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The Art of Signaling: Fifty Years of Coding Theory
, 1998
"... In 1948 Shannon developed fundamental limits on the efficiency of communication over noisy channels. The coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero. Fifty years later, codes for the Gaus ..."
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In 1948 Shannon developed fundamental limits on the efficiency of communication over noisy channels. The coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero. Fifty years later, codes for the Gaussian channel have been discovered that come close to these fundamental limits. There is now a substantial algebraic theory of errorcorrecting codes with as many connections to mathematics as to engineering practice, and the last 20 years have seen the construction of algebraicgeometry codes that can be encoded and decoded in polynomial time, and that beat the Gilbert–Varshamov bound. Given the size of coding theory as a subject, this review is of necessity a personal perspective, and the focus is reliable communication, and not source coding or cryptography. The emphasis is on connecting coding theories for Hamming and Euclidean space and on future challenges, specifically in data networking, wireless communication, and quantum information theory.
BiCMOS circuits for analog Viterbi decoders
 IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process
, 1998
"... ..."
Optimal sequence detection and optimal symbolbysymbol detection: similar algorithms
 IEEE Trans. Comm
, 1982
"... AbstractAn algorithm is derived which performs optimal symbolbysymbol detection of a pulse amplitude modulated sequence. The algorithm is similar to the Viterhi algorithm with the optimality criterion optimal symbol detection rather than optimal sequence detection. A salient common feature is the ..."
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AbstractAn algorithm is derived which performs optimal symbolbysymbol detection of a pulse amplitude modulated sequence. The algorithm is similar to the Viterhi algorithm with the optimality criterion optimal symbol detection rather than optimal sequence detection. A salient common feature is the merge phenomenon which allows common decisions to be made before the entire sequence is received.
Differential Signaling with Reduced Number of Paths
 in IEEE Transactions on Circuit and SystemsII: Analog and Signal Processing
, 2001
"... ..."
An Integrated 200MHz 3.3V BiCMOS ClassIV PartialResponse Analog Viterbi Decoder
 IEEE J. SolidState Circuits
, 1998
"... Analog Viterbi decoders have recently been shown to be viable alternatives to their digital counterparts. In fact, a commercial analog classIV partialresponse sequence detector for magnetic read channels has already been reported. Analog decoders offer the advantages of reduced power and size prim ..."
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Cited by 5 (0 self)
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Analog Viterbi decoders have recently been shown to be viable alternatives to their digital counterparts. In fact, a commercial analog classIV partialresponse sequence detector for magnetic read channels has already been reported. Analog decoders offer the advantages of reduced power and size primarily due to the elimination of the A/D. The analog Viterbi decoder described here is less complex and more robust compared to other reported realizations. The decoder is based on a new derivation of the differencemetric algorithm which is developed from an analog implementation perspective. This has resulted in a decrease in hardware complexity thereby making an analog approach more attractive for today's demanding highspeed, lowpower, and smallsize applications, such as magnetic diskdrive storage systems. The decoder was fabricated in a 0.8m BiCMOS process. It consists of two timeinterleaved dicodes and the interleaving circuitry. The decoder was tested at up to 100 MS/s. However, si...
Partialresponse
"... signaling for phasechange optical data storage without electronic equalization ..."
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signaling for phasechange optical data storage without electronic equalization
Channel Coding for High Speed Links
, 2007
"... All rights reserved. This thesis explores the benefit of channel coding for highspeed backplane or chiptochip interconnects, referred to as the highspeed links. Although both powerconstrained and bandwidthlimited, the highspeed links need to support data rates in the Gbps range at low error pro ..."
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All rights reserved. This thesis explores the benefit of channel coding for highspeed backplane or chiptochip interconnects, referred to as the highspeed links. Although both powerconstrained and bandwidthlimited, the highspeed links need to support data rates in the Gbps range at low error probabilities. Modeling the highspeed link as a communication system with noise and intersymbol interference (ISI), this work identifies three operating regimes based on the underlying dominant error mechanisms. The resulting framework is used to identify the conditions under which standard error control codes perform optimally, incur an impractically large overhead, or provide the optimal performance in the form of a single parity check code. For the regime where the standard error control codes are impractical, this thesis introduces lowcomplexity
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"... the estimate of source bits {ai}. For the nth OFDM symbol duration, the vector consisting of N output samples of S/P converter is expressed as where yn = [ynN,ynN+1, ·· ·,ynN+N−1] T = HnGdn + wn (2) dn =[dnM,dnM+1, ·· ·,dnM+M−1] T and Hn and wn are Npoint FFT of channel impulse response and additi ..."
