Communication systems that perform iterations between equalizer and decoder at the receiver are known as iterative or turbo equalization systems. These iterative systems can achieve large performance gains (in terms of bit error rates) when compared to their non-iterative counterparts. A major issue in such schemes is that optimal equalization methods are too complex for practical implementation when dealing with large-memory channels and/or higher-order modulations. This problem has received a lot of attention in the specialized literature and several suboptimal low-complexity equalization methods have been proposed. One such method makes use of the jointly Gaussian approach for equalization and was shown to be equivalent to minimum mean-square error linear equalization. In this paper an extension of the jointly Gaussian approach for equalization, dubbed extended jointly Gaussian approach, is proposed. This extension improves the bit error rate performance of the system at the expense of a controllable increase in computational complexity. Signal-to-distortion analysis, EXIT charts and bit error rate curves are used to assess the performance of this new method.

We conduct a code search, restricted to the recently introduced class of generalized punctured convolutional codes, under the minimal trellis complexity measure defined by McEliece and Lin. For the same decoding complexity and the same code rate, new codes are compared to well-known existing classes of convolutional codes. Some of the best convolutional codes (in a distance spectrum sense) of existing and new trellis complexities are tabulated.