36 research outputs found
Soft-decision equalization techniques for frequency selective MIMO channels
Multi-input multi-output (MIMO) technology is an emerging solution for high data rate wireless communications. We develop soft-decision based equalization techniques for frequency selective MIMO channels in the quest for low-complexity equalizers with BER performance competitive to that of ML sequence detection.
We first propose soft decision equalization (SDE), and demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered, and linear in the signal constellation size. Building upon the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems.
Motivated by the need for low-complexity receiver processing, we further present an alternative low-complexity soft-decision equalization approach for frequency selective MIMO communication systems. With the help of iterative processing, two detection and estimation schemes based on second-order statistics are harmoniously put together to yield a two-part receiver structure: local multiuser detection (MUD) using soft-decision Probabilistic Data Association (PDA) detection, and dynamic noise-interference tracking using Kalman filtering. The proposed Kalman-PDA detector performs local MUD within a sub-block of the received data instead of over the entire data set, to reduce the computational load. At the same time, all the inter-ference affecting the local sub-block, including both multiple access and inter-symbol interference, is properly modeled as the state vector of a linear system, and dynamically tracked by Kalman filtering. Two types of Kalman filters are designed, both of which are able to track an finite impulse response (FIR) MIMO channel of any memory length. The overall algorithms enjoy low complexity that is only polynomial in the number of information-bearing bits to be detected, regardless of the data block size.
Furthermore, we introduce two optional performance-enhancing techniques: cross- layer automatic repeat request (ARQ) for uncoded systems and code-aided method for coded systems. We take Kalman-PDA as an example, and show via simulations that both techniques can render error performance that is better than Kalman-PDA alone and competitive to sphere decoding.
At last, we consider the case that channel state information (CSI) is not perfectly known to the receiver, and present an iterative channel estimation algorithm. Simulations show that the performance of SDE with channel estimation approaches that of SDE with perfect CSI
Advanced Coding Techniques with Applications to Storage Systems
This dissertation considers several coding techniques based on Reed-Solomon (RS) and low-density parity-check (LDPC) codes. These two prominent families of error-correcting codes have attracted a great amount of interest from both theorists and practitioners and have been applied in many communication scenarios. In particular, data storage systems have greatly benefited from these codes in improving the reliability of the storage media.
The first part of this dissertation presents a unified framework based on rate-distortion (RD) theory to analyze and optimize multiple decoding trials of RS codes. Finding the best set of candidate decoding patterns is shown to be equivalent to a covering problem which can be solved asymptotically by RD theory. The proposed approach helps understand the asymptotic performance-versus-complexity trade-off of these multiple-attempt decoding algorithms and can be applied to a wide range of decoders and error models.
In the second part, we consider spatially-coupled (SC) codes, or terminated LDPC convolutional codes, over intersymbol-interference (ISI) channels under joint iterative decoding. We empirically observe the phenomenon of threshold saturation whereby the belief-propagation (BP) threshold of the SC ensemble is improved to the maximum a posteriori (MAP) threshold of the underlying ensemble. More specifically, we derive a generalized extrinsic information transfer (GEXIT) curve for the joint decoder that naturally obeys the area theorem and estimate the MAP and BP thresholds. We also conjecture that SC codes due to threshold saturation can universally approach the symmetric information rate of ISI channels.