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the estimate of source bits {ai}. For the nth OFDM symbol duration, the vector consisting of N output samples of S/P converter is expressed as where yn = [ynN,ynN+1, ·· ·,ynN+N−1] T = HnGdn + wn (2) dn =[dnM,dnM+1, ·· ·,dnM+M−1] T and Hn and wn are Npoint FFT of channel impulse response and additive noise, respectively, in the nth OFDM symbol interval. Suppose the channel in timeinvariant during an OFDM symbol interval, the channel matrix is a diagonal matrix with diagonal elements {Hn,0, Hn,1, ·· ·,Hn,N−1}, which is the Npoint FFT of the timedomain multipath channel impulse response. From the correlatively coding matrix, it is observed that the received signal, {ynM+m, for m =0, 1, ···N − 1}, is the convolution of the coefficients {Gm,0, Gm,1, ·· ·,Gm,L} with the symbols {dmM, dmM+1, ·· · , dmM+M−1}, and deteriorated by the channel gain Hn,m and additive noise wn,m. There are many method to estimate the symbols in the vector dn, such as zeroforcing (ZF) receiver, minimum meansquareerror (MMSE) receiver, maximum likelihood (ML) receiver [10], etc. As the symbols in dn =[dnM,dmM+1, ·· ·,dmM+M−1] T are estimated, the estimation of the coded and interleaved bits, cn = [cnMNc, ·· · , cnMNc+Nc−1, c (nM+1)Nc, ·· · , c (nM+1)Nc+Nc−1, ····· ·,c (nM+M−1)Nc, ·· ·,c (n+1)MNc−1] T, with dimension MNc × 1, are obtained by inverting the mapping from c k to dn done at the transmitter. After that, the estimated sequence {ck} is deinterleaved to acquire the data sequence {bk}, which is fed to the channel decoder to obtain the final estimate of the source data sequence {ai}. III. DETECTOR AND DECODER As illustrated in Fig. 2, the receiver received the signal {y n}, and has the capability to estimate the source data bits {ai}. Conventionally, the detector and the decoder are conjugated to reach this job. On the other hand, an advanced receiver can produce soft detection and decoding and iteratively exchange the soft information between detector and decoder to refine the estimate of the data bits. The advanced signal processing is illustrated in the following.
Practical Applications of Coding Invited Paper
"... AbstractCoding applications have grown rapidly in the past several years with costeffective performance demonstrated on several channels. Convolutional coding with softdecision Viterbi decoding has emerged as a standard technique and is particularly well adapted to the communication satellite cha ..."
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AbstractCoding applications have grown rapidly in the past several years with costeffective performance demonstrated on several channels. Convolutional coding with softdecision Viterbi decoding has emerged as a standard technique and is particularly well adapted to the communication satellite channel. Decoder implementations are discussed and examples are cited. Robustness of code performance is emphasized and instances of actual coding gain surpassing theoretical or basic coding gain are given. Some promising future directions are noted. I A.
19 Spectrum Control
"... Coding, which refers to the translation between the userprovided information bits (source bits) and the transmitted data symbols (coded symbols), Errorcontrol coding, whose aim is to mitigate the effects of noise, was discussed in Chapters 12 and 13. This chapter discusses the use of coding to con ..."
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Coding, which refers to the translation between the userprovided information bits (source bits) and the transmitted data symbols (coded symbols), Errorcontrol coding, whose aim is to mitigate the effects of noise, was discussed in Chapters 12 and 13. This chapter discusses the use of coding to control the statistics of the data symbols, thereby introducing a measure of control over the spectrum of the transmitted signal. For example, undesired correlations among information bits can be removed by scrambling, which is a reversible transformation of the bits in a way that affects the statistics. Alternatively, the spectrum can be controlled by introducing a controlled correlation among data symbols in the form of redundancy (the remaining sections). In Chapters 12 and 13 we saw applications of redundancy to the correction and prevention of channel errors. One way to control the spectrum is through the design of a line code (Sections 19.2 and 19.3). One major motivation in baseband systems is the problem of baseline wander introduced by the a.c. coupling inherent in transformers and broadband amplifiers. This phenomenon is described in Section 19.1. In Section 19.2 a number of different types of line codes for baseband systems are described, most of them oriented toward control of baseline wander.