Joakim Jaldén

On the complexity of sphere decoding in digital communications

Sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications. In some cases, the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure. Another claim is that although worst-case complexity is exponential, the expected complexity of the algorithm is polynomial. Herein, we study the expected complexity where the problem size is defined to be the number of symbols jointly detected, and our main result is that the expected complexity is exponential for fixed signal-to-noise ratio (SNR), contrary to previous claims. The sphere radius, which is a parameter of the algorithm, must be chosen to ensure a nonvanishing probability of solving the detection problem. This causes the exponential complexity since the squared radius must grow linearly with problem size. The rate of linear increase is, however, dependent on the noise variance, and thus, the rate of the exponential function is strongly dependent on the SNR. Therefore sphere decoding can be efficient for some SNR and problems of moderate size, even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size.

Objective comparison of particle tracking methods

Particle tracking is of key importance for quantitative analysis of intracellular dynamic processes from time-lapse microscopy image data. Because manually detecting and following large numbers of individual particles is not feasible, automated computational methods have been developed for these tasks by many groups. Aiming to perform an objective comparison of methods, we gathered the community and organized an open competition in which participating teams applied their own methods independently to a commonly defined data set including diverse scenarios. Performance was assessed using commonly defined measures. Although no single method performed best across all scenarios, the results revealed clear differences between the various approaches, leading to notable practical conclusions for users and developers.

A Benchmark for Comparison of Cell Tracking Algorithms

Motivation: Automatic tracking of cells in multidimensional time-lapse fluorescence microscopy is an important task in many biomedical applications. A novel framework for objective evaluation of cell tracking algorithms has been established under the auspices of the IEEE International Symposium on Biomedical Imaging 2013 Cell Tracking Challenge. In this article, we present the logistics, datasets, methods and results of the challenge and lay down the principles for future uses of this benchmark. Results: The main contributions of the challenge include the creation of a comprehensive video dataset repository and the definition of objective measures for comparison and ranking of the algorithms. With this benchmark, six algorithms covering a variety of segmentation and tracking paradigms have been compared and ranked based on their performance on both synthetic and real datasets. Given the diversity of the datasets, we do not declare a single winner of the challenge. Instead, we present and discuss the results for each individual dataset separately. Availability and implementation: The challenge Web site (http://www.codesolorzano.com/celltrackingchallenge) provides access to the training and competition datasets, along with the ground truth of the training videos. It also provides access to Windows and Linux executable files of the evaluation software and most of the algorithms that competed in the challenge. Contact: codesolorzano@unav.es Supplementary information: Supplementary data are available at Bioinformatics online.

On using an adaptive neural network to predict lung tumor motion during respiration for radiotherapy applications

In this study we address the problem of predicting the position of a moving lung tumor during respiration on the basis of external breathing signals--a technique used for beam gating, tracking, and other dynamic motion management techniques in radiation therapy. We demonstrate the use of neural network filters to correlate tumor position with external surrogate markers while simultaneously predicting the motion ahead in time, for situations in which neither the breathing pattern nor the correlation between moving anatomical elements is constant in time. One pancreatic cancer patient and two lung cancer patients with mid/upper lobe tumors were fluoroscopically imaged to observe tumor motion synchronously with the movement of external chest markers during free breathing. The external marker position was provided as input to a feed-forward neural network that correlated the marker and tumor movement to predict the tumor position up to 800 ms in advance. The predicted tumor position was compared to its observed position to establish the accuracy with which the filter could dynamically track tumor motion under nonstationary conditions. These results were compared to simplified linear versions of the filter. The two lung cancer patients exhibited complex respiratory behavior in which the correlation between surrogate marker and tumor position changed with each cycle of breathing. By automatically and continuously adjusting its parameters to the observations, the neural network achieved better tracking accuracy than the fixed and adaptive linear filters. Variability and instability in human respiration complicate the task of predicting tumor position from surrogate breathing signals. Our results show that adaptive signal-processing filters can provide more accurate tumor position estimates than simpler stationary filters when presented with nonstationary breathing motion.