In the third part, a similar analysis is used to analyze the MAP thresholds of LDPC codes for several multiuser systems, namely a noisy Slepian-Wolf problem and a multiple access channel with erasures. We provide rigorous analysis and derive upper bounds on the MAP thresholds which are shown to be tight in some cases. This analysis is a first step towards proving threshold saturation for these systems which would imply SC codes with joint BP decoding can universally approach the entire capacity region of the corresponding systems
Soft-Decoding-Based Strategies for Relay and Interference Channels: Analysis and Achievable Rates Using LDPC Codes
We provide a rigorous mathematical analysis of two communication strategies:
soft decode-and-forward (soft-DF) for relay channels, and soft partial
interference-cancelation (soft-IC) for interference channels. Both strategies
involve soft estimation, which assists the decoding process. We consider LDPC
codes, not because of their practical benefits, but because of their analytic
tractability, which enables an asymptotic analysis similar to random coding
methods of information theory. Unlike some works on the closely-related
demodulate-and-forward, we assume non-memoryless, code-structure-aware
estimation. With soft-DF, we develop {\it simultaneous density evolution} to
bound the decoding error probability at the destination. This result applies to
erasure relay channels. In one variant of soft-DF, the relay applies Wyner-Ziv
coding to enhance its communication with the destination, borrowing from
compress-and-forward. To analyze soft-IC, we adapt existing techniques for
iterative multiuser detection, and focus on binary-input additive white
Gaussian noise (BIAWGN) interference channels. We prove that optimal
point-to-point codes are unsuitable for soft-IC, as well as for all strategies
that apply partial decoding to improve upon single-user detection (SUD) and
multiuser detection (MUD), including Han-Kobayashi (HK).Comment: Accepted to the IEEE Transactions on Information Theory. This is a
major revision of a paper originally submitted in August 201
Spatially Coupled LDPC Codes Constructed from Protographs
In this paper, we construct protograph-based spatially coupled low-density
parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or
uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L,
we obtain a flexible family of code ensembles with varying rates and frame
lengths that can share the same encoding and decoding architecture for
arbitrary L. We demonstrate that the resulting codes combine the best features
of optimized irregular and regular codes in one design: capacity approaching
iterative belief propagation (BP) decoding thresholds and linear growth of
minimum distance with block length. In particular, we show that, for
sufficiently large L, the BP thresholds on both the binary erasure channel
(BEC) and the binary-input additive white Gaussian noise channel (AWGNC)
saturate to a particular value significantly better than the BP decoding
threshold and numerically indistinguishable from the optimal maximum
a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all
variable nodes in the coupled chain have degree greater than two,
asymptotically the error probability converges at least doubly exponentially
with decoding iterations and we obtain sequences of asymptotically good LDPC
codes with fast convergence rates and BP thresholds close to the Shannon limit.
Further, the gap to capacity decreases as the density of the graph increases,
opening up a new way to construct capacity achieving codes on memoryless
binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor
A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions
Low-density parity-check (LDPC) convolutional codes (or spatially-coupled
codes) were recently shown to approach capacity on the binary erasure channel
(BEC) and binary-input memoryless symmetric channels. The mechanism behind this
spectacular performance is now called threshold saturation via spatial
coupling. This new phenomenon is characterized by the belief-propagation
threshold of the spatially-coupled ensemble increasing to an intrinsic noise
threshold defined by the uncoupled system. In this paper, we present a simple
proof of threshold saturation that applies to a wide class of coupled scalar
recursions. Our approach is based on constructing potential functions for both
the coupled and uncoupled recursions. Our results actually show that the fixed
point of the coupled recursion is essentially determined by the minimum of the
uncoupled potential function and we refer to this phenomenon as Maxwell
saturation. A variety of examples are considered including the
density-evolution equations for: irregular LDPC codes on the BEC, irregular
low-density generator matrix codes on the BEC, a class of generalized LDPC
codes with BCH component codes, the joint iterative decoding of LDPC codes on
intersymbol-interference channels with erasure noise, and the compressed
sensing of random vectors with i.i.d. components.Comment: This article is an extended journal version of arXiv:1204.5703 and
has now been accepted to the IEEE Transactions on Information Theory. This
version adds additional explanation for some details and also corrects a
number of small typo
UNDERWATER COMMUNICATIONS WITH ACOUSTIC STEGANOGRAPHY: RECOVERY ANALYSIS AND MODELING
In the modern warfare environment, communication is a cornerstone of combat competence. However, the increasing threat of communications-denied environments highlights the need for communications systems with low probability of intercept and detection. This is doubly true in the subsurface environment, where communications and sonar systems can reveal the tactical location of platforms and capabilities, subverting their covert mission set. A steganographic communication scheme that leverages existing technologies and unexpected data carriers is a feasible means of increasing assurance of communications, even in denied environments. This research works toward a covert communication system by determining and comparing novel symbol recovery schemes to extract data from a signal transmitted under a steganographic technique and interfered with by a simulated underwater acoustic channel. We apply techniques for reliably extracting imperceptible information from unremarkable acoustic events robust to the variability of the hostile operating environment. The system is evaluated based on performance metrics, such as transmission rate and bit error rate, and we show that our scheme is sufficient to conduct covert communications through acoustic transmissions, though we do not solve the problems of synchronization or equalization.Lieutenant, United States NavyApproved for public release. Distribution is unlimited
The Error Probability of Generalized Perfect Codes via the Meta-Converse
We introduce a definition of perfect and quasiperfect codes for discrete symmetric channels based on the
packing and covering properties of generalized spheres whose
shape is tilted using an auxiliary probability measure. This
notion generalizes previous definitions of perfect and quasiperfect codes and encompasses maximum distance separable
codes. The error probability of these codes, whenever they exist,
is shown to coincide with the estimate provided by the metaconverse lower bound. We illustrate how the proposed definition
naturally extends to cover almost-lossless source-channel coding
and lossy compression.ER
Universality for Multi-terminal Problems via Spatial Coupling
Consider the problem of designing capacity-achieving codes for multi-terminal communication scenarios. For point-to-point communication problems, one can optimize a single code to approach capacity, but for multi-terminal problems this translates to optimizing a single code to perform well over the entire region of channel parameters. A coding scheme is called universal if it allows reliable communication over the entire achievable region promised by information theory.
It was recently shown that terminated low-density parity-check convolutional codes (also known as spatially-coupled low-density parity-check ensembles) have belief-propagation thresholds that approach their maximum a-posteriori thresholds. This phenomenon, called "threshold saturation via spatial-coupling," was proven for binary erasure channels and then for binary memoryless symmetric channels. This approach provides us with a new paradigm for constructing capacity approaching codes. It was also conjectured that the principle of spatial coupling is very general and that the phenomenon of threshold saturation applies to a very broad class of graphical models.
In this work, we consider a noisy Slepian-Wolf problem (with erasure and binary symmetric channel correlation models) and the binary-input Gaussian multiple access channel, which deal with correlation between sources and interference at the receiver respectively. We derive an area theorem for the joint decoder and empirically show that threshold saturation occurs for these multi-user scenarios. We also show that the outer bound derived using the area theorem is tight for the erasure Slepian-Wolf problem and that this bound is universal for regular LDPC codes with large left degrees. As a result, we demonstrate near-universal performance for these problems using spatially-coupled coding systems
Orthogonal Multiple Access with Correlated Sources: Feasible Region and Pragmatic Schemes
In this paper, we consider orthogonal multiple access coding schemes, where
correlated sources are encoded in a distributed fashion and transmitted,
through additive white Gaussian noise (AWGN) channels, to an access point (AP).
At the AP, component decoders, associated with the source encoders, iteratively
exchange soft information by taking into account the source correlation. The
first goal of this paper is to investigate the ultimate achievable performance
limits in terms of a multi-dimensional feasible region in the space of channel
parameters, deriving insights on the impact of the number of sources. The
second goal is the design of pragmatic schemes, where the sources use
"off-the-shelf" channel codes. In order to analyze the performance of given
coding schemes, we propose an extrinsic information transfer (EXIT)-based
approach, which allows to determine the corresponding multi-dimensional
feasible regions. On the basis of the proposed analytical framework, the
performance of pragmatic coded schemes, based on serially concatenated
convolutional codes (SCCCs), is discussed