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A model for a binary additive noise communication channel with memory is introduced. The channel noise process, which is generated according to a ball sampling mechanism involving a queue of finite length M, is a stationary ergodic Mth-order Markov source. The channel properties are analyzed and several of its statistical and information-theoretical quantities (e.g., block transition distribution, autocorrelation function (ACF), capacity, and error exponent) are derived in either closed or easily computable form in terms of its four parameters. The capacity of the queue-based channel (QBC) is also analytically and numerically compared for a variety of channel conditions with the capacity of other binary models, such as the well-known Gilbert-Elliott channel (GEC), the Fritchman channel, and the finite-memory contagion channel. We also investigate the modeling of the traditional GEC using this QBC model. The QBC parameters are estimated by minimizing the Kullback-Leibler divergence rate between the probability of noise sequences generated by the GEC and the QBC, while maintaining identical bit-error rates (BER) and correlation coefficients. The accuracy of fitting the GEC via the QBC is evaluated in terms of ACF, channel capacity, and error exponent. Numerical results indicate that the QBC provides a good approximation of the GEC for various channel conditions; it thus offers an interesting alternative to the GEC while remaining mathematically tractable.