Computational Complexity of Iterative Processes

The theory of optimal algorithmic processes is part of computational complexity. This paper deals with analytic computational complexity. The relation between the goodness of an iteration algorithm and its new function evaluation and memory requirements are analyzed. A new conjecture is stated

An Efficient Water-Filling Algorithm for Power Allocation in OFDM-Based Cognitive Radio Systems

In this paper, we present a new water-filling algorithm for power allocation in Orthogonal Frequency Division Multiplexing (OFDM) – based cognitive radio systems. The conventional water-filling algorithm cannot be directly employed for power allocation in a cognitive radio system, because there are more power constraints in the cognitive radio power allocation problem than in the classic OFDM system. In this paper, a novel algorithm based on iterative water-filling is presented to overcome such limitations. However, the computational complexity in iterative water-filling is very high. Thus, we explore features of the water-filling algorithm and propose a low-complexity algorithm using power-increment or power-decrement water-filling processes. Simulation results show that our proposed algorithms can achieve the optimal power allocation performance in less time than the iterative water-filling algorithms

Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers

In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system, and the design of data structures to take advantage of serial, coarse grain parallel and massively parallel computer architectures, are considered in detail. We put forward arguments as to why integration of the system within a sparse simplex solver is important and outline how the system is designed to achieve this integration

Irregular Generic Detection Aided Iterative Downlink SDMA Systems

Abstract—When an iterative-decoding aided system is configured to operate at a near-capacity performance, an excessive complexity may be imposed by the iterative process. In this paper, we propose the novel framework of generic detection, which invokes appropriately amalgamated multiple detectors. Hence the proposed Irregular Generic Detection (IrGD) algorithm may reduce the complexity of iterative detectors. We show in the context of an iterative Down-Link (DL) Space Division Multiple Access (SDMA) system that the proposed IrGD may indeed reduce the complexity of the iterative receiver. The IrGD aided DL-SDMA system detects the appropriate fractions of the received bitstream with the aid of different detectors. This allows us to match the Extrinsic Information Transfer (EXIT) curve of the detector to that of the channel decoder, hence facilitating a near-capacity operation, which reducing the detection complexity by about 28% compared to a powerful near-Maximum-Likelihood (ML) sphere detector benchmark system