strategy called compute-and-forward. Compute-and-forward is a novel paradigm that tries to incorporate the idea of network coding within the physical layer and hence is often referred to as physical layer network coding. The main idea is to exploit the superposition nature of the wireless medium to directly compute or decode functions of transmitted signals at intermediate relays in a net- work. Thus, the coding performed at the physical layer serves the purpose of error correction as well as permits recovery of functions of transmitted signals. For the bidirectional relaying problem with Gaussian channels, it has been shown by Wilson et al. and Nam et al. that the compute-and-forward paradigm is asymptotically optimal and achieves the capacity region to within 1 bit; however, similar results beyond the memoryless case are still lacking. This is mainly because channels with memory would destroy the lattice structure that is most crucial for the compute-and-forward paradigm. Hence, how to extend compute-and-forward to such channels has been a challenging issue. This motivates this study of the extension of compute-and-forward to channels with memory, such as inter-symbol interference. The bidirectional relaying problem with parallel Gaussian channels is also studied, which is a relevant model for the Gaussian bidirectional channel with inter-symbol interference and that with multiple-input multiple-output channels. Motivated by the recent success of linear finite-field deterministic model, we first investigate the corresponding deterministic parallel bidirectional relay channel and fully characterize its capacity region. Two compute-and-forward schemes are then proposed for the Gaussian model and the capacity region is approximately characterized to within a constant gap. The design of coding schemes for the compute-and-forward paradigm with low decoding complexity is then considered. Based on the separation-based framework proposed previously by Tunali et al., this study proposes a family of constellations that are suitable for the compute-and-forward paradigm. Moreover, by using Chinese remainder theorem, it is shown that the proposed constellations are isomorphic to product fields and therefore can be put into a multilevel coding framework. This study then proposes multilevel coding for the proposed constellations and uses multistage decoding to further reduce decoding complexity