TY - JOUR
T1 - Operational duality between lossy compression and channel coding
AU - Gupta, Ankit
AU - Verdú, Sergio
N1 - Funding Information:
Manuscript received January 21, 2009; revised June 27, 2010; accepted December 09, 2010. Date of current version May 25, 2011. This work was partially supported by NSF Grants CCF-0635154 and CCF-0728445. This paper was presented in part at the 2009 Information Theory and Applications Workshop, San Diego, CA. A. Gupta is with Samsung Telecommunications America, Richardson, TX 75082 USA (e-mail: gupta.ankit@samsung.com). S. Verdú is with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: verdu@princeton.edu). Communicated by E. Yang, Associate Editor for Source Coding. Digital Object Identifier 10.1109/TIT.2011.2136910
PY - 2011/6
Y1 - 2011/6
N2 - We explore the duality between lossy compression and channel coding in the operational sense: whether a capacity-achieving encoder-decoder sequence achieves the rate-distortion function of the dual problem when the channel decoder [encoder] is the source compressor [decompressor, resp.], and vice versa. We show that, if used as a lossy compressor, the maximum-likelihood channel decoder of a randomly chosen capacity-achieving codebook achieves the rate-distortion function almost surely. However, operational duality does not hold for every capacity achieving encoder-decoder sequence, or rate-distortion achieving compressor-decompressor sequence. We show that there exist optimal channel coding [lossy compression] schemes, which fail when used for the dual lossy compression [channel coding resp.] problem.
AB - We explore the duality between lossy compression and channel coding in the operational sense: whether a capacity-achieving encoder-decoder sequence achieves the rate-distortion function of the dual problem when the channel decoder [encoder] is the source compressor [decompressor, resp.], and vice versa. We show that, if used as a lossy compressor, the maximum-likelihood channel decoder of a randomly chosen capacity-achieving codebook achieves the rate-distortion function almost surely. However, operational duality does not hold for every capacity achieving encoder-decoder sequence, or rate-distortion achieving compressor-decompressor sequence. We show that there exist optimal channel coding [lossy compression] schemes, which fail when used for the dual lossy compression [channel coding resp.] problem.
KW - Channel coding with cost constraints
KW - discrete memoryless channels
KW - discrete memoryless sources
KW - lossy data compression
KW - rate-distortion theory
KW - source-channel coding duality
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U2 - 10.1109/TIT.2011.2136910
DO - 10.1109/TIT.2011.2136910
M3 - Article
AN - SCOPUS:79957629039
SN - 0018-9448
VL - 57
SP - 3171
EP - 3179
JO - IRE Professional Group on Information Theory
JF - IRE Professional Group on Information Theory
IS - 6
M1 - 5773027
ER -