High-resolution bounds in lossy coding of a real memoryless source are considered when side information is present. Let X be a "smooth" source and let Y be the side information. First we treat the case when both the encoder and the decoder have access to Y and we establish an asymptotically tight (high-resolution) formula for the conditional rate-distortion function R/sub X|Y/(D) for a class of locally quadratic distortion measures which may be functions of the side information. We then consider the case when only the decoder has access to the side information (i.e., the "Wyner-Ziv problem"). For side-information-dependent distortion measures, we give an explicit formula which tightly approximates the Wyner-Ziv rate-distortion function R/sup WZ/(D) for small D under some assumptions on the joint distribution of X and Y. These results demonstrate that for side-information-dependent distortion measures the rate loss R/sup WZ/(D)-R/sub X|Y/(D) can be bounded away from zero in the limit of small D. This contrasts the case of distortion measures which do not depend on the side information where the rate loss vanishes as D/spl rarr/0.
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机译：存在辅助信息时，要考虑真实无记忆源的有损编码中的高分辨率界限。令X为“平滑”源，让Y为辅助信息。首先，我们处理编码器和解码器都可以访问Y的情况，并针对一类局部条件为条件速率失真函数R / sub X | Y /（D）建立渐近严格（高分辨率）公式二次失真测量，可能是辅助信息的函数。然后，我们考虑仅解码器有权访问辅助信息的情况（即“ Wyner-Ziv问题”）。对于依赖于边信息的失真测度，我们给出了一个明确的公式，在关于X和Y的联合分布的一些假设下，该公式紧密逼近小D的Wyner-Ziv速率失真函数R / sup WZ /（D）。证明对于依赖于边信息的失真度量，速率损失R / sup WZ /（D）-R / sub X | Y /（D）可以在小D的范围内限制为零。不依赖于速率损失消失为D / spl rarr / 0的辅助信息的失真测度。
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