This paper presents the design of multiple description trellis-coded quantizers that are optimized for transmitting data over multiple noisy channels. A multiple description channel-optimized trellis-coded quantization (MDCOTCQ) scheme is developed whereby all trellis-coded quantizers (side and central) are designed to operate over the binary symmetric channel with a given bit error rate (BER). Using the tensor product of trellises, an expression of the multi-channel transition probability matrix is derived. This formulation enables the construction of multiple description channel-optimized trellis-coded quantizers for arbitrary bit rates and arbitrary channel bit error rates. The proposed MDCOTCQ system enables the transmission of compressed data over noisy diversity or packet-based communication systems, and enables outstanding robustness to channel or packet loss. Examples are presented to illustrate the performance of the proposed MDCOTCQ-based source coder.