On Limits of Performance of DNA Microarrays

DNA microarray technology relies on the hybridization process which is stochastic in nature. Probabilistic cross-hybridization of non-specific targets, as well as the shot-noise originating from specific targets binding, are among the many obstacles for achieving high accuracy in DNA microarray analysis. In this paper, we use statistical model of hybridization and cross-hybridization processes to derive a lower bound (viz., the Cramer-Rao bound) on the minimum mean-square error of the target concentrations estimation. A preliminary study of the Cramer-Rao bound for estimating the target concentrations suggests that, in some regimes, cross-hybridization may, in fact, be beneficial—a result with potential ramifications for probe design, which is currently focused on minimizing cross-hybridization

On joint maximum-likelihood estimation of PCR efficiency and initial amount of target

We consider the problem of estimating unknown parameters of the real-time polymerase chain reaction (RTPCR) from noisy observations. The joint ML estimator of the RT-PCR efficiency and the initial number of DNA target molecules is derived. The mean-square error performance of the estimator is studied via simulations. The simulation results indicate that the proposed estimator significantly outperforms a competing technique

Sphere-constrained ML detection for frequency-selective channels

The maximum-likelihood (ML) sequence detection problem for channels with memory is investigated. The Viterbi algorithm (VA) provides an exact solution. Its computational complexity is linear in the length of the transmitted sequence, but exponential in the channel memory length. On the other hand, the sphere decoding (SD) algorithm also solves the ML detection problem exactly, and has expected complexity which is a low-degree polynomial (often cubic) in the length of the transmitted sequence over a wide range of signal-to-noise ratios. We combine the sphere-constrained search strategy of SD with the dynamic programming principles of the VA. The resulting algorithm has the worst-case complexity determined by the VA, but often significantly lower expected complexity

Iterative decoding for MIMO channels via modified sphere decoding

In recent years, soft iterative decoding techniques have been shown to greatly improve the bit error rate performance of various communication systems. For multiantenna systems employing space-time codes, however, it is not clear what is the best way to obtain the soft information required of the iterative scheme with low complexity. In this paper, we propose a modification of the Fincke-Pohst (sphere decoding) algorithm to estimate the maximum a posteriori probability of the received symbol sequence. The new algorithm solves a nonlinear integer least squares problem and, over a wide range of rates and signal-to-noise ratios, has polynomial-time complexity. Performance of the algorithm, combined with convolutional, turbo, and low-density parity check codes, is demonstrated on several multiantenna channels. The results for systems that employ space-time modulation schemes seem to indicate that the best performing schemes are those that support the highest mutual information between the transmitted and received signals, rather than the best diversity gain

ML Estimation of DNA Initial Copy Number in Polymerase Chain Reaction (PCR) Processes

Estimation of DNA copy number in a given biological sample is an extremely important problem in genomics. This problem is especially challenging when the number of the DNA strands is minuscule, which is often the case in applications such as pathogen and genetic mutation detection. A recently developed technique, real-time polymerase chain reaction (PCR), amplifies the number of initial target molecules by replicating them through a series of thermal cycles. Ideally, the number of target molecules doubles at the end of each cycle. However, in practice, due to biochemical noise the efficiency of the PCR reaction, defined as the fraction of target molecules which are successfully copied during a cycle, is always less than 1. In this paper, we formulate the problem of joint maximum-likelihood estimation of the PCR efficiency and the initial DNA copy number. As indicated by simulation studies, the performance of the proposed estimator is superior with respect to competing statistical approaches. Moreover, we compute the Cramer-Rao lower bound on the mean-square estimation error

Modeling the kinetics of hybridization in microarrays

Conventional fluorescent-based microarrays acquire data after the hybridization phase. In this phase the targets analytes (i.e., DNA fragments) bind to the capturing probes on the array and supposedly reach a steady state. Accordingly, microarray experiments essentially provide only a single, steady-state data point of the hybridization process. On the other hand, a novel technique (i.e., realtime microarrays) capable of recording the kinetics of hybridization in fluorescent-based microarrays has recently been proposed in [5]. The richness of the information obtained therein promises higher signal-to-noise ratio, smaller estimation error, and broader assay detection dynamic range compared to the conventional microarrays. In the current paper, we develop a probabilistic model of the kinetics of hybridization and describe a procedure for the estimation of its parameters which include the binding rate and target concentration. This probabilistic model is an important step towards developing optimal detection algorithms for the microarrays which measure the kinetics of hybridization, and to understanding their fundamental limitations

PEP Analysis of the SDP Based Joint Channel Estimation and Signal Detection

In multi-antenna communication systems, channel information is often not known at the receiver. To fully exploit bandwidth resources of the system and ensure practical feasibility of the receiver, channel parameters are often estimated blindly and then employed in the design of signal detection algorithms. Instead of separating channel estimation from signal detection, in this paper we focus on the joint channel estimation and signal detection problem in a single-input multiple-output (SIMO) system. It is well known that finding solution to this optimization requires solving an integer maximization of a quadratic form and is, in general, an NP hard problem. To solve it, we propose an approximate algorithm based on the semi-definite program (SDP) relaxation. We derive a bound on the pairwise probability of error (PEP) of the proposed algorithm and show that, the algorithm achieves the same diversity as the exact maximum-likelihood (ML) decoder. The computed PEP implies that, over a wide range of system parameters, the proposed algorithm requires moderate increase in the signal-to-noise ratio (SNR) in order to achieve performance comparable to that of the ML decoder but with often significantly lower complexit

On Recovery of Sparse Signals in Compressed DNA Microarrays

Currently, DNA micro arrays comprising tens of thousands of probe spots are employed to test entire genomes in a single experiment. Typically, each microarray spot contains a large number of copies of a single probe, and hence collects only a single data point. This is a wasteful use of the sensing resources in comparative DNA microarray experiments, where a test sample is measured relative to a reference sample. Since only a small fraction of the total number of genes represented by the two samples is differentially expressed, a large fraction of a microarray does not provide any useful information. To this end, in this paper we consider an alternative microarray design wherein each spot is a composite of several different probes, and the total number of spots is potentially much smaller than the number of genes being tested. Fewer spots directly translates to significantly lower costs due to cheaper array manufacturing, simpler image acquisition and processing, and smaller amount of genomic material needed for experiments. To recover signals from compressed microarray measurements, we leverage ideas from compressive sampling. Experimental verification of the proposed methodology is presented

An H-infinity based lower bound to speed up the sphere decoder

It is well known that maximum-likelihood (ML) decoding in many digital communication schemes reduces to solving an integer least problem, which is NP hard in the worst-case. On the other hand, it has recently been shown that, over a wide range of dimensions and signal-to-noise ratios (SNR), the sphere decoder can be used to find the exact solution with an expected complexity that is roughly cubic in the dimension of the problem. However, the computational complexity of sphere decoding becomes prohibitive if the SNR is too low and/or if the dimension of the problem is too large. In recent work M. Stonjic et al. (2005), we have targeted these two regimes and attempted to find faster algorithms by employing a branch-and-bound technique based on convex relaxations of the original integer least-squares problem. In this paper, using ideas from H∞ estimation theory, we propose new lower bounds that are generally tighter than the ones obtained in M. Stonjic et al. (2005). Simulation results snow the advantages, in terms of computational complexity, of the new H∞-based branch-and-bound algorithm over the ones based on convex relaxation, as well as the original sphere decoder