Information Theory And Coding By Giridhar K Pdf


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The Present Application for Patent is related to the following co-pending U. Patent Applications, each of which is filed concurrently herewith, assigned to the assignee hereof, and expressly incorporated by reference herein:. Luby, et al. The following issued patents are expressly incorporated by reference herein for all purposes:.

Transmission of files between a sender and a recipient over a communications channel has been the subject of much literature. Preferably, a recipient desires to receive an exact copy of data transmitted over a channel by a sender with some level of certainty. Where the channel does not have perfect fidelity which covers most all physically realizable systems , one concern is how to deal with data lost or garbled in transmission.

Lost data erasures are often easier to deal with than corrupted data errors because the recipient cannot always tell when corrupted data is data received in error.

Typically, the particular code used is chosen based on some information about the infidelities of the channel through which the data is being transmitted and the nature of the data being transmitted.

For example, where the channel is known to have long periods of infidelity, a burst error code might be best suited for that application. Where only short, infrequent errors are expected a simple parity code might be best. In particular applications, there is a need for handling more than one level of service. For example, a broadcaster might broadcast two levels of service, wherein a device capable of receiving only one level receives an acceptable set of data and a device capable of receiving the first level and the second level uses the second level to improve on the data of the first level.

An example of this is FM radio, where some devices only received the monaural signal and others received that and the stereo signal. One characteristic of this scheme is that the higher layers are not normally useful without the lower layers. For example, if a radio received the secondary, stereo signal, but not the base signal, it would not find that particularly useful, whereas if the opposite occurred, and the primary level was received but not the secondary level, at least some useful signal could be provided.

For this reason, the primary level is often considered more worthy of protection relative to the secondary level. In the FM radio example, the primary signal is sent closer to baseband relative to the secondary signal to make it more robust.

Similar concepts exist in data transport and broadcast systems, where a first level of data transport is for a basic signal and a second level is for an enhanced layer. An example is H. An example is a 1 megabit per second mbps base layer and a 1 mbps enhancement layer. In general, if a receiver is able to decode all of the base layer, the receiver can provide a useful output and if the receiver is able to decode all of the enhancement layer the receiver can provide an improved output, however if the receiver cannot decode all of the base layer, decoding the enhancement layer does not normally provide anything useful.

With FEC, a transmitter, or some operation, module or device operating for the transmitter, will encode the data to be transmitted such that the receiver is able to recover the original data from the transmitted encoded data even in the presence of erasures and or errors.

Because of the differential in the effects of loss of one layer versus another, different coding might be used for different layers. For example, the data for a base layer might be transmitted with additional data representing FEC coding of the data in the base layer, followed by the data of the enhanced layer with additional data representing FEC coding of the data in the base layer and the enhanced layer.

With this approach, the latter FEC coding can provide additional assurances that the base layer can be successfully decoded at the receiver. While such a layered approach might be useful in certain applications, it can be quite limiting in other applications.

For example, the above approach can be impractical for efficiently decoding a union of two or more layers using some encoding symbols generated from one of the layers and other encoding symbols generated from the combination of the two or more layers.

Data can be encoded by assigning source symbols to base blocks, assigning base blocks to source blocks and encoding each source block into encoding symbols, where at least one pair of source blocks is such they have at least one base block in common with both source blocks of the pair and at least one base block not in common with the other source block of the pair.

The encoding of a source block can be independent of content of other source blocks. Decoding to recover all of a desired set of the original source symbols can be done from a set of encoding symbols from a plurality of source blocks wherein the amount of encoding symbols from the first source block is less than the amount of source data in the first source block and likewise for the second source block.

In specific embodiments, an encoder can encode source symbols into encoding symbols and a decoder can decode those source symbols from a suitable number of encoding symbols. The number of encoding symbols from each source block can be less than the number of source symbols in that source block and still allow for complete decoding.