Worst- and average-case complexity of LLL lattice reduction in MIMO wireless systems

Lattice reduction by means of the LLL algorithm has been previously suggested as a powerful preprocessing tool that allows to improve the performance of suboptimal detectors and to reduce the complexity of optimal MIMO detectors. The complexity of the LLL algorithm is often cited as polynomial in the dimension of the lattice. In this paper we argue that this statement is not correct when made in the MIMO context. Specifically, we demonstrate that in typical communication scenarios the worst-case complexity of the LLL algorithm is not even finite. For i.i.d. Rayleigh fading channels, we further prove that the average LLL complexity is polynomial and that the probability for an atypically large number of LLL iterations decays exponentially.

Fixed-Complexity Soft MIMO Detection via Partial Marginalization

This paper presents a new approach to soft demodulation for MIMO channels. The proposed method is an approximation to the exact a posteriori probability-per-bit computer. The main idea is to marginalize the posterior density for the received data exactly over the subset of the transmitted bits that are received with the lower signal-to-noise-ratio (SNR), and marginalize this density approximately over the remaining bits. Unlike the exact demodulator, whose complexity is huge due to the need for enumerating all possible combinations of transmitted constellation points, the proposed method has very low complexity. The algorithm has a fully parallel structure, suitable for implementation in parallel hardware. Additionally, its complexity is fixed, which makes it suitable for pipelined implementation. We also show how the method can be extended to the situation when the receiver has only partial channel state information, and how it can be modified to take soft-input into account. Numerical examples illustrate its performance on slowly fading 4 times 4 and 6 times 6 complex MIMO channels.

Parallel Implementation of a Soft Output Sphere Decoder

Transmission at rates close to capacity over fading multiple antenna channels can be achieved by concatenating inner space-time block codes and powerful outer codes such as turbo or LDPC codes. However, in such systems, computation of the required soft information, or log-likelihood ratios (LLR), for the bits transmitted over the channel is rather complex and some form of approximations are typically used. Herein, we show how the complexity of computing the max-log approximation of the LLR can be reduced by computing all LLR values simultaneously using a parallel sphere decoder implementation

The Error Probability of the Fixed-Complexity Sphere Decoder

The fixed-complexity sphere decoder (FSD) has been previously proposed for multiple-input multiple-output (MIMO) detection in order to overcome the two main drawbacks of the sphere decoder (SD), namely its variable complexity and its sequential structure. Although the FSD has shown remarkable quasi-maximum-likelihood (ML) performance and has resulted in a highly optimized real-time implementation, no analytical study of its performance existed for an arbitrary MIMO system. Herein, the error probability of the FSD is analyzed, proving that it achieves the same diversity as the maximum-likelihood detector (MLD) independent of the constellation used. In addition, it can also asymptotically yield ML performance in the high-signal-to-noise ratio (SNR) regime. Those two results, together with its fixed complexity, make the FSD a very promising algorithm for uncoded MIMO detection.

An exponential lower bound on the expected complexity of sphere decoding

The sphere decoding algorithm is an efficient algorithm used to solve the maximum likelihood detection problem in several digital communication systems. The sphere decoding algorithm has previously been claimed to have polynomial expected complexity. While it is true that the algorithm has an expected complexity comparable to that of other polynomial time algorithms for problems of moderate size it is a misconception that the expected number of operations asymptotically grow as a polynomial function of the problem size. In order to illustrate this point we derive an exponential lower bound on the expected complexity of the sphere decoder.

Full Diversity Detection in MIMO Systems with a Fixed-Complexity Sphere Decoder

The fixed-complexity sphere decoder (FSD) has been previously proposed for multiple input-multiple output (MIMO) detection to overcome the two main drawbacks of the original sphere decoder (SD), namely its variable complexity and sequential structure. As such, the FSD is highly suitable for hardware implementation and has shown remarkable performance through simulations. Herein, we explore the theoretical aspects of the algorithm and prove that the FSD achieves the same diversity order as the maximum likelihood detector (MLD). Further, we show that the coding loss can be made negligible in the high signal to noise ratio (SNR) regime with a significantly lower complexity than that of the MLD.