Error exponents in scalable source coding

The characterization of the set of achievable rate and distortion values for scalable source coding is extended to additionally account for error exponents, namely, the negative normalized asymptotic log likelihood of error events at different layers. The "error" at each layer is defined as the event that the source block is not reproduced within the prespecified fidelity at the corresponding decoder. We consider separate error events at each layer so as to allow a tradeoff analysis for the error exponents when the rate and distortion values are fixed. For two-step coding of discrete memoryless sources, we derive a single-letter characterization of the region of all achievable 6-tuples (R₁, R₂, E₁, E₂, D₁, D₂), i.e., the rate, error exponent, and distortion levels at each layer. We also analyze the special case of successive refinability, where (R₁, E₁, D₁) and (R₂, E₂, D₂) individually achieve the nonscalable bounds. A surprising outcome of the analysis is that for any D₁, D₂, and E₁, there exists a finite threshold Eˆ₂≥E₁ such that successive refinability is ensured for all E₂≥Eˆ₂.