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This paper studies the random-coding exponent of joint source-channel codingfor a scheme where source messages are assigned to disjoint subsets (referredto as classes), and codewords are independently generated according to adistribution that depends on the class index of the source message. Fordiscrete memoryless systems, two optimally chosen classes and productdistributions are found to be sufficient to attain the sphere-packing exponentin those cases where it is tight.

A Derivation of the Source-Channel Error Exponent using Non-identical Product Distributions