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The Burrows-Wheeler Transform (BWT) is a block sorting algorithm which has been proven to be useful in compressing text data . More recently, schemes based on the BWT have been proposed for lossless data compression using LDPC and Fountain codes, as well as for joint source-channel coding of sources with memory. In this paper we propose a source-controlled Turbo coding scheme for the transmission of sources with memory over AWGN channels also based on the Burrows-Wheeler Transform. Our approach combines the BWT with a Turbo code and employs different energy allocation techniques for the encoded symbols before their transmission. Simulation results show that the performance of the designed scheme is close (within 1.5 dB) to the theoretical Shannon limit.