We introduce an expurgation method for source coding with side information that enables direct dual-domain derivations of expurgated error exponents. Dual-domain methods yield optimization problems over few parameters, with any sub-optimal choice resulting in an achievable exponent, as opposed to primal-domain optimization over distributions. In addition, dual-domain methods naturally allow for general alphabets and/or memory. We derive two such expurgated error exponents for different random-coding ensembles in the case where the decoder is possibly mismatched with respect to the source and side information joint distribution. We show the better of the exponents coincides with the Csiszár-Körner exponent obtained via a graph decomposition lemma. We show some numerical examples that illustrate the differences between the two exponents and show that in the case of source coding without side information, the expurgated exponent coincides with the error exponent of the source optimal code.

翻译：本文提出了一种用于带边信息信源编码的净化方法，该方法能够直接推导出净化误差指数的双域表达式。双域方法产生仅涉及少数参数的优化问题，任何次优参数选择均可得到可达指数，这与在分布上进行原始域优化形成对比。此外，双域方法天然适用于一般字母表和/或记忆性信源。针对解码器可能不匹配于信源与边信息联合分布的情况，我们针对不同的随机编码集合推导了两种此类净化误差指数。我们证明了较优的指数与通过图分解引理获得的Csiszár-Körner指数一致。通过数值算例展示了两种指数之间的差异，并证明在无边信息信源编码情形下，净化指数与信源最优码的误差指数相符。