In a more specific embodiment where a first source block comprises a first base block and a second source block comprises the first base block and a second base block, a decoder can recover all of the first base block and second base block from a set of encoding symbols from the first source block and a set of encoding symbols from the second source block where the amount of encoding symbols from the first source block is less than the amount of source data in the first source block, and likewise for the second source block, wherein the number of symbol operations in the decoding process is substantially smaller than the square of the number of source symbols in the second source block.

It should be understood that the specific embodiments described in Appendix A are not limiting examples of the invention and that some aspects of the invention might use the teachings of Appendix A while others might not.

It should also be understood that limiting statements in Appendix A may be limiting as to requirements of specific embodiments and such limiting statements might or might not pertain the claimed inventions and, therefore, the claim language need not be limited by such limiting statements. To facilitate understanding, identical reference numerals have been used where possible to designate identical elements that are common to the figures, except that suffixes may be added, where appropriate, to differentiate such elements.

The images in the drawings are simplified for illustrative purposes and are not necessarily depicted to scale. The appended drawings illustrate exemplary configurations of the disclosure and, as such, should not be considered as limiting the scope of the disclosure that may admit to other equally effective configurations. Correspondingly, it has been contemplated that features of some configurations may be beneficially incorporated in other configurations without further recitation.

The present invention is not limited to specific types of data being transmitted. However in examples herein, it will be assumed that the data could be transmitted is represented by a sequence of one or more source symbols and that each source symbol has a particular size, sometimes measured in bits.

While it is not a requirement, in these examples, the source symbol size is also the size of encoding symbols. In the terminology used herein, the data to be conveyed is represented by a number of source symbols, where K is used to represent that number.

In some cases, K is known in advance. For example, when the data to be conveyed is a file of unknown size and an integer multiple of the source symbol size, K would simply be the integer that is that multiple. However, it might also be the case that K is not known in advance of the transmission, or is not known until after the transmission has already started.

For example, where the transmitter is transmitting a data stream as the transmitter receives the data and does not have an indication of when the data stream might end. An encoder generates encoding symbols based on source symbols. Herein, the number of encoding symbols is often referred to as N. Information theory holds that if all source symbol values are equally possible, perfect recovery of the K source symbols requires at least K encoding symbols to be received assuming the same size for source symbols and encoding symbols in order to fully recover the K source symbols.

Thus, the code rate using FEC is usually less than one. In many instances, lower code rates allow for more redundancy and thus more reliability, but at a cost of lower bandwidth and possibly increased computing effort.

Likewise, each encoding symbol has a value and an index, the latter being to distinguish one encoding symbol from another, and also can be represented in computer- or electronically-readable form. Thus, it should be understood that often a symbol and its physical representation can be used interchangeably in descriptions. Depending on the codes used, the source symbols can be entirely recovered from the received encoding symbols which might be all repair symbols or some source symbols and some repair symbols.

In a non-systematic encoder, the encoding symbols might include some of the source symbols, but it is possible that all of the encoding symbols are repair symbols. When a decoder decodes input symbols, typically an additional step is needed to get to the source symbols, which is typically the ultimate goal of the decoder.

One efficient code is a simple parity check code, but the robustness is often not sufficient. Another code that might be used is a rateless code such as the chain reaction codes described in U.

Files can be of known size such as a one megabyte image stored on a hard disk or can be of unknown size such as a file taken from the output of a streaming source. Either way, the file is a sequence of source symbols, where each source symbol has a position in the file and a value.

Transmission is the process of transmitting data from one or more senders to one or more recipients through a channel in order to deliver a file. A sender is also sometimes referred to as the transmitter.

If one sender is connected to any number of recipients by a perfect channel, the received data can be an exact copy of the input file, as all the data will be received correctly. Here, we assume that the channel is not perfect, which is the case for most real-world channels. Of the many channel imperfections, two imperfections of interest are data erasure and data incompleteness which can be treated as a special case of data erasure. Data erasure occurs when the channel loses or drops data.

If a packet network is used, one or more symbol, or perhaps portions of symbols, are included in a packet for transmission and each packet is assumed to have been correctly received or not at all.

