Decoding Hidden Markov Models Faster Than Viterbi Via Online Matrix-Vector (max, +)-Multiplication

In this paper, we present a novel algorithm for the maximum a posteriori decoding (MAPD) of time-homogeneous Hidden Markov Models (HMM), improving the worst-case running time of the classical Viterbi algorithm by a logarithmic factor. In our approach, we interpret the Viterbi algorithm as a repeated computation of matrix-vector $(\max, +)$-multiplications. On time-homogeneous HMMs, this computation is online: a matrix, known in advance, has to be multiplied with several vectors revealed one at a time. Our main contribution is an algorithm solving this version of matrix-vector $(\max,+)$-multiplication in subquadratic time, by performing a polynomial preprocessing of the matrix. Employing this fast multiplication algorithm, we solve the MAPD problem in $O(mn^2/ \log n)$ time for any time-homogeneous HMM of size $n$ and observation sequence of length $m$, with an extra polynomial preprocessing cost negligible for $m > n$. To the best of our knowledge, this is the first algorithm for the MAPD problem requiring subquadratic time per observation, under the only assumption -- usually verified in practice -- that the transition probability matrix does not change with time.Comment: AAAI 2016, to appea

An Analytical Model of Packet Collisions in IEEE 802.15.4 Wireless Networks

Numerous studies showed that concurrent transmissions can boost wireless network performance despite collisions. While these works provide empirical evidence that concurrent transmissions may be received reliably, existing signal capture models only partially explain the root causes of this phenomenon. We present a comprehensive mathematical model that reveals the reasons and provides insights on the key parameters affecting the performance of MSK-modulated transmissions. A major contribution is a closed-form derivation of the receiver bit decision variable for arbitrary numbers of colliding signals and constellations of power ratios, timing offsets, and carrier phase offsets. We systematically explore the root causes for successful packet delivery under concurrent transmissions across the whole parameter space of the model. We confirm the capture threshold behavior observed in previous studies but also reveal new insights relevant for the design of optimal protocols: We identify capture zones depending not only on the signal power ratio but also on time and phase offsets.Comment: Accepted for publication in the IEEE Transactions on Wireless Communications under the title "On the Reception of Concurrent Transmissions in Wireless Sensor Networks.

Advanced digital modulation: Communication techniques and monolithic GaAs technology

Communications theory and practice are merged with state-of-the-art technology in IC fabrication, especially monolithic GaAs technology, to examine the general feasibility of a number of advanced technology digital transmission systems. Satellite-channel models with (1) superior throughput, perhaps 2 Gbps; (2) attractive weight and cost; and (3) high RF power and spectrum efficiency are discussed. Transmission techniques possessing reasonably simple architectures capable of monolithic fabrication at high speeds were surveyed. This included a review of amplitude/phase shift keying (APSK) techniques and the continuous-phase-modulation (CPM) methods, of which MSK represents the simplest case

The Effects of Morpheme and Prosody Instruction on Middle School Spelling

A single case design was used to investigate the impact of two types of instruction on middle school students’ spelling. Phase 1 emphasized morphology awareness instruction (MAI) and phase 2 employed the addition of prosody awareness instruction (PAI). In order to compare the effects of MAI and PAI, spelling scores were gathered from eight students over a 12-week period. The children attended two 30-minute sessions each week. Two of the participants were high performing students, three were typical learners, and three students were experiencing pronounced difficulties in all areas of literacy. The scores of seven out of eight participants indicated a positive response to both phases with the majority of high scores falling in the prosody phase. The effect size (ES) of the overall improvement across the eight students was measured using Tau-U. The ES for morphology the morphology condition compared to baseline was .793, p \u3c .001. The ES for prosody compared to morphology was for prosody compared to morphology was .810, p \u3c .001. Instruction in prosody awareness seems to hold promise as one avenue for rapidly building spelling consciousness in students with diverse learning profiles

Effect of an Intensive Intervention on the Early Literacy Skills of Kindergarten Students Identified as Most at Risk for Future Reading Difficulties

There is limited research investigating the individualized effects of early literacy interventions on kindergarten students who are most at risk for reading failure at school entry. In this study, a multiple baseline design was used to measure the effect of an early literacy intervention on the alphabet knowledge and phonological awareness of kindergarten students identified as most at risk. First, a two-stage screening process consisting of measures of alphabet knowledge, phonological awareness, and rapid automatic naming was employed to identify those students with the lowest overall skill level from the entire at-risk kindergarten population from one school building. The nine students with the lowest skill level were selected to receive more intensive intervention services than were typically offered to at-risk kindergarten students. The intervention consisted of both code-focused and meaning-focused components and was delivered daily for 25 minutes in small groups of three students for a total of 60 instructional sessions. The intervention was implemented at three different points in time, resulting in three baseline and three intervention phases. During baseline and intervention phases, two alphabet knowledge measures and one phonological awareness measure were repeatedly administered to all participants. Data was analyzed through systematic comparison of within and between phase patterns, such as performance level, trend, variability, non-overlap of data points, and immediacy of effect. Analysis was enhanced using the conservative dual criterion approach. Results indicated that an experimental effect was evident after the first and second introduction of the independent variable but not at time three, weakening the claim of a cause and effect relationship between the independent and dependent variables. Differences in performance level and trend in the data were evident for five students on letter name knowledge, six students on letter sound knowledge, and six students on first sound identification skills