Joint equalization and coding for intersymbol interference channels

We present a novel scheme that combines decision feedback equalization (DFE) with high-rate error-detection coding in an efficient manner. The proposed scheme is shown to considerably outperform the conventional practice on channels with high SNR, such as those encountered in twisted-pair telephony systems. In order to analyze the performance of our method, we introduce an approximate mathematical model taking into account the error propagation phenomenon. Based on this model, upper and lower bounds on the overall probability of error are developed. These show that a simple low-redundancy error-detecting code, when properly integrated with the equalizer, can make the overall probability of error several orders of magnitude lower than that obtained with the conventional DFE, or with a DFE followed by an error-correcting code. Computer simulations of the proposed method have been performed for several channels, including the so-called high-bit-rate digital subscriber line (HDSL) test-loop 4, which is known to have a considerable amount of intersymbol interference. For all these channels, our results show that a reduction in the probability of error by more than three orders of magnitude can be obtained using codes of rate 0.96 and above. This, in turn, translates into power savings (coding gain) of 2.5 to 3 dB.