Source fidelity over fading channels: Erasure codes versus scalable codes

We consider the transmission of a Gaussian source through a block fading channel. Assuming each block is decoded independently, the received distortion depends on the tradeoff between quantization accuracy and probability of outage. Namely, higher quantization accuracy requires a higher channel code rate, which increases the probability of outage. Here we evaluate the received mean distortion with erasure coding across blocks as a function of the code length. We also evaluate the performance of scalable, or multi-resolution coding in which coded layers are superimposed, and the layers are sequentially decoded. In addition to analyzing a finite number of layers, we evaluate the mean distortion at high Signal-to-Noise Ratios as the number of layers becomes infinite. As the block length of the erasure code increases to infinity, the received distortion converges to a deterministic limit, which is less than the mean distortion with an infinite-layer scalable coding scheme. However, for the same standard deviation in received distortion, infinite layer scalable coding performs slightly better than erasure coding.