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Fifty Years of Shannon Theory
, 1998
"... A brief chronicle is given of the historical development of the central problems in the theory of fundamental limits of data compression and reliable communication. ..."
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Cited by 49 (1 self)
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A brief chronicle is given of the historical development of the central problems in the theory of fundamental limits of data compression and reliable communication.
New Upper Bounds on Error Exponents
"... We derive new upper bounds on the error exponents for the maximum likelihood decoding and error detecting in the binary symmetric channels. This is an improvement on the straightline bound by ShannonGallagerBerlekamp (1967) and the McElieceOmura (1977) minimum distance bound. For the probability ..."
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Cited by 27 (6 self)
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We derive new upper bounds on the error exponents for the maximum likelihood decoding and error detecting in the binary symmetric channels. This is an improvement on the straightline bound by ShannonGallagerBerlekamp (1967) and the McElieceOmura (1977) minimum distance bound. For the probability of undetected error the new bounds are better than the recent bound by AbdelGhaffar (1997) and the minimum distance and straightline bounds by Levenshtein (1978, 1989). We further extend the range of rates where the undetected error exponent is known to be exact. Keywords: Error exponents, Undetected error, Maximum likelihood decoding, Distance distribution, Krawtchouk polynomials. Submitted to IEEE Transactions on Information Theory 1 Introduction A classical problem of the information theory is to estimate probabilities of undetected and decoding errors when a block code is used for information transmission over a binary symmetric channel (BSC). We will study here exponential bounds ...
Distance distribution of binary codes and the error probability of decoding
 IEEE TRANS. INFORM. THEORY
, 2005
"... We address the problem of bounding below the probability of error under maximumlikelihood decoding of a binary code with a known distance distribution used on a binarysymmetric channel (BSC). An improved upper bound is given for the maximum attainable exponent of this probability (the reliability ..."
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Cited by 15 (1 self)
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We address the problem of bounding below the probability of error under maximumlikelihood decoding of a binary code with a known distance distribution used on a binarysymmetric channel (BSC). An improved upper bound is given for the maximum attainable exponent of this probability (the reliability function of the channel). In particular, we prove that the “random coding exponent ” is the true value of the channel reliability for codes rate in some interval immediately below the critical rate of the channel. An analogous result is obtained for the Gaussian channel.
Lower bounds on the error probability of block codes based on improvements on de Caen’s inequality
 IEEE TRANS. INFORM. THEORY
, 2004
"... New lower bounds on the error probability of block codes with maximumlikelihood decoding are proposed. The bounds are obtained by applying a new lower bound on the probability of a union of events, derived by improving on de Caen’s lower bound. The new bound includes an arbitrary function to be op ..."
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Cited by 14 (0 self)
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New lower bounds on the error probability of block codes with maximumlikelihood decoding are proposed. The bounds are obtained by applying a new lower bound on the probability of a union of events, derived by improving on de Caen’s lower bound. The new bound includes an arbitrary function to be optimized in order to achieve the tightest results. Since the optimal choice of this function is known, but leads to a trivial and useless identity, we find several useful approximations for it, each resulting in a new lower bound. For the additive white Gaussian noise (AWGN) channel and the binarysymmetric channel (BSC), the optimal choice of the optimization function is stated and several approximations are proposed. When the bounds are further specialized to linear codes, the only knowledge on the code used is its weight enumeration. The results are shown to be tighter than the latest bounds in the current literature, such as those by Seguin and by Keren and Litsyn. Moreover, for the BSC, the new bounds widen the range of rates for which the union bound analysis applies, thus improving on the bound to the error exponent compared with the de Caenbased bounds.
Supplement to: Code Spectrum and Reliability Function: Binary Symmetric Channel
, 2007
"... A much simpler proof of Theorem 1 from [1] is presented below, using notation and formulas numeration of [1]. The text below replaces the subsection General case from §4 of [1, p. 11]. General case. In the general case for some ω we are interested in a pairs (xi, xj) with dij = ωn. But there may exi ..."
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Cited by 1 (1 self)
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A much simpler proof of Theorem 1 from [1] is presented below, using notation and formulas numeration of [1]. The text below replaces the subsection General case from §4 of [1, p. 11]. General case. In the general case for some ω we are interested in a pairs (xi, xj) with dij = ωn. But there may exist a pairs (xk, xl) with dkl < ωn. Using the “cleaning” procedure [2] we show that the influence of such pairs (xk, xl) on the value Pe is not large. It will allow us to reduce the general case to the model one. Note that if 1 n log Xmax(t, ω) = o(1) , n → ∞ , (S.1) then from (27) and (28) we get 1 1 log n Pe + min 0≤t≤1 min t log
Fifty Years of Shannon Theory
, 1998
"... A brief chronicle is given of the historical development of the central problems in the theory of fundamental limits of data compression and reliable communication. ..."
Abstract
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A brief chronicle is given of the historical development of the central problems in the theory of fundamental limits of data compression and reliable communication.
Tradeoff Between Source and Channel Coding for Erasure Channels
, 2005
"... Abstract — In this paper, we investigate the optimal tradeoff between source and channel coding for channels with bit or packet erasure. Upper and Lower bounds on the optimal channel coding rate are computed to achieve minimal endtoend distortion. The bounds are calculated based on a combination o ..."
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Abstract — In this paper, we investigate the optimal tradeoff between source and channel coding for channels with bit or packet erasure. Upper and Lower bounds on the optimal channel coding rate are computed to achieve minimal endtoend distortion. The bounds are calculated based on a combination of sphere packing, straight line and expurgated error exponents and also high rate vector quantization theory. By modeling a packet erasure channel in terms of an equivalent bit erasure channel, we obtain bounds on the packet size for a specified limit on the distortion. Index terms–Joint source and channel coding, binary erasure channel, packet erasure, error exponent, high rate vector quantization. I.