Information Theory And Coding By K Giridhar Pdf Free
Brie Hoffler
The document provides information about the syllabus for the course "Information Theory & Error Correction Coding". It discusses the details of the final exam which has two parts worth 50 marks total. Part A is 20 marks and covers topics like channel capacity, coding models, error control types, and linear block codes. Part B is 30 marks and covers additional topics such as linear block codes, convolutional codes, decoding algorithms, and error correction capabilities. It also provides background information on discrete channels, channel capacity theorem, Shannon's channel coding theorem, and the purpose of channel coding. Key concepts discussed include linear codes, block codes, convolutional codes, encoding, decoding, and error detection/correction techniques.Read less
Information Theory: Introduction, Measure of information, Information content of message, Average Information content of symbols in Long Independent sequences, Average Information content of symbols in Long dependent sequences, Markov Statistical Model for Information Sources, Entropy and Information rate of Mark off Sources
Error Control Coding: Introduction, Examples of Error control coding, methods of Controlling Errors, Types of Errors, types of Codes, Linear Block Codes: matrix description of Linear Block Codes, Error detection & Correction capabilities ofLinear Block Codes, Single error correction Hamming code, Table lookup Decoding using Standard Array.
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The olfactory bulb processes inputs from olfactory receptor neurons (ORNs) through two levels: the glomerular layer at the site of input, and the granule cell level at the site of output to the olfactory cortex. The sequence of action of these two levels has not yet been examined. We analyze this issue using a novel computational framework that is scaled up, in three-dimensions (3D), with realistic representations of the interactions between layers, activated by simulated natural odors, and constrained by experimental and theoretical analyses. We suggest that the postulated functions of glomerular circuits have as their primary role transforming a complex and disorganized input into a contrast-enhanced and normalized representation, but cannot provide for synchronization of the distributed glomerular outputs. By contrast, at the granule cell layer, the dendrodendritic interactions mediate temporal decorrelation, which we show is dependent on the preceding contrast enhancement by the glomerular layer. The results provide the first insights into the successive operations in the olfactory bulb, and demonstrate the significance of the modular organization around glomeruli. This layered organization is especially important for natural odor inputs, because they activate many overlapping glomeruli.
A network of neurons in the olfactory bulb (OB) implements information processing functions that are necessary for odor recognition. The network is organized into two layers. In the first layer, the olfactory nerves end in modules called glomeruli, where they connect to the dendrites of mitral and tufted cells, and interneurons called juxtaglomerular cells. At the second level, the mitral and tufted cells connect to granule cell interneurons which are modulated by deep short axon cells. The mitral and tufted cells connected to a given glomerulus form what we call a glomerular unit (GU), that is obviously central to processing the olfactory input.
To understand the full sequence of processing in the olfactory bulb, the olfactory glomerular layer needs to be subjected to the same combination of experimental and computational analysis. Experimental studies indicate that the processing involves complex interactions between the multiple cell types (Aungst et al., 2003; Wachowiak and Shipley, 2006; Whitesell et al., 2013). This presents a much more difficult obstacle to analysis than the relatively direct interactions between the mitral and granule cells at the deep layer. Abstract modeling reflects this complexity (e.g., Benjaminsson et al., 2013), and experimental constraints equivalent to those at the granule cell level are still lacking. As a consequence, there is no realistic 3D model at present for the successive processing that occurs at the two levels in the olfactory bulb.
In summary, the results obtained with this model suggest that a complex input signal is processed by the olfactory bulb in a multistage manner. Each processing layer is independently needed but not sufficient to operate on the input in a specific way in order to obtain an output that will be further decorrelated and recombined over space and time at the next stage, in the olfactory cortex.
All simulations were carried out with a fully integrated NEURON+Python parallel environment (NEURON v7.3, Hines and Carnevale, 1997) on a BlueGene/Q IBM supercomputer (CINECA, Bologna, Italy). The model and simulation files specifically used for this work will be available for public download in the ModelDB section of the Senselab database suite ( , acc.n.185318).
