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Data inherently including memory can be compressed using either equal or variable length coding. This paper proposes a novel method to compress the data with memory by using equal length code words while maintaining the error correction capability. The main drawback of variable length coding (VLC) is that because of the boundary problem, it is very sensitive to errors, which results in many cases in long burst errors due to error propagation. However, VLC is optimal in the sense of minimizing the expected length of the codeword. To reduce the compression rate using equal length code, a technique called multiple label mapping (MLM) is employed in this paper. Furthermore, MLM is extended with a fine tuning block to achieve compression rates as close to the Shannon limit as possible. Simulation results for symbol error rate (SER) evaluation as well as EXIT analysis indicate that the proposed technique can achieve compression rates very close to the VLC performance while maintaining the error correction capability. Furthermore, it is shown that the SER performance of the proposed joint source-channel coding scheme is very close to the Shannon limit.