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.

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.

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-Lovász-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.

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.