Communication under Strong Asynchronism

We consider asynchronous communication over point-to-point discrete memoryless channels. The transmitter starts sending one block codeword at an instant that is uniformly distributed within a certain time period, which represents the level of asynchronism. The receiver, by means of a sequential decoder, must isolate the message without knowing when the codeword transmission starts but being cognizant of the asynchronism level A. We are interested in how quickly can the receiver isolate the sent message, particularly in the regime where A is exponentially larger than the codeword length N, which we refer to as `strong asynchronism.' This model of sparse communication may represent the situation of a sensor that remains idle most of the time and, only occasionally, transmits information to a remote base station which needs to quickly take action. The first result shows that vanishing error probability can be guaranteed as N tends to infinity while A grows as Exp(N*k) if and only if k does not exceed the `synchronization threshold,' a constant that admits a simple closed form expression, and is at least as large as the capacity of the synchronized channel. The second result is the characterization of a set of achievable strictly positive rates in the regime where A is exponential in N, and where the rate is defined with respect to the expected delay between the time information starts being emitted until the time the receiver makes a decision. As an application of the first result we consider antipodal signaling over a Gaussian channel and derive a simple necessary condition between A, N, and SNR for achieving reliable communication.Comment: 26 page

Deletion codes in the high-noise and high-rate regimes

The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a focus on constructing efficiently decodable codes for the two extreme regimes of high-noise and high-rate. Specifically, we construct polynomial-time decodable codes with the following trade-offs (for any eps > 0): (1) Codes that can correct a fraction 1-eps of deletions with rate poly(eps) over an alphabet of size poly(1/eps); (2) Binary codes of rate 1-O~(sqrt(eps)) that can correct a fraction eps of deletions; and (3) Binary codes that can be list decoded from a fraction (1/2-eps) of deletions with rate poly(eps) Our work is the first to achieve the qualitative goals of correcting a deletion fraction approaching 1 over bounded alphabets, and correcting a constant fraction of bit deletions with rate aproaching 1. The above results bring our understanding of deletion code constructions in these regimes to a similar level as worst-case errors

Fundamental Bounds and Approaches to Sequence Reconstruction from Nanopore Sequencers

Nanopore sequencers are emerging as promising new platforms for high-throughput sequencing. As with other technologies, sequencer errors pose a major challenge for their effective use. In this paper, we present a novel information theoretic analysis of the impact of insertion-deletion (indel) errors in nanopore sequencers. In particular, we consider the following problems: (i) for given indel error characteristics and rate, what is the probability of accurate reconstruction as a function of sequence length; (ii) what is the number of `typical' sequences within the distortion bound induced by indel errors; (iii) using replicated extrusion (the process of passing a DNA strand through the nanopore), what is the number of replicas needed to reduce the distortion bound so that only one typical sequence exists within the distortion bound. Our results provide a number of important insights: (i) the maximum length of a sequence that can be accurately reconstructed in the presence of indel and substitution errors is relatively small; (ii) the number of typical sequences within the distortion bound is large; and (iii) replicated extrusion is an effective technique for unique reconstruction. In particular, we show that the number of replicas is a slow function (logarithmic) of sequence length -- implying that through replicated extrusion, we can sequence large reads using nanopore sequencers. Our model considers indel and substitution errors separately. In this sense, it can be viewed as providing (tight) bounds on reconstruction lengths and repetitions for accurate reconstruction when the two error modes are considered in a single model.Comment: 12 pages, 5 figure

Moving in time: simulating how neural circuits enable rhythmic enactment of planned sequences

Many complex actions are mentally pre-composed as plans that specify orderings of simpler actions. To be executed accurately, planned orderings must become active in working memory, and then enacted one-by-one until the sequence is complete. Examples include writing, typing, and speaking. In cases where the planned complex action is musical in nature (e.g. a choreographed dance or a piano melody), it appears to be possible to deploy two learned sequences at the same time, one composed from actions and a second composed from the time intervals between actions. Despite this added complexity, humans readily learn and perform rhythm-based action sequences. Notably, people can learn action sequences and rhythmic sequences separately, and then combine them with little trouble (Ullén & Bengtsson 2003). Related functional MRI data suggest that there are distinct neural regions responsible for the two different sequence types (Bengtsson et al. 2004). Although research on musical rhythm is extensive, few computational models exist to extend and inform our understanding of its neural bases. To that end, this article introduces the TAMSIN (Timing And Motor System Integration Network) model, a systems-level neural network model capable of performing arbitrary item sequences in accord with any rhythmic pattern that can be represented as a sequence of integer multiples of a base interval. In TAMSIN, two Competitive Queuing (CQ) modules operate in parallel. One represents and controls item order (the ORD module) and the second represents and controls the sequence of inter-onset-intervals (IOIs) that define a rhythmic pattern (RHY module). Further circuitry helps these modules coordinate their signal processing to enable performative output consistent with a desired beat and tempo.Accepted manuscrip

PCM telemetry data compression study, phase II Quarterly report, 25 Nov. 1965 - 25 Feb. 1966

Model analyses and computer simulations used in data compression study for improved pulse code modulation telemetry link