The adversarial joint source-channel problem

This paper introduces the problem of joint source-channel coding in the setup where channel errors are adversarial and the distortion is worst case. Unlike the situation in the case of stochastic source-channel model, the separation principle does not hold in adversarial setup. This surprising observation demonstrates that designing good distortion-correcting codes cannot be done by serially concatenating good covering codes with good error-correcting codes. The problem of the joint code design is addressed and some initial results are offered.

[1]  A. N. Shiryayev The Theory of Transmission of Information , 1993 .

[2]  M. Chiani Error Detecting and Error Correcting Codes , 2012 .

[3]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[4]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[5]  Aaron D. Wyner,et al.  Coding Theorems for a Discrete Source With a Fidelity CriterionInstitute of Radio Engineers, International Convention Record, vol. 7, 1959. , 1993 .

[6]  Toby Berger,et al.  Rate distortion theory : a mathematical basis for data compression , 1971 .

[7]  Andrei N. Kolmogorov,et al.  On the Shannon theory of information transmission in the case of continuous signals , 1956, IRE Trans. Inf. Theory.

[8]  Venkatesan Guruswami,et al.  A Lower Bound on List Size for List Decoding , 2005, IEEE Trans. Inf. Theory.

[9]  Michael Gastpar,et al.  To code, or not to code: lossy source-channel communication revisited , 2003, IEEE Trans. Inf. Theory.

[10]  Yuval Kochman,et al.  The dispersion of joint source-channel coding , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[11]  Robert J. McEliece,et al.  New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities , 1977, IEEE Trans. Inf. Theory.

[12]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[13]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[14]  Gérard D. Cohen,et al.  Covering Codes , 2005, North-Holland mathematical library.

[15]  Peter Elias,et al.  Error-correcting codes for list decoding , 1991, IEEE Trans. Inf. Theory.