On separation of source and channel coding in the finite block length regime

This paper investigates the validity of Shannon's separation theorem in the finite block length regime. Under optimal tradeoffs between source rate and channel block error probability obtained from finite block length analysis, noisy channel quantizers based on joint source-channel coding principles are shown to outperform the separate quantizer designed via Lloyd-Max in terms of end-to-end distortion. Numerical results for the scalar case under the binary symmetric channel and discrete-input memoryless channel demonstrate that the separation of source and channel coding no longer holds in the finite block length regime, but the advantages of joint designs may be large or small depending on the system configuration.