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Recent work in [1]-[3] quantified, in the form of a complexity exponent, the computational resources required for ML and lattice sphere decoding to achieve a certain diversity-multiplexing performance. For a specific family of layered lattice designs and a specific set of decoding orderings, this complexity was shown to be an exponential function in the number of codeword bits and was shown to meet a universal upper bound on complexity exponents. The same results raised the question of whether complexity reductions away from the universal upper bound are feasible, for example, with a proper choice of decoder (ML vs lattice), or with a proper choice of lattice codes and decoding ordering policies. The current work addresses this question by first showing that for almost any full-rate DMT optimal lattice code, there exists no decoding ordering policy that can reduce the complexity exponent of ML or lattice based sphere decoding away from the universal upper bound, i.e., that a randomly picked lattice code (randomly and uniformly drawn from an ensemble of DMT optimal lattice designs) will almost surely be such that no decoding ordering policy can provide exponential complexity reductions away from the universal upper bound. As a byproduct of this, the current work proves the fact that ML and (MMSE-preprocessed) lattice decoding share the same complexity exponent for a very broad setting, which now includes almost any DMT optimal code (again randomly drawn) and all decoding order policies. Under a basic richness of codes assumption, this is in fact further extended to hold, with probability one, over all full-rate codes. Under the same assumption, the result allows for a meaningful rate-reliability-complexity tradeoff that holds, almost surely in the random choice of the full-rate lattice design and which holds irrespective of the decoding ordering policy. This tradeoff can be used to, for example, describe the optimal achievable diversity gain of ML or lattice sphere decoding in the presence of limited computational resources. {\textcopyright} 2013 IEEE.

Department of Electrical Engineering

World University root node

IEEE International Symposium on Information Theory - Proceedings

Rate-reliability-complexity tradeoff for ML and lattice decoding of full-rate codes

This study identifies the first lattice decoding solution that achieves, in the general outage-limited multiple-input multiple-output (MIMO) setting and in the high-rate and high-signal-to-noise ratio limit, both a vanishing gap to the error performance of the exact solution of regularized lattice decoding, as well as a computational complexity that is subexponential in the number of codeword bits and in the rate. The proposed solution employs Lenstra-Lenstra-Lov{\'{a}}sz-based lattice reduction (LR)-aided regularized (lattice) sphere decoding and proper timeout policies. These performance and complexity guarantees hold for most MIMO scenarios, most fading statistics, all channel dimensions and all full-rate lattice codes. In sharp contrast to the aforementioned very manageable complexity, the complexity of other standard preprocessed lattice decoding solutions is revealed here to be extremely high. Specifically, this study has quantified the complexity of regularized lattice (sphere) decoding and has proved that the computational resources required by this decoder to achieve a good rate-reliability performance are exponential in the lattice dimensionality and in the number of codeword bits and it in fact matches, in common scenarios, the complexity of ML-based sphere decoders. Through this sharp contrast, this study was able to, for the first time, rigorously demonstrate and quantify the pivotal role of LR as a special complexity reducing ingredient. {\textcopyright} 1963-2012 IEEE.

Fulltext

IEEE Transactions on Information Theory

Achieving a vanishing SNR gap to exact lattice decoding at a subexponential complexity

The work analyzes the computational-complexity savings that a single bit of feedback can provide in the computationally intense setting of non-ergodic MIMO communications. Specifically we derive upper bounds on the feedback-aided complexity exponent required for the broad families of ML-based and lattice based decoders to achieve the optimal diversity-multiplexing behavior. The bounds reveal a complexity that is reduced from being exponential in the number of codeword bits, to being at most exponential in the rate. Finally the derived savings are met by practically constructed ARQ schemes, as well as simple lattice designs, decoders and computation-halting policies. {\textcopyright} 2012 IEEE.

