We compare ECG data compression algorithms based on signal entropy for a given mean-square-error (MSE) compression distortion. By defining the distortion in terms of the MSE and assuming the ECG signal to be a Gaussian process we are able to estimate theoretical rate distortion bounds from average ECG power spectra. These rate distortion bounds give estimates of the minimum bits per second (bps) required for storage of ECG data with a given MSE regardless of compression method. From average power spectra of the MIT/BIH arrhythmia database we have estimated rate distortion bounds for ambulatory ECG data, both before and after average beat subtraction. These rate distortion estimates indicate that, regardless of distortion, average beat subtraction reduces the theoretical minimum data rate required for ECG storage by approximately 100 bits per second (bps). Our estimates also indicate that practical ambulatory recording requires a compression distortion on the order of 11 microV rms. We have compared the performance of common ECG compression algorithms on data from the MIT/BIH database. We sampled and quantized the data to give distortion levels of 2, 5, 8, 11, and 14 microV rms. These results indicate that, when sample rates and quantization levels are chosen for optimal rate distortion performance, minimum data rates can be achieved by average beat subtraction followed by first differencing of the residual signal. Achievable data rates approximate our theoretical estimates at low distortion levels and are within 60 bps at higher distortion levels.