Joint Source–Channel Coding Error Exponent for Discrete Communication Systems With Markovian Memory

Zhong, Yangfan; Alajaji, Fady; Campbell, L. L.

doi:10.1109/tit.2007.909092

Cited by 18 publications

(19 citation statements)

References 17 publications

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“…(107) Remark 6. Many existing papers [7], [11], [8] discussed the separation scheme, and they focused on the value P s (e s,k,A , d s,A,k ) * P c (e c,A,n , d c,n,A ). However, they did not give a rigorous derivation of this value.…”

Section: A Formulation For Separation Codingmentioning

confidence: 99%

“…To resolve this problem, we often consider the channel coding with the message subject to the non-uniform distribution. Such a problem is called source-channel joint coding and has been actively studied by several researchers [12], [10], [11], [6], [9], [8]. As a simple case, we often assume that the message is subject to the independent and identical distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the capacity is given as the ratio of the conventional channel capacity to the entropy of the message. Several studies [12], [10], [11] derived the exponential decreasing rate of the decoding error probability in this setting. Recently, while Wang-Ingber-Kochman [6] and Kostina-Verdú [9], [24] discussed the second-order coefficient in this problem, The material in this paper will be presented in part at the 2017 IEEE International Symposium on Information Theory (ISIT 2017), Aachen (Germany), 25-30 June 2017.…”

Section: Introductionmentioning

confidence: 99%

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Second order analysis for joint source-channel coding with Markovian source

Yaguchi

Hayashi

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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We derive the second order rates of joint source-channel coding, whose source obeys an irreducible and ergodic Markov process when the channel is a discrete memoryless, while a previous study solved it only in a special case. We also compare the joint source-channel scheme with the separation scheme in the second order regime while a previous study made a notable comparison only with numerical calculation. To make these two notable progress, we introduce two kinds of new distribution families, switched Gaussian convolution distribution and * -product distribution, which are defined by modifying the Gaussian distribution.

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Section: A Formulation For Separation Codingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Second order analysis for joint source-channel coding with Markovian source

Yaguchi

Hayashi

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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“…Since related work concerning the finite-length analysis is reviewed in Section 1.1 , we only review work related to the asymptotic analysis here. Some studies on Markov chains for the large deviation regime have been reported [ 40 , 41 , 42 ]. The derivation in [ 40 ] used the Markov-type method.…”

Section: Introductionmentioning

confidence: 99%

“…A drawback of this method is that it involves a term that stems from the number of types, which does not affect the asymptotic analysis, but does hurt the finite-length analysis. Our achievability is derived by following a similar approach as in [ 41 , 42 ], i.e., the Perron–Frobenius theorem, but our derivation separates the single-shot part and the evaluation of the Rényi entropy, and thus is more transparent. Furthermore, the converse part of [ 41 , 42 ] is based on the Shannon–McMillan–Breiman limiting theorem and does not yield finite-length bounds.…”

Section: Introductionmentioning

confidence: 99%

Finite-Length Analyses for Source and Channel Coding on Markov Chains

Hayashi

Watanabe

2020

Entropy

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We study finite-length bounds for source coding with side information for Markov sources and channel coding for channels with conditional Markovian additive noise. For this purpose, we propose two criteria for finite-length bounds. One is the asymptotic optimality and the other is the efficient computability of the bound. Then, we derive finite-length upper and lower bounds for coding length in both settings so that their computational complexity is efficient. To discuss the first criterion, we derive the large deviation bounds, the moderate deviation bounds, and second order bounds for these two topics, and show that these finite-length bounds achieves the asymptotic optimality in these senses. For this discussion, we introduce several kinds of information measure for transition matrices.

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Error Exponents for Asymmetric Two-User Discrete Memoryless Source-Channel Systems

Zhong

Alajaji

Campbell

2007

2007 IEEE International Symposium on Information Theory

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Abstract-Consider transmitting two discrete memoryless correlated sources, consisting of a common and a private source, over a discrete memoryless multi-terminal channel with two transmitters and two receivers. At the transmitter side, the common source is observed by both encoders but the private source can only be accessed by one encoder. At the receiver side, both decoders need to reconstruct the common source, but only one decoder needs to reconstruct the private source. We hence refer to this system by the asymmetric 2-user source-channel system. In this work, we derive a universally achievable joint source-channel coding (JSCC) error exponent pair for the 2-user system by using a technique which generalizes Csiszár's method [3] for the pointto-point (single-user) discrete memoryless source-channel system. We next investigate the largest convergence rate of asymptotic exponential decay of the system (overall) probability of erroneous transmission, i.e., the system JSCC error exponent. We obtain lower and upper bounds for the exponent. As a consequence, we establish the JSCC theorem with single letter characterization.

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Joint Source–Channel Coding Error Exponent for Discrete Communication Systems With Markovian Memory

Cited by 18 publications

References 17 publications

Second order analysis for joint source-channel coding with Markovian source

Second order analysis for joint source-channel coding with Markovian source

Finite-Length Analyses for Source and Channel Coding on Markov Chains

Error Exponents for Asymmetric Two-User Discrete Memoryless Source-Channel Systems

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