A Lower Bound on the Expected Distortion of Joint Source-Channel Coding
Author(s)
Kochman, Yuval; Ordentlich, Or; Polyanskiy, Yury
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© 1963-2012 IEEE. We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the long-standing open problem of finding the rate of convergence of the smallest attainable expected distortion to its asymptotic value, as a function of the blocklength n. Our main result is that in general the convergence rate is not faster than n{-1/2}. In particular, we show that for the problem of transmitting i.i.d uniform bits over a binary symmetric channels with Hamming distortion, the smallest attainable distortion (bit error rate) is at least Omega (n{-1/2}) above the asymptotic value, if the 'bandwidth expansion ratio' is above 1.
Date issued
2020Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems; Massachusetts Institute of Technology. Institute for Data, Systems, and SocietyJournal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)