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System identification is studied in which the system output is quantized, transmitted through a digital communication channel, and observed afterwards. This paper explores strong convergence, efficiency, and complexity of identification algorithms under colored noise and dependent communication channels. It first presents algorithms for certain core identification problems using quantized observations on the basis of empirical measures and nonlinear mappings. Strong consistency (with-probability-one convergence) is established under ??-mixing noises. Furthermore, with pre-quantization signal processing, it is shown that certain modified algorithms can achieve asymptotic efficiency under correlated noises. To improve convergence speeds, quantization threshold adaptation algorithms are introduced. These results are then used to study the impact of communication channels on system identification under dependent channels. The concept of fisher information ratio is introduced to characterize such impact. It is shown that the fisher information ratio can be calculated from certain channel characteristic matrices. The relationship between the fisher information ratio and Shannon's channel capacity is discussed from the angle of time and space information. The methods of identification input designs that link general system parameters to core identification problems are reviewed.