On the Universality of Spatially Coupled LDPC Codes Over Intersymbol Interference Channels

TL;DR

The paper tackles the problem of achieving universal performance for spatially coupled LDPC codes over intersymbol interference channels with memory under erasures and AWGN. It introduces exact input/output transfer functions for the BCJR detector, enabling precise density-evolution-based thresholds (BP and MAP) and entropy-based comparisons across channel models. The results show threshold saturation with spatial coupling and, importantly, that the BP thresholds can closely approach the symmetric information rate for multiple ISI channels, supporting universal SIR attainment with a single code. This has practical significance for robust receiver design in channels with memory, where entropy-based metrics resolve discrepancies between erasure and Gaussian noise models.

Abstract

In this paper, we derive the exact input/output transfer functions of the optimal a-posteriori probability channel detector for a general ISI channel with erasures. Considering three channel impulse responses of different memory as an example, we compute the BP and MAP thresholds for regular spatially coupled LDPC codes with joint iterative detection and decoding. When we compare the results with the thresholds of ISI channels with Gaussian noise we observe an apparent inconsistency, i.e., a channel which performs better with erasures performs worse with AWGN. We show that this anomaly can be resolved by looking at the thresholds from an entropy perspective. We finally show that with spatial coupling we can achieve the symmetric information rates of different ISI channels using the same code.

Figures (3)

• Figure 1: Block diagram showing the transmitter and the ISI channel.
• Figure 2: Compact graph representation for equalization with a (3,6) SC-LDPC code with coupling memory $m=1$.
• Figure 3: Transfer functions for the three channels for $\delta=1$.