Rate-Optimal Streaming Codes for Channels With Burst and Random Erasures

In this paper, we design erasure-correcting codes for channels with burst and random erasures, when a strict decoding delay constraint is in place. We consider the sliding-window-based packet erasure model proposed by Badr et al., where any time-window of width w contains either up to a random erasures or an erasure burst of length at most b. One needs to recover any erased packet with a strict decoding delay deadline of τ, where erasures are as per the channel model. Presently existing rate-optimal constructions in the literature require, in general, a field-size which grows exponential in τ, as long as a/τ remains a constant. In this work, we present a new rate-optimal code construction covering all channel and delay parameters, which requires an O(τ²) field-size. As a special case, when (b - a) = 1, we have a field-size linear in τ. We also present two other constructions having linear fieldsize, under certain constraints on channel and decoding delay parameters. As a corollary, we obtain low field-size, rate-optimal convolutional codes for any given column distance and column span. Simulations indicate that the newly proposed streaming code constructions offer lower packet-loss probabilities compared to existing schemes, for selected instances of Gilbert-Elliott and Fritchman channels.

I. Introduction

Reliable communication at low-latency often comes up as an important requirement in the design of next-generation communication systems, including 5G, augmented reality and IoT. Low latency is particularly crucial for real-time multimedia applications, autonomous navigation and V2X (vehicle-to-everything) communications, ‘working and playing’ in the cloud, automation and remote management, tele-medicine and several other mission-critical scenarios [2]. A recent study [3] estimates that IP video traffic, a single use case of low-latency communication, will account for 82 percent of all consumer Internet traffic by 2021, up from 73 percent in 2016. The challenge of enabling delay-constrained communication is further exacerbated by issues arising out of noise, interference, fading, routing, mobility and reliability requirements. In order to ensure robust performance under such a wide range of operating conditions, networks provide for error detection, concealment and correction schemes at multiple layers. These error control strategies can be classified under two broad heads; retransmission strategies, like Automatic Repeat Request (ARQ) