Variable-Length Coding with Feedback: Finite-Length Codewords and Periodic Decoding

Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of single-user memoryless channels. Recently Polyanskiy et al. studied the benefit of variable-length feedback with termination (VLFT) codes in the non-asymptotic regime. In that work, achievability is based on an infinite length random code and decoding is attempted at every symbol. The coding rate backoff from capacity due to channel dispersion is greatly reduced with feedback, allowing capacity to be approached with surprisingly small expected latency. This paper is mainly concerned with VLFT codes based on finite-length codes and decoding attempts only at certain specified decoding times. The penalties of using a finite block-length $N$ and a sequence of specified decoding times are studied. This paper shows that properly scaling $N$ with the expected latency can achieve the same performance up to constant terms as with $N = \infty$. The penalty introduced by periodic decoding times is a linear term of the interval between decoding times and hence the performance approaches capacity as the expected latency grows if the interval between decoding times grows sub-linearly with the expected latency.Comment: 8 pages. A shorten version is submitted to ISIT 201

A Rate-Compatible Sphere-Packing Analysis of Feedback Coding with Limited Retransmissions

Recent work by Polyanskiy et al. and Chen et al. has excited new interest in using feedback to approach capacity with low latency. Polyanskiy showed that feedback identifying the first symbol at which decoding is successful allows capacity to be approached with surprisingly low latency. This paper uses Chen's rate-compatible sphere-packing (RCSP) analysis to study what happens when symbols must be transmitted in packets, as with a traditional hybrid ARQ system, and limited to relatively few (six or fewer) incremental transmissions. Numerical optimizations find the series of progressively growing cumulative block lengths that enable RCSP to approach capacity with the minimum possible latency. RCSP analysis shows that five incremental transmissions are sufficient to achieve 92% of capacity with an average block length of fewer than 101 symbols on the AWGN channel with SNR of 2.0 dB. The RCSP analysis provides a decoding error trajectory that specifies the decoding error rate for each cumulative block length. Though RCSP is an idealization, an example tail-biting convolutional code matches the RCSP decoding error trajectory and achieves 91% of capacity with an average block length of 102 symbols on the AWGN channel with SNR of 2.0 dB. We also show how RCSP analysis can be used in cases where packets have deadlines associated with them (leading to an outage probability).Comment: To be published at the 2012 IEEE International Symposium on Information Theory, Cambridge, MA, USA. Updated to incorporate reviewers' comments and add new figure

Increasing Flash Memory Lifetime by Dynamic Voltage Allocation for Constant Mutual Information

The read channel in Flash memory systems degrades over time because the Fowler-Nordheim tunneling used to apply charge to the floating gate eventually compromises the integrity of the cell because of tunnel oxide degradation. While degradation is commonly measured in the number of program/erase cycles experienced by a cell, the degradation is proportional to the number of electrons forced into the floating gate and later released by the erasing process. By managing the amount of charge written to the floating gate to maintain a constant read-channel mutual information, Flash lifetime can be extended. This paper proposes an overall system approach based on information theory to extend the lifetime of a flash memory device. Using the instantaneous storage capacity of a noisy flash memory channel, our approach allocates the read voltage of flash cell dynamically as it wears out gradually over time. A practical estimation of the instantaneous capacity is also proposed based on soft information via multiple reads of the memory cells.Comment: 5 pages. 5 figure

Feedback Communication Systems with Limitations on Incremental Redundancy

This paper explores feedback systems using incremental redundancy (IR) with noiseless transmitter confirmation (NTC). For IR-NTC systems based on {\em finite-length} codes (with blocklength $N$) and decoding attempts only at {\em certain specified decoding times}, this paper presents the asymptotic expansion achieved by random coding, provides rate-compatible sphere-packing (RCSP) performance approximations, and presents simulation results of tail-biting convolutional codes. The information-theoretic analysis shows that values of $N$ relatively close to the expected latency yield the same random-coding achievability expansion as with $N = \infty$. However, the penalty introduced in the expansion by limiting decoding times is linear in the interval between decoding times. For binary symmetric channels, the RCSP approximation provides an efficiently-computed approximation of performance that shows excellent agreement with a family of rate-compatible, tail-biting convolutional codes in the short-latency regime. For the additive white Gaussian noise channel, bounded-distance decoding simplifies the computation of the marginal RCSP approximation and produces similar results as analysis based on maximum-likelihood decoding for latencies greater than 200. The efficiency of the marginal RCSP approximation facilitates optimization of the lengths of incremental transmissions when the number of incremental transmissions is constrained to be small or the length of the incremental transmissions is constrained to be uniform after the first transmission. Finally, an RCSP-based decoding error trajectory is introduced that provides target error rates for the design of rate-compatible code families for use in feedback communication systems.Comment: 23 pages, 15 figure

From Observers to Participants: Joining the Scientific Community

In this essay, we have integrated the voices of our mentors and students to explore 45 years of undergraduate research experiences and their role in shaping our scientific community. In considering our collective experiences, we see undergraduate involvement in research as a rich source of community development, one that has both touched our lives and influenced our teaching

A Precise Water Abundance Measurement for the Hot Jupiter WASP-43b

The water abundance in a planetary atmosphere provides a key constraint on the planet's primordial origins because water ice is expected to play an important role in the core accretion model of planet formation. However, the water content of the Solar System giant planets is not well known because water is sequestered in clouds deep in their atmospheres. By contrast, short-period exoplanets have such high temperatures that their atmospheres have water in the gas phase, making it possible to measure the water abundance for these objects. We present a precise determination of the water abundance in the atmosphere of the 2 $M_\mathrm{Jup}$ short-period exoplanet WASP-43b based on thermal emission and transmission spectroscopy measurements obtained with the Hubble Space Telescope. We find the water content is consistent with the value expected in a solar composition gas at planetary temperatures (0.4-3.5x solar at 1 $\sigma$ confidence). The metallicity of WASP-43b's atmosphere suggested by this result extends the trend observed in the Solar System of lower metal enrichment for higher planet masses.Comment: Accepted to ApJL; this version contains three supplemental figures that are not included in the published paper. See also our companion paper "Thermal structure of an exoplanet atmosphere from phase-resolved emission spectroscopy" by Stevenson et a

Microbial Reduction of U(VI) under Alkaline Conditions: Implications for Radioactive Waste Geodisposal

Although there is consensus that microorganisms significantly influence uranium speciation and mobility in the subsurface under circumneutral conditions, microbiologically mediated U(VI) redox cycling under alkaline conditions relevant to the geological disposal of cementitious intermediate level radioactive waste, remains unexplored. Here, we describe microcosm experiments that investigate the biogeochemical fate of U(VI) at pH 10–10.5, using sediments from a legacy lime working site, stimulated with an added electron donor, and incubated in the presence and absence of added Fe(III) as ferrihydrite. In systems without added Fe(III), partial U(VI) reduction occurred, forming a U(IV)-bearing non-uraninite phase which underwent reoxidation in the presence of air (O2) and to some extent nitrate. By contrast, in the presence of added Fe(III), U(VI) was first removed from solution by sorption to the Fe(III) mineral, followed by bioreduction and (bio)magnetite formation coupled to formation of a complex U(IV)-bearing phase with uraninite present, which also underwent air (O2) and partial nitrate reoxidation. 16S rRNA gene pyrosequencing showed that Gram-positive bacteria affiliated with the Firmicutes and Bacteroidetes dominated in the post-reduction sediments. These data provide the first insights into uranium biogeochemistry at high pH and have significant implications for the long-term fate of uranium in geological disposal in both engineered barrier systems and the alkaline, chemically disturbed geosphere

Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models

Recent studies have applied dimensionality reduction methods to understand how the multi-dimensional structure of neural population activity gives rise to brain function. It is unclear, however, how the results obtained from dimensionality reduction generalize to recordings with larger numbers of neurons and trials or how these results relate to the underlying network structure. We address these questions by applying factor analysis to recordings in the visual cortex of non-human primates and to spiking network models that self-generate irregular activity through a balance of excitation and inhibition. We compared the scaling trends of two key outputs of dimensionality reduction—shared dimensionality and percent shared variance—with neuron and trial count. We found that the scaling properties of networks with non-clustered and clustered connectivity differed, and that the in vivo recordings were more consistent with the clustered network. Furthermore, recordings from tens of neurons were sufficient to identify the dominant modes of shared variability that generalize to larger portions of the network. These findings can help guide the interpretation of dimensionality reduction outputs in regimes of limited neuron and trial sampling and help relate these outputs to the underlying network structure

Reintegrating Biology through the Nexus of Energy, Information, and Matter

Information, energy, and matter are fundamental properties of all levels of biological organization, and life emerges from the continuous flux of matter, energy, and information. This perspective piece defines and explains each of the three pillars of this nexus. We propose that a quantitative characterization of the complex interconversions between matter, energy, and information that compose this nexus will help us derive biological insights that connect phenomena across different levels of biological organization. We articulate examples from multiple biological scales that highlight how this nexus approach leads to a more complete understanding of the biological system. Metrics of energy, information, and matter can provide a common currency that helps link phenomena across levels of biological organization. The propagation of energy and information through levels of biological organization can result in emergent properties and system-wide changes that impact other hierarchical levels. Deeper consideration of measured imbalances in energy, information, and matter can help researchers identify key factors that influence system function at one scale, highlighting avenues to link phenomena across levels of biological organization and develop predictive models of biological systems