Capacity of a Class of Deterministic Relay Channels

The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y_1 = f(X, Y), and a separate communication link from the relay to the receiver with capacity R_0, is shown to be C(R_0) = \max_{p(x)} \min \{I(X;Y)+R_0, I(X;Y, Y_1) \}. Thus every bit from the relay is worth exactly one bit to the receiver. Two alternative coding schemes are presented that achieve this capacity. The first scheme, ``hash-and-forward'', is based on a simple yet novel use of random binning on the space of relay outputs, while the second scheme uses the usual ``compress-and-forward''. In fact, these two schemes can be combined together to give a class of optimal coding schemes. As a corollary, this relay capacity result confirms a conjecture by Ahlswede and Han on the capacity of a channel with rate-limited state information at the decoder in the special case when the channel state is recoverable from the channel input and the output.Comment: 17 pages, submitted to IEEE Transactions on Information Theor

Proximity to clinical care and time to resolution following an abnormal cancer screening in an urban setting

Thesis (M.S.)--Boston UniversityBarriers to care have been identified as a major factor in cancer health disparities. Previous research at Boston Medical Center (BMC) found that women referred from community health centers (CHCs) following abnormal breast cancer screening took longer to achieve diagnostic resolution than women referred from a BMC-based practice, consistent with research showing longer delays and worse outcomes for disadvantaged urban populations. It is not known whether this difference relates to the additional distance to BMC. To evaluate the effect of proximity from subjects' residence to the site of clinical care on time to diagnostic resolution in this urban setting we conducted a secondary analysis using data collected as part of the Boston Patient Navigation Research Program (PNRP). The database included all women who had a breast or cervical cancer screening abnormality at six Federally-qualified CHCs from January 2007 to June 2009. Using geocoded home address data captured at the time of registration, we calculated straight-line distances to the location of the diagnostic evaluation, which was the CHC for subjects with a cervical abnormality or BMC for subjects with a breast abnormality, and plotted the time to diagnostic resolution versus distance to site of care. We used proportional hazards regression models to examine the effect of distance to site of care on time to resolution, adjusting for CHC, subject age, race/ethnicity, language, and insurance. Results. We geocoded addresses for 1512 of 1544 subjects (98%). Among the diverse group of subjects with a breast screening abnormality (36% Black, 33% Hispanic; 44% non-English speaking), there was no significant difference in adjusted hazard ratios based on distance to care in 1,000 meter units (adjusted Hazard Ratio 1.00, 95% CI 0.99 -1.01). Similarly, among those with a cervical screening abnormality (22% Black, 21% Hispanic; 15% non-English), there was no significant difference in adjusted hazard ratios based on distance to care in 1,000 meter units (adjusted Hazard Ratio 1.01, 95% CI 1.00- 1.02). Conclusions. Increased distance between residence and clinic alone is not a barrier to diagnostic resolution for this vulnerable urban population receiving care at a CHC who had an abnormal cancer screening exam

Synthesis of Distributed Longitudinal Control Protocols for a Platoon of Autonomous Vehicles

We develop a framework for control protocol synthesis for a platoon of autonomous vehicles subject to temporal logic specifications. We describe the desired behavior of the platoon in a set of linear temporal logic formulas, such as collision avoidance, close spacing or comfortability. The problem of decomposing a global specification for the platoon into distributed specification for each pair of adjacent vehicles is hard to solve. We use the invariant specifications to tackle this problem and the decomposition is proved to be scalable.. Based on the specifications in Assumption/Guarantee form, we can construct a two-player game (between the vehicle and its closest leader) locally to automatically synthesize a controller protocol for each vehicle. Simulation example for a distributed vehicles control problem is also shown