On Doped SC-LDPC Codes for Streaming

TL;DR

This paper develops a scaling law to predict error rates of doped SC-LDPC codes in streaming over erasure channels, demonstrating that doping can improve throughput compared to full termination.

Contribution

It introduces a novel scaling law for doped SC-LDPC codes in streaming, enabling accurate error rate prediction and showing doping's advantages over full termination.

Findings

Scaling law accurately predicts error rates.

Doping can outperform full termination in streaming.

Periodic doping increases achievable rates.

Abstract

In streaming applications, doping improves the performance of spatially-coupled low-density parity-check (SC-LDPC) codes by creating reduced-degree check nodes in the coupled chain. We formulate a scaling law to predict the bit and block error rate of periodically-doped semi-infinite SC-LDPC code ensembles streamed over the binary erasure channel under sliding window decoding for a given finite component block length. The scaling law assumes that with some probability doping is equivalent to full termination and triggers two decoding waves; otherwise, decoding performs as if the coupled chain had not been doped at all. We approximate that probability and use the derived scaling laws to predict the error rates of SC-LDPC code ensembles in the presence of doping. The proposed scaling law provides accurate error rate predictions. We further use it to show that in streaming applications periodic doping can yield higher rates than periodic full termination for the same error-correcting performance.