We consider the design of quantizers in a parameter identification setting under an H/sup /spl infin// criterion. Motivated by the communication constraints arising in systems employing networks, we are interested in answering the question of how coarse the quantization may be without sacrificing performance in identification. We make use of feedback in the communication and show that the H/sup /spl infin// identification problem induces a class of quantizers similar to logarithmic ones. We then show through examples that the proposed identifier is advantageous over a more conventional prefiltering scheme, especially when the quantization error is large.