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In this paper we consider serially concatenated and iteratively decoded irregular variable length coding (IrVLC) combined with preceded differential space-time spreading (DSTS) aided multidimensional sphere packing (SP) modulation designed for near-capacity joint source and channel coding. The IrVLC scheme comprises a number of component variable length coding (VLC) codebooks having different coding rates for the sake of encoding particular fractions of the input source symbol stream. The relative length of these source-stream fractions can be chosen with the aid of extrinsic information transfer (EXIT) charts in order to shape the EXIT curve of the IrVLC codec, so that an open EXIT chart tunnel may be created even at low Eb/N0 values that are close to the capacity bound of the channel. These schemes are shown to be capable of operating within 0.9 dB of the DSTS-SP channel's capacity bound using an average interleaver length of 113,100 bits and an effective bandwidth efficiency of 1 bit/s/Hz, assuming ideal Nyquist filtering. By contrast, the equivalent-rate regular VLC-based bench- marker scheme was found to be capable of operating at 1.4 dB from the capacity bound, which is about 1.56 times the corresponding discrepancy of the proposed IrVLC-aided scheme.