With FEC, the transmitter encodes data, by providing additional information, or the like, to make up for information that might be lost in transit and the FEC encoding is typically done in advance of exact knowledge of the errors, attempting to prevent errors in advance. In general, a communication channel is that which connects the sender and the recipient for data transmission.

The communication channel could be a real-time channel, where the channel moves data from the sender to the recipient as the channel gets the data, or the communication channel might be a storage channel that stores some or all of the data in its transit from the sender to the recipient. An example of the latter is disk storage or other storage device. In that example, a program or device that generates data can be thought of as the sender, transmitting the data to a storage device.

The recipient is the program or device that reads the data from the storage device. The mechanisms that the sender uses to get the data onto the storage device, the storage device itself and the mechanisms that the recipient uses to get the data from the storage device collectively form the channel.

If there is a chance that those mechanisms or the storage device can lose data, then that would be treated as data erasure in the communication channel. An encoder will operate to generate encoding symbols from the source symbols it is provided and will do so according to the erasure code it is provided or programmed to implement. When a set of encoding symbols is generated from one block, those encoding symbols can be used in combination with one another to recover that one block.

The neighborhood set might be a very sparse subset of the scope of the encoding symbol. Many block erasure codes, including chain reaction codes e. One example of a measurement of sparseness is the ratio of the number of symbols in the neighborhood set that an encoding symbol depends on to the number of symbols in the block.

For some codes, such as Raptor codes, encoding symbols are not generated directly from source symbols of the block, but instead from other intermediate symbols that are themselves generated from source symbols of the block. In any case, for Raptor codes, the neighborhood set can be much smaller than the size of the scope which is equal to the number of source symbols in the block of these encoding symbols.

In these cases where efficient encoding and decoding is a concern and the resulting code construction is sparse, the neighborhood set of an encoding symbol can be much smaller than its scope, and different encoding symbols may have different neighborhood sets even when generated from the same scope.

Since the blocks of a block erasure code are disjoint, the encoding symbols generated from one block cannot be used to recover symbols from a different block because they contain no information about that other block.

Typically, the design of codes, encoders and decoders for such disjoint block erasure codes behave a certain way due to the nature of the code. As a consequence, the decoding efficiency of the block erasure codes when applied to decode overlapping blocks is much worse than the decoding efficiency of these codes when applied to what they were designed for, i.

Where a systematic code is used and all of the encoding symbols are received correctly, the extras the repair symbols are not needed at the receiver, but if some source symbols are lost or erased in transit, the repair symbols can be used to repair such a situation so that the decoder can recover the missing source symbols.

With these definitions in mind, various embodiments will now be described. In an encoder, encoding symbols are generated from source symbols, input parameters, encoding rules and possibly other considerations. Because the encoder is block-based, a given encoding symbol depends only on source symbols within one source block and possibly other details , or alternatively, depends only on source symbols within its scope, and does not depend on source symbols outside of its source block or scope.

Block erasure codes are useful for allowing efficient encoding, and efficient decoding. For example, once a receiver successfully recovers all of the source symbols for a given source block, the receiver can halt processing of all other received encoding symbols that encode for source symbols within that source block and instead focus on encoding symbols for other source blocks.

In a simple block erasure encoder, the source data might be divided into fixed-size, contiguous and non-overlapping source blocks, i. Elastic erasure codes are different from block erasure codes in several ways. One is that elastic erasure code encoders and decoders operate more efficiently when faced with unions of overlapping blocks. For some of the elastic erasure code methods described herein, the generated encoding symbols are sparse, i.

For example, the size of the neighborhood set of each encoding symbol might be the square root of K when it is generated from a block of K source symbols, i.

Information Theory And Coding - ITC Study Materials

Create a Ning Network! Liberty Attendance Center - Class of Srinivas, K. Giridhar, and R. Koilpillai, "Orthogonal Decode and Forward. Kalyani, S.. Sorry, out of stock..

Information Theory and Coding — Information Theory and Coding releases state of the art international research that significantly improves the study of information and programming theory as well as their applications to network coding, cryptography, computational complexity theory, finite fields, Boolean functions and related scientific disciplines that make use of information. Class is cancelled on Tuesday, February A makeup class will be scheduled. Information theory and coding by j s chitode pdf List of ebooks and manuels about Information theory and coding by j s chitode pdf Third Edition Chitode. In neural coding, information theory can be used to precisely quantify the reliability of stimulus—response functions, and its usefulness in this context was recognized early 5,6,7,8. Download PDF.

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Pre-processed space-time trellis codes Abstract: Tarokh et al. If the wireless channels are static or fade very slowly, the channel state information can be sent back to the transmitter using a low bit rate feedback path. In such a situation, it may be possible to mitigate the effects of signal cancellation due to simultaneous transmission, by using some sort of pre-processing technique at the transmitter which incorporates the channel knowledge.

K.Giridhar

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Publications Please click here pdf for a list of recent journal publications and granted patents arising out of our research work. Most of the earlier publications are listed below. Journals [1] K. Giridhar, J. Shynk, and R.

The Present Application for Patent is related to the following co-pending U. Patent Applications, each of which is filed concurrently herewith, assigned to the assignee hereof, and expressly incorporated by reference herein:. Luby, et al. The following issued patents are expressly incorporated by reference herein for all purposes:.

information theory, coding and cryptography

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Код, не поддающийся взлому. Сьюзан вздохнула, мысли ее вернулись к Цифровой крепости. Она не могла поверить, что такой алгоритм может быть создан, но ведь доказательство налицо - у нее перед глазами. ТРАНСТЕКСТ не может с ним справиться. Сьюзан подумала о Стратморе, о том, как мужественно он переносит тяжесть этого испытания, делая все необходимое, сохраняя спокойствие во время крушения.

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Стратмор - человек гордый и властный, наблюдение за ним следует организовать так, чтобы никоим образом не подорвать его авторитета.

ГЛАВА 105 Огненный шар, рвущийся наверх сквозь миллионы силиконовых чипов, производил ни на что не похожий звук. Треск лесного пожара, вой торнадо, шипение горячего гейзера… все они слились в гуле дрожащего корпуса машины. Это было дыхание дьявола, ищущее выхода и вырывающееся из закрытой пещеры. Стратмор так и остался стоять на коленях, парализованный ужасающим, неуклонно приближающимся звуком. Самый дорогой компьютер в мире на его глазах превращался в восьмиэтажный ад.

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 Что ты говоришь? - засмеялся Стратмор.  - Что же ты предлагаешь. Открыть дверь и вызвать сотрудников отдела систем безопасности, я угадал. - Совершенно. Будет очень глупо, если вы этого не сделаете.

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Единственный терминал в шифровалке, с которого разрешалось обходить фильтры Сквозь строй, принадлежал Стратмору. Когда коммандер заговорил, в его голосе звучали ледяные нотки: - Мистер Чатрукьян, я не хочу сказать, что вас это не касается, но фильтры обошел.  - Очевидно, что Стратмор с трудом сдерживает гнев.  - Я уже раньше объяснял вам, что занят диагностикой особого рода.

Она не могла поверить, что такой алгоритм может быть создан, но ведь доказательство налицо - у нее перед глазами. ТРАНСТЕКСТ не может с ним справиться. Сьюзан подумала о Стратморе, о том, как мужественно он переносит тяжесть этого испытания, делая все необходимое, сохраняя спокойствие во время крушения. Иногда она видела в нем что-то от Дэвида.

Хотя большинство отделов АНБ работали в полном составе семь дней в неделю, по субботам в шифровалке было тихо. По своей природе математики-криптографы - неисправимые трудоголики, поэтому существовало неписаное правило, что по субботам они отдыхают, если только не случается нечто непредвиденное. Взломщики шифров были самым ценным достоянием АНБ, и никто не хотел, чтобы они сгорали на работе. Сьюзан посмотрела на корпус ТРАНСТЕКСТА, видневшийся справа.

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