Robust Performance Over Changing Intersymbol Interference Channels by Spatial Coupling

TL;DR

This paper addresses the problem of robust coding for ISI channels under changing channel conditions and detectors. It leverages spatially coupled LDPC codes to achieve threshold saturation, enabling near-$SIR$ performance with a single code across multiple ISI channels and detectors, without transmitter channel knowledge. The results show SC-LDPC codes dramatically improve BP thresholds across CH-i, CH-ii, and CH-iii, and that with a suboptimal LMMSE detector the coupled system still approaches BCJR performance, making LMMSE competitive in practical settings. The work thus presents a practically valuable, channel-agnostic coding strategy for turbo equalization in ISI channels, reducing design complexity and detector requirements while maintaining high performance.

Abstract

We show that spatially coupled low-density parity-check (LDPC) codes yield robust performance over changing intersymbol interfere (ISI) channels with optimal and suboptimal detectors. We compare the performance with classical LDPC code design which involves optimizing the degree distribution for a given (known) channel. We demonstrate that these classical schemes, despite working very good when designed for a given channel, can perform poorly if the channel is exchanged. With spatially coupled LDPC codes, however, we get performances close to the symmetric information rates with just a single code, without the need to know the channel and adapt to it at the transmitter. We also investigate threshold saturation with the linear minimum mean square error (LMMSE) detector and show that with spatial coupling its performance can get remarkably close to that of an optimal detector for regular LDPC codes.

Figures (6)

• Figure 1: Block diagram showing the transmitter and the ISI channel.
• Figure 2: Factor graph of turbo equalization with an irregular LDPC code.
• Figure 3: Compact graph representation for equalization with a (3,6) SC-LDPC code with coupling memory $m=1$.
• Figure 4: Simulation results with BCJR detector. Dashed lines show the performance of the irregular code optimized for CH-ii while solid lines are for that of the (6,12) with $m=6$. The solid short vertical lines are the corresponding SIRs while the long vertical lines with diamonds mark the BP thresholds.
• Figure 5: Approximating the coupled threshold of an (6,12) LDPC code and LMMSE equalizer for CH-ii using the EXIT chart paradigm. The net area between the curve is zero at $\frac{E_{\text{b}}}{N_0}=1.85$ dB.