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The aim of this paper was to study interactions between R-R intervals and respiratory phases in healthy children during night-time sleep using a novel technique based on joint symbolic dynamics. We investigated overnight polysomnography data of 40 healthy children. The R-R time series were extracted from electrocardiograms (ECG) and respiratory phases were obtained from abdominal sensors using the Hilbert transform. Both the series were transformed into ternary symbol vectors based on the changes between two successive R-R intervals or respiratory phases, respectively. Subsequently, words of length `2' were formed and the correspondence between words of the two series for each sleep stage was determined to quantify cardio-respiratory interaction. We found a significantly higher percentage of similarity in the joint symbolic dynamics of R-R intervals and respiratory phases during slow-wave (SW) sleep compared to any other sleep stage. There was, however, no significant effect of age, gender or BMI on cardio-respiratory interaction. In conclusion, joint symbolic dynamics provides a novel efficient technique for the analysis of cardio-respiratory interaction.