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In this paper we propose a novel irregular variable length coding (IrVLC) scheme for near-capacity joint source and channel coding. We employ a number of component variable length coding (VLC) codebooks having different coding rates for encoding particular fractions of the input source symbol stream. These fractions may be chosen with the aid of extrinsic information transfer (EXIT) charts in order to shape the inverted EXIT curve of the IrVLC codec for ensuring that it does not cross the EXIT curve of a serially concatenated channel codec. In this way, an open EXIT chart tunnel may be created even at low Eb/N0 values that are close to the capacity bound of the channel. We propose iteratively decoded serially concatenated IrVLC designs amalgamated with Trellis coded modulation (TCM). These schemes are shown to be capable of operating within 0.6 dB of the uncorrelated narrowband Rayleigh fading channel's capacity bound using an average interleaver length of 217,500 bits and an effective bandwidth efficiency of 1.56 bit/s/Hz, assuming ideal Nyquist filtering. By contrast, the equivalent-rate regular VLC-based bench-marker schemes were found to be capable of operating at a higher distance of 1.1 dB from the capacity bound, which is nearly twice that of the proposed IrVLC-TCM scheme. Additionally, an irregular convolutional coiling (IrCC) based bench-marker was found to be capable of operating at 0.8 dB from the capacity bound, owing to its slightly eroded performance when operating with the considered interleaver length.