Spatially-Coupled Precoded Rateless Codes

TL;DR

This paper introduces a new class of spatially-coupled rateless codes combining SC-LDGM and SC-LDPC codes, achieving capacity with bounded complexity and vanishing error rates as the block size grows.

Contribution

It proposes a novel concatenated SC-LDGM and SC-LDPC code design, providing a tight lower bound on the asymptotic overhead and demonstrating capacity achievement with bounded degree.

Findings

Asymptotic overhead approaches zero with large block size.

Decoding error rate can be made arbitrarily small.

Bounded maximum degree is sufficient for capacity achievement.

Abstract

Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and decoders. Aref and Urbanke investigated the potential advantage of universal achieving-capacity property of proposed spatially-coupled (SC) low-density generator matrix (LDGM) codes. However the decoding error probability of SC-LDGM codes is bounded away from 0. In this paper, we investigate SC-LDGM codes concatenated with SC low-density parity-check codes. The proposed codes can be regarded as SC Hsu-Anastasopoulos rateless codes. We derive a lower bound of the asymptotic overhead from stability analysis for successful decoding by density evolution. The numerical calculation reveals that the lower bound is tight. We observe that with a sufficiently large number of information bits, the asymptotic overhead and the decoding error rate approach 0 with bounded maximum degree.