This paper considers the joint compression and enhancement problem for speech signal in the presence of noise. Recently, the SoundStream codec, which relies on end-to-end joint training of an encoder-decoder pair and a residual vector quantizer by a combination of adversarial and reconstruction losses,has shown very promising performance, especially in subjective perception quality. In this work, we provide a theoretical result to show that, to simultaneously achieve low distortion and high perception in the presence of noise, there exist an optimal two-stage optimization procedure for the joint compression and enhancement problem. This procedure firstly optimizes an encoder-decoder pair using only distortion loss and then fixes the encoder to optimize a perceptual decoder using perception loss. Based on this result, we construct a two-stage training framework for joint compression and enhancement of noisy speech signal. Unlike existing training methods which are heuristic, the proposed two-stage training method has a theoretical foundation. Finally, experimental results for various noise and bit-rate conditions are provided. The results demonstrate that a codec trained by the proposed framework can outperform SoundStream and other representative codecs in terms of both objective and subjective evaluation metrics. Code is available at \textit{https://github.com/jscscloris/SEStream}.
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