Layered Constructions for Low-Delay Streaming Codes

TL;DR

This paper introduces layered error correction codes called MiDAS for low-delay streaming, achieving near-optimal rates and improved error resilience over channels with burst and random erasures.

Contribution

It proposes a layered construction for streaming codes that attains near-optimal rates and handles complex erasure patterns, extending previous work to unequal source and channel rates.

Findings

MiDAS codes achieve near-optimal rate for certain erasure channels.

Numerical results show significant reduction in residual loss probability.

Layered approach effectively manages burst and random erasures.

Abstract

We propose a new class of error correction codes for low-delay streaming communication. We consider an online setup where a source packet arrives at the encoder every $M$ channel uses, and needs to be decoded with a maximum delay of $T$ packets. We consider a sliding-window erasure channel --- $\cC(N,B,W)$ --- which introduces either up to $N$ erasures in arbitrary positions, or $B$ erasures in a single burst, in any window of length $W$. When $M=1$, the case where source-arrival and channel-transmission rates are equal, we propose a class of codes --- MiDAS codes --- that achieve a near optimal rate. Our construction is based on a {\em layered} approach. We first construct an optimal code for the $\cC(N=1,B,W)$ channel, and then concatenate an additional layer of parity-check symbols to deal with $N>1$. When $M > 1$, the case where source-arrival and channel-transmission rates are unequal, we characterize the capacity when $N=1$ and $W \ge M(T+1),$ and for $N>1$, we propose a construction based on a layered approach. Numerical simulations over Gilbert-Elliott and Fritchman channel models indicate significant gains in the residual loss probability over baseline schemes. We also discuss the connection between the error correction properties of the MiDAS codes and their underlying column distance and column span.