The synaptic plasticity rule was identical to that used in previous work (introduced in Migliore et al., 2007). Briefly, all synaptic weights started at zero and, in response to an odor input, each component (inhibitory or excitatory) of each dendrodendritic synapse changed according to the local spiking activity in the lateral dendrite of the mitral cell or in the granule cell synapse. As discussed in detail elsewhere (e.g., Migliore et al., 2010; Yu et al., 2014), the formation of synaptic clusters consistent with those observed experimentally is a robust process that can be understood by considering the follow dynamics:
Therefore, as long as: (1) action potentials backpropagate along the mitral cell lateral dendrites, (2) granule cells form dendrodendritic connections, and (3) LTD and LTP are induced by different levels of synaptic activity, a column will form independently from the specific learning rule.
In all cases, simulations were carried out using a 1 Hz sniffing frequency, with each sniff eliciting up to 85 spikes in each mitral cell; stimulation length was 7 s for the learning phase and 5 s for testing.
In order to compare and analyze the response to different odors we need the odor-response curve for each of our odor-glomerulus pairs. Since this information is not experimentally available, the next step is thus to implement these curves from suitable assumptions for all the parameters. For example, experimentally, the Hill coefficient, n, is quite variable, in the range [0.1,18] (e.g., Rospars et al., 2008; Cruz and Lowe, 2013; Marasco et al., 2016), and Fmax can be considered to be an intrinsic neuronal property related to the maximum activity that can be generated by any given ORN. For simplicity, in this paper we fixed their value to 2 and 25, respectively, for all cases. From the raw data (Vincis et al., 2012) we have the GLi for all of our odor-glomerulus pairs at a single concentration. We call this concentration cV and assume cV=1. For ηi (modulating the maximal response at high concentrations) and Ki (related to the concentration at which there is half-maximal activation), there are several experimental findings (e.g., Wachowiak and Cohen, 2001; Rospars et al., 2008; Cruz and Lowe, 2013), showing that each odor-glomerulus pair can exhibit an apparently arbitrary combination of these parameters. To derive their values, it would be necessary and sufficient to find two independent equations for each odor-glomerulus pair. We determined these equations as follows.
There are different neuron populations at the glomerular layer (GL) level (Aungst et al., 2003). The current view is that they interact among themselves and with an odor input to implement two major mechanisms:
The synaptic conductance in each mitral cell (Equation 1) thus takes into account both the (presynaptic) ORN response to a given odor concentration (Equation 2) and its (postsynaptic) modulation by glomerular processing, Equations (3) and (4). Unless otherwise noted, the overall input in each glomerulus was represented in all figures (using color coded circles) as the average signal activated in the 5 MCs belonging to it.
The total simulation time was first divided in bins of equal size, with each bin set to 1 if it contains at least one spike and 0 otherwise. The probability that any two MCs generate a spike within the same time bin, which can be considered as a measure of synchronization, was estimated by exploring the spikes generated within a sliding time window, as explained in detail in Figure S2; the information content carried out by synchronous spikes can be calculated from their probability (see the Results).
Information about an odor is contained in the activity of the olfactory receptor neurons (ORNs), which are organized in functional classes, each expressing a particular receptor (Buck, 1993; Sullivan et al., 1994). To understand better the input/output (I/O) operations of the olfactory bulb, it is thus necessary to have first a physiologically plausible representation of the signal that is delivered to any mitral cell, representing an odor and its concentration. This can be expected to be particularly important for natural odors, which appear to activate many ORN types with a complex spatiotemporal distribution (Vincis et al., 2012). We start from the experimental findings (Carey et al., 2009) suggesting that, during a sniff, the axons of a homogeneous population of ORNs converging onto a single glomerulus generate a typical signal with precise temporal pattern dynamics (Figure 1A). These axons release glutamate, which excites AMPA and NMDA receptors on the mitral cell dendritic tufts (reviewed in Shepherd et al., 2004). Importantly, the peak amplitude of this pattern changes with odor identity and concentration, but not its temporal dynamics (Cruz and Lowe, 2013).
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