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Wireless Mesh Networks (WMNs) support the cost-effective broadband access for Internet users. Although today's IEEE 802.11 PHY and MAC specifications provide multi-channel and multi-rate capabilities, exploiting available channels and data rates is a critical issue to guarantee high network performance. In multi-rate wireless networks, high-rate links heavily suffer from performance degradation due to the presence of low-rate links. This problem is often referred to as performance anomaly. In this paper, we propose a Rate-Based Channel Assignment (RB-CA) algorithm to alleviate performance anomaly in multi-channel multi-rate WMNs. By exploiting multiple channels, the proposed algorithm alters a low-rate single-hop path to a high-rate multi-hop path. With RB-CA, a large volume of traffics in WMNs can be simultaneously delivered from or to the Internet via multiple non-overlapping channels as well as high-rate links. Extensive ns-2 simulation experiments have been performed to evaluate the performance of RB-CA and compared it with the existing WMN architecture. Our simulation results show that RB-CA outperforms existing scheme in terms of packet delivery ratio and end-to-end delay.