Feedback-aided complexity reductions in ML and lattice decoding

T{\'{e}}l{\'{e}}com ParisTech

Rate-Reliability-Complexity limits in ML and lattice based decoding for MIMO, multiuser and cooperative communications

Proc. Int. Zurich Seminar on Communications (IZS)

Complexity analysis for ML-based sphere decoder achieving a vanishing performance-gap to brute force ML decoding,”

This work establishes the diversity-multiplexing tradeoff (DMT) of the four-phase decode-and-forward (DF) protocol in the half-duplex, non-separated two-way relay channel. We consider a fading channel model where the source relay links are Rayleigh distributed but the direct link between sources is left more general as Nakagami-m distributed and investigate for any possible gains in the achievable DMT using four-phase hybrid broadcast (HBC) protocol, as compared to three-phase time-division broadcast (TDBC) protocol. For the statistically symmetric case of Rayleigh fading and asymmetric fading with more stable direct link (m > 1), the optimal DMT of the HBC protocol is computed and is shown to be achieved by a three-phase orthogonal variant, TDBC protocol. The operational meaning of this result is that the multiple access channel (MAC) phase of HBC protocol is not necessary to achieve optimal performance, this results in a simplification of the communication protocol. For less stable direct link (1/2 ≤ m < 1), the analysis establishes that the MAC phase of HBC protocol is necessary to achieve optimal DMT. {\textcopyright} 2011 IEEE.

IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC

Diversity-multiplexing tradeoff for the non-separated two-way relay DF channel

This work identifies the first lattice decoding solution that achieves, in the most general outage-limited MIMO setting and the high rate and high SNR limit, both a vanishing gap to the error-performance of the exact solution of regularized lattice decoding, as well as a computational complexity that is subexponential in the number of codeword bits as well as the rate. The proposed solution employs lattice reduction (LR)-aided regularized (lattice) sphere decoding and proper timeout policies. In light of the fact that, prior to this work, a vanishing gap was generally attributed only to full lattice searches that have exponential complexity, in conjunction with the fact that subexponential complexity was generally attributed to early-terminated (linear) solutions which have though a performance gap that can be up to exponential in dimension and/or rate, the work constitutes the first proof that subexponential complexity need not come at the cost of exponential reductions in lattice decoding error performance. Finally, these performance and complexity guarantees hold for the most general MIMO setting, for all reasonable fading statistics, all channel dimensions and all lattice codes. {\textcopyright} 2011 IEEE.

2011 49th Annual Allerton Conference on Communication, Control and Computing, Allerton 2011

Vanishing the gap to exact lattice search at a subexponential complexity: LR-aided regularized decoding

We consider the role of independent single antenna relays in allowing for interference cancellation and for multiplexing of uplink and downlink communications, in the presence of multiple interfering users. For a specific practical scenario of interest, we construct interference neutralization schemes that are simple, distributed and which encode over both space and time, to achieve performance improvements over basic TDMA schemes. These improvements are quantified in terms of the achievable degrees of freedom (DOF), where asymptotic analysis reveals that in specific cases, these simple techniques achieve optimal DOF performance. {\textcopyright} 2011 IEEE.

2011 Information Theory and Applications Workshop, ITA 2011 - Conference Proceedings

Interference neutralization for separated multiuser uplink-downlink with distributed relays

In the setting of computer vision algorithmic searches often aim to identify an object of interest inside large sets of images or videos. Towards reducing the often astronomical complexity of this search one can use pruning to filter out objects that are sufficiently distinct from the object of interest thus resulting in a pruning gain of an overall reduced search space. Motivated by practical computer vision based scenarios such as time-constrained human identification in biometric-based video surveillance systems we analyze the stochastic behavior of time-restricted search pruning over large and unstructured data sets which are furthermore random and varying and where in addition pruning itself is not fully reliable but is instead prone to errors. In this stochastic setting we apply the information theoretic method of types as well as information divergence techniques to explore the natural tradeoff that appears between pruning gain and reliability and proceed to study the typical and atypical gainreliability behavior giving insight on how often pruning might fail to substantially reduce the search space. The result as is applies to a plethora of computer vision based applications where efficiency and reliability are intertwined bottlenecks in the overall system performance and the simplicity of the obtained expressions allows for rigorous and insightful assessment of the pruning gain-reliability behavior in such applications as well as for intuition into designing general object recognition systems. {\textcopyright} 2011 IEEE.

Proceedings of the IEEE International Conference on Computer Vision

Search pruning in video surveillance systems: Efficiency-reliability tradeoff

The work establishes the asymptotic rate of decay for the probability of node isolation in bounded wireless sensor networks, in the high density regime. In this regime, the exposition reveals the role of the most isolated neighborhoods of the bounding region in exponentially increasing the average probability of isolation. The problem is treated for a large family of random spatial distributions of nodes, random shapes of node coverage areas and random topography of the network's bounding region. Different examples are presented to insightfully describe the detrimental effect of boundedness in network isolation. Finally we address different aspects relating to extremely isolating bounding regions and densities that vary exponentially in time. {\textcopyright} 2010 IEEE.