On Non-Binary Constellations for Channel Encoded Physical Layer Network Coding

This thesis investigates channel-coded physical layer network coding, in which the relay directly transforms the noisy superimposed channel-coded packets received from the two end nodes, to the network-coded combination of the source packets. This is in contrast to the traditional multiple-access problem, in which the goal is to obtain each message explicitly at the relay. Here, the end nodes $A$ and $B$ choose their symbols, $S_A$ and $S_B$, from a small non-binary field, $\mathbb{F}$, and use non-binary PSK constellation mapper during the transmission phase. The relay then directly decodes the network-coded combination ${aS_A+bS_B}$ over $\mathbb{F}$ from the noisy superimposed channel-coded packets received from two end nodes. Trying to obtain $S_A$ and $S_B$ explicitly at the relay is overly ambitious when the relay only needs $aS_B+bS_B$. For the binary case, the only possible network-coded combination, ${S_A+S_B}$ over the binary field, does not offer the best performance in several channel conditions. The advantage of working over non-binary fields is that it offers the opportunity to decode according to multiple decoding coefficients $(a,b)$. As only one of the network-coded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of decoding coefficients. In this thesis, we compare different constellation mappers and prove that not all of them have distinct performance in terms of frame error rate. Moreover, we derive a lower bound on the frame error rate performance of decoding the network-coded combinations at the relay. Simulation results show that if we adopt concatenated Reed-Solomon and convolutional coding or low density parity check codes at the two end nodes, our non-binary constellations can outperform the binary case significantly in the sense of minimizing the frame error rate and, in particular, the ternary constellation has the best frame error rate performance among all considered cases

Comprehensive Head Motion Correction For Functional Magnetic Resonance Imaging

Head motion artifacts are major confounds that limit use of functional magnetic resonance imaging (fMRI) in neuroscience research and clinical settings. Prospective motion correction is a promising candidate solution for head motion in fMRI that ideally allows the image plane to remain fixed with respect to the moving head (i.e., in the moving reference frame). Prospective motion correction has been shown to correct successfully for rigid body movement artifacts, but residual geometric distortion due to dynamic magnetic field nonuniformities and dynamic changes in receiver coil sensitivity profiles in the moving reference frame still remain a problem. This thesis focuses on three objectives. First, I investigated and corrected for the influence of respiratory effects on the performance of dynamic geometric correction using Phase Labeling for Additional Coordinate Encoding (PLACE). It was demonstrated that PLACE combined with the dynamic off-resonance in k-space (DORK) method, and temporal averaging substantially improved fMRI data quality in comparison to the results obtained by standard processing and static geometric distortion correction. Second, I verified that appreciable signal artifacts occur due to coil sensitivity changes in fMRI maps in presence of overt head motion with prospective motion correction using Prospective Acquisition CorrEction (PACE) technique [1]. Sensitivity map compensations were shown to suppress these artifacts and provide improved fMRI results Third, I studied signal artifacts resulted from the head motion between the coil sensitivity map measurement (i.e., the calibration step) and data acquisition for fMRI with parallel-imaging reconstruction methods using two parallel imaging schemes: sensitivity encoding (SENSE) and generalized autocalibrating partially parallel acquisitions (GRAPPA) with acceleration factors 2 and 4. Coil sensitivity map compensations were shown to improve fMRI results obtained with PACE in the presence of overt head motion compared to those obtained with no overt head motion. Overall, prospective motion correction, integrated dynamic geometric distortion correction, and coil sensitivity map correction present an appealing compound approach for suppressing rigid and non-rigid motion artifacts during fMRI. This thesis has developed robust and comprehensive head motion correction strategies that ultimately will expand the patient populations for which fMRI can be performed robustlyPh.D

Group mean, standard deviation, and range of p-p head motion for time series data collection for subjects (a) at rest and (b) during task-based fMRI. ΔSI, ΔRL, and ΔAP denote displacements in the superior-inferior, right-left, and anterior-posterior directions, respectively; roll, pitch and yaw denote the angular rotations about the SI, RL and AP axes, respectively.

<p>Group mean, standard deviation, and range of p-p head motion for time series data collection for subjects (a) at rest and (b) during task-based fMRI. ΔSI, ΔRL, and ΔAP denote displacements in the superior-inferior, right-left, and anterior-posterior directions, respectively; roll, pitch and yaw denote the angular rotations about the SI, RL and AP axes, respectively.</p

tSD maps of three different slices for at rest scans (scan e) of a representative subject after: 1) no further processing, 2) sPLACE, 3) dPLACE, and 6) DORK and dPLACE with DMA.

<p>Maps of the percent signal change achieved by the combined approach 6) compared to no further processing 1) are shown at the far right.</p

Four sample dPLACE+DORK+DMA displacement maps for a representative subject at different time points during task-based fMRI (scan f).

<p>The static displacement map generated by sPLACE is shown for comparison.</p

Activation brain maps for a representative subject after no further processing (baseline), sPLACE and DORK+dPLACE+DMA on two brain slices.

<p>Activation brain maps for a representative subject after no further processing (baseline), sPLACE and DORK+dPLACE+DMA on two brain slices.</p

Phantom experiment results: Temporal standard deviation (tSD) maps in the absence (first row) and presence (second row) of simulated respiration after: 1) no further processing, 2) sPLACE, 3) dPLACE, 4) dPLACE with DMA, 5) DORK and dPLACE, and 6) DORK and dPLACE with DMA.

<p>Phantom experiment results: Temporal standard deviation (tSD) maps in the absence (first row) and presence (second row) of simulated respiration after: 1) no further processing, 2) sPLACE, 3) dPLACE, 4) dPLACE with DMA, 5) DORK and dPLACE, and 6) DORK and dPLACE with DMA.</p

Summary of all imaging runs.

<p>Summary of all imaging runs.</p