A Lower Bound on the Expected Distortion of Joint Source-Channel Coding

02/21/2019

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by   Yuval Kochman, et al.

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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 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 Ω(n^-1/2) above the asymptotic value, if the "bandwidth expansion ratio" is above 1.