Threshold saturation of spatially-coupled codes on intersymbol-interference channels

Recently, it has been observed that terminated low-density-parity-check (LDPC) convolutional codes (or spatially-coupled codes) appear to approach the capacity universally across the class of binary memoryless channels. This is facilitated by the “threshold saturation” effect whereby the belief-propagation (BP) threshold of the spatially-coupled ensemble is boosted to the maximum a-posteriori (MAP) threshold of the underlying constituent ensemble. In this paper, we consider spatially-coupled codes over intersymbol-interference (ISI) channels under joint iterative decoding where we empirically show that threshold saturation also occurs. This can be observed by first identifying the GEXIT curve that naturally obeys the general area theorem. From this curve, the corresponding MAP and the BP threshold estimates are then numerically obtained. Given the fact that regular LDPC codes can achieve the symmetric information rate (SIR) under MAP decoding, we conjecture that spatially-coupled codes with joint iterative decoding can universally approach the SIR of ISI channels.