The straightforward application of Shannon's separation principle may entail a significant suboptimality in practical systems with limited coding delay and complexity. This is particularly evident when the lossy source code is based on entropy-coded quantization. In fact, it is well known that entropy coding is not robust to residual channel errors. In this paper, a joint source-channel coding scheme is advocated that combines the advantages and simplicity of entropy-coded quantization with the robustness of linear codes. The idea is to combine entropy coding and channel coding into a single linear encoding stage. If the channel is symmetric, the scheme can asymptotically achieve the optimal rate-distortion limit. However, its advantages are more clearly evident under finite coding delay and complexity. The sequence of quantization indices is decomposed into bitplanes, and each bitplane is independently mapped onto a sequence of channel coded symbols. The coding rate of each bitplane is chosen according to the bitplane conditional entropy rate. The use of systematic raptor encoders is proposed, in order to obtain a continuum of coding rates with a single basic encoding algorithm. Simulations show that the proposed scheme can outperform the separated baseline scheme for finite coding length and comparable complexity and, as expected, it is much more robust to channel errors in the case of channel capacity mismatch.
Empirical rate-distortion study of compressive sensing-based joint source-channel coding