Spatially-Coupled Precoded Rateless Codes with Bounded Degree Achieve the Capacity of BEC under BP decoding

TL;DR

This paper proves that spatially-coupled precoded rateless codes with bounded degree can achieve the capacity of the BEC under belief propagation decoding, addressing a key limitation of traditional Raptor codes.

Contribution

The paper introduces a novel class of spatially-coupled precoded rateless codes that attain capacity with bounded degree under BP decoding, unlike traditional Raptor codes.

Findings

Achieve capacity of BEC with bounded degree codes

Spatial coupling enables capacity achievement under BP decoding

Addresses unbounded degree requirement in Raptor codes

Abstract

Raptor codes are known as precoded rateless codes that achieve the capacity of BEC. However the maximum degree of Raptor codes needs to be unbounded to achieve the capacity. In this paper, we prove that spatially-coupled precoded rateless codes achieve the capacity with bounded degree under BP decoding.