Spatially-Coupled MacKay-Neal Codes Universally Achieve the Symmetric Information Rate of Arbitrary Generalized Erasure Channels with Memory

TL;DR

This paper demonstrates that spatially-coupled MacKay-Neal codes can universally achieve the symmetric information rate over erasure channels with memory, even without full channel knowledge, using belief propagation decoding.

Contribution

It proves that SC-MN codes with bounded degree universally attain the SIR of arbitrary erasure channels with memory, expanding their applicability.

Findings

SC-MN codes achieve the SIR universally.

Decoding performance is analyzed using potential functions.

The approach applies to channels with memory.

Abstract

This paper investigates the belief propagation decoding of spatially-coupled MacKay-Neal (SC-MN) codes over erasure channels with memory. We show that SC-MN codes with bounded degree universally achieve the symmetric information rate (SIR) of arbitrary erasure channels with memory. We mean by universality the following sense: the sender does not need to know the whole channel statistics but needs to know only the SIR, while the receiver estimates the transmitted codewords from channel statistics and received words. The proof is based on potential function.