This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight.

This work was supported in part by the European Research Council under Grant 259663, in part by the European Union under the 7th Framework Programme under Grant FP7-PEOPLE-2009-IEF 252663, Grant FP7-PEOPLE-2011-CIG 303633, Grant FP7-PEOPLE-2012-CIG 333680, and Grant FP7-PEOPLE-2013-IEF 329837, and in part by the Spanish Ministry of Economy and Competitiveness under Grant CSD2008-00010, Grant TEC2009-14504-C02-01, Grant TEC2012-38800-C03-01, Grant TEC2012-38800-C03-03, and Grant RYC-2011-08150.