R. Fano. Transmission of Information. MIT Press, Cambridge, 1961.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the 1970 s, it wasn t until the publication of an accessible implementation [14] that it achieved the popularity it has today. Over the past ten years arithmetic coding has been refined and its advantages and disadvantages over rival compression schemes, particularly Hu#man [9] and Shannon Fano [5] coding, have been elucidated. Arithmetic coding produces a theoretically optimal compression under much weaker assumptions than Hu#man and Shannon Fano, and can compress within one bit of the limit imposed by Shannon s Noiseless Coding Theorem [13] Additionally, arithmetic coding is well suited ....

R. M. Fano. Transmission of Information. MIT Press, Cambridge MA, and Wiley, NY, 1961.

....predictable. In this section, we use the point wise mutual information between adjacent syllables to estimate how well a syllable can be predicted from the preceding one, and show that there is a correlation between mutual information scores and prosodic strength. Point wise mutual information [10, 5] is a measure of how strongly two events axe associated, and is defined as I(a; b) log2(P(a, b) P(a)P(b) 11) where P(a) is the probability of the event a, P(b) is the probability of the event b, and P(a, b) is the probability of a and b occurring together. If a and b axe independent events, ....

FANO, R. Transmission of Information. MIT Press, 1961.

....it is not su#cient as a filtering mechanism. Confidence overemphasizes common items as consequents and rare items as antecedents (e.g. Key West =# United States ) The consequent in such cases rarely adds much meaning to a topic identifier. Instead of confidence we use mutual information [34]: log 2 P (x, y) P (x)P (y) This is a measure of correlation strength, i.e. the ratio of the actual probability of a frequent itemset occurring in a document to the probability of them occurring together by chance. This measure emphasizes relatively rare items that generally occur ....

R. Fano, Transmission of Information, MIT Press, 1961.

....derived in the next section, are tighter than these bounds, and non trivial for a larger range of signal to noise ratios. 3. IMPROVED BOUNDS Many bounds for the decoding error probability of a block or convolutional code are based on the following simple inequality, originally introduced by Fano [4], and repeatedly used in [1] see also [5 8] Let E be a decoding error event. Consider the two disjoint events corresponding to few , F , and many , M, errors. Then P (E) P (E F)P (F) P (E M)P (M) # # P (E F)P (F) P (M) P (E , F) P (M) 24) 6 Di#erent ....

R. M. Fano, Transmission of Information, MIT Press, 1961.

....same length and rate. This paper is broken into three sections, each dealing with a different channel, the binary symmetric channel (BSC) the binary erasure channel (BEC) and the additive white Gaussian noise (AWGN) channel. Each section begins with a numerical evaluation of the classic (e.g. [1] [4] lower bound on the codeword error rate for an code operating on the chanManuscript received March 27, 1997; revised March 23, 1998. This work was supported by a Grant from NSF s Networking and Communications Research Division. S. J. MacMullan was with the Department of Electrical ....

R. Fano, Transmission of Information. Cambridge, MA: MIT Press, 1961.

....and corpora of sufficient size been made available to the research community [32, 100] in order to perform some of the many experiments implied by the structuralist perspective. Word associations can be extracted from corpora by borrowing the information theoretic measure of mutual information [84, 86, 48, 37]; if P (x) and P (y) are the independent probabilities of events x and y, then the mutual information, I(x; y) is I(x; y) log P (x; y) P (x)P (y) 4:1) This measure compares how likely x and y are to occur together in the case of words, this means serial occurrence, so that I(x; y) is ....

R. Fano. Transmission of Information. M.I.T. Press, 1961.

....Shannon who provided the theoretical basis for the eld of information theory. Information theory is a eld whose initial development is largely attributed to Claude Shannon [Sha 48] and others such as Norbert Weiner [Wie 48] logarithmic measure) Wie 49] credited in [Sha 48] Robert Fano [Fan 61] credited in [Sha 48] David Hu man [Huf 52] Gilbert [Gil 52] and McMillan [McM 53] 1 The mid 1940s through the mid 1950s laid down a mathematical basis not only for data compression but 1 Although the statistician R. A. Fischer in 1925 introduced in the technical sense a de nition of ....

Robert M. Fano, Transmission of Information, MIT Press, Cambridge MA, 1961.

.... (IT) as the mathematical infrastructure, because it is the best possible approach to deal with manipulation of information [35] Shannon in a 1948 classical paper laid down the foundations of IT [36] IT has had a tremendous impact in the design of efficient and reliable communication systems [8] [12] because it is able to answer two key questions: what is the best possible (minimal) code for our data, and what is the maximal amount of information which can be transferred through a particular channel. In spite of its practical origins, IT is a deep mathematical theory concerned with the very ....

....questions: what is the best possible (minimal) code for our data, and what is the maximal amount of information which can be transferred through a particular channel. In spite of its practical origins, IT is a deep mathematical theory concerned with the very essence of the communication process [12].IT has also impacted statistics [22] and statistical mechanics by providing a clearer understanding of the nature of entropy as illustrated by Jaynes [19] These advances are predicated however on the specification of the data distributions, which is not realistic for the design of learning ....

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Fano R., "Transmission of information", MIT Press, 1961.

....either the probability of taking the left branch is between 1 3 and 2 3 (we call such a node a balanced node) or the branch with higher probability is a leaf of the tree. Examples of such codes are those de ned by the bits sent by the client in protocol Computation ecient, and Fano codes [4]. Let E( be the expected codeword length using the code on a string x i drawn from the distribution D. Using an argument similar to the proof of Theorem 1, we show that E( O(H(D) 1) We rst point out that along any path from the root to a leaf, there can be at most one branch ....

R.M. Fano. Transmission of Information. MIT Press, Cambridge, Mass., 1961.

....and corpora of sufficient size been made available to the research community [31, 84] to allow them to perform some of the many experiments indicated by a structuralist perspective. Word associations can be extracted from corpora by borrowing the information theoretic measure of mutual information [67, 69, 43, 34]; if P (x) and P (y) are the independent probabilities of events x and y, then the mutual information, M(x; y) is M(x; y) log P (x; y) P (x)P (y) 1) This measure compares how likely x and y are to occur together in the case of words, this means serial occurrence, so that M(x; y) is not ....

R. Fano. Transmission of Information. M.I.T. Press, 1961.

....decision tree construction is NP complete even in three dimensions. 19 Thanks to Kevin Van Horn for pointing this out. 31 2.6. 2 Other analytical results Goodman and Smyth [174] showed that greedy top down induction of decision trees is directly equivalent to a form of Shannon Fano prefix coding [131]. A consequence of this result is that top down tree induction (using mutual information) is necessarily suboptimal in terms of average tree depth. Trees of maximal size generated by the CART algorithm [44] have been shown to have an error rate bounded by twice the Bayes error rate, and to be ....

R. M. Fano. Transmission of Information. MIT Press, Cambridge, MA, 1961.

....[BCW90] and [W91] 2.1.2. Coding A statistical coder assigns a code to each string based on the probabilities given by the model. For a static or semi adaptive model, Huffman coding, ShannonFano coding and arithmetic coding attempt to assign short codes to frequently occurring input strings [F49, H52, FW78]. Dynamic Huffman coding and arithmetic coding are examples of statistical coders that work in conjunction with an adaptive model [K82, V87, RL79, L84, WNC87] Codeword based statistical coders replace input strings by codewords to obtain a more compact representation of the input. Huffman coding ....

Fano, R. M. Transmission of Information, M.I.T. Press, Cambridge, Mass., 1949.

....ratio. This is only true, however, under the constraints that each source message is mapped to a unique codeword and that the compressed text is the concatenation of the codewords for the source messages. An earlier algorithm, due independently to Shannon and Fano [Shannon and Weaver 1949; Fano 1949], is not guaranteed to provide optimal codes, but approaches optimal behavior as the number of messages approaches infinity. The Huffman algorithm is also of importance because it has provided a foundation upon which other data compression techniques have built and a benchmark to which they may be ....

Fano, R. M. 1949. Transmission of Information. M. I. T. Press, Cambridge, Mass.

....either the probability of taking the left branch is between 1 3 and 2 3 (we call such a node a balanced node) or the branch with higher probability is a leaf of the tree. Examples of such codes are those defined by the bits sent by the client in protocol Computation efficient, and Fano codes [3]. Let E( be the expected codeword length using the code on a string x i drawn from the distribution D. Using an argument similar to the proof of Theorem 1, we show that E( O(H(D) 1) We first point out that along any path from the root to a leaf, there can be at most one branch that ....

R.M. Fano. Transmission of Information. MIT Press, Cambridge, Mass., 1961.

....last set in the partition (denoted X r ) contains exactly 1 string. Also note that each set X j either contains only one string, or contains between 1 3 and 2 3 of the remaining probability weight. We can compare the partition of the strings into the sets X i with the construction of a Fano code [5] (see also [4] To construct a Fano code, the strings are likewise sorted in order of probability, and then divided into as close to two equally probable sets as possible. The first bit of the codeword is assigned to a 1 if the string lies in the first set, and a 0 if the string lies in the ....

....either the probability of taking the left branch is between 1 3 and 2 3 (we call such a node a balanced node) or the branch with higher probability is a leaf of the tree. Examples of such codes are those defined by the bits sent by the client in protocol Computation efficient, and Fano codes [5]. Let E( be the expected codeword length using the code on a string x i drawn from the distribution D. Using an argument similar to the proof of Theorem 1, we show that E( O(1 H(D) As before, along any path from the root to a leaf, there is at most one node that is not balanced. ....

R.M. Fano. Transmission of Information. MIT Press, Cambridge, Mass., 1961.

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R. Fano. Transmission of Information. MIT Press, Cambridge, 1961.

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R.M.Fano, Transmission of Information, Cambridge : MIT Press, 1961. 32

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Fano, R. M. Transmission of Information. Wiley, New York, 1961.

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R. M. Fano. Transmission of Information. MIT Press, Cambridge, MA, 1961.

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Fano, R. 1961. Transmission of Information. New York, New York: MIT Press.

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R.M. Fano, "Transmission of Information", John Wiley and Sons, New York, pp. 168--178, 1961.

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R. Fano., Transmission of information, MIT Press, (1961).

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R. M. Fano, Transmission of Information. Cambridge, Mass.: MIT Press & Wiley, 1961.

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R. M. Fano, Transmission of Information. Cambridge, Mass.: MIT Press and Wiley, 1961.

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R. M. Fano, Transmission of Information, MIT Press, 1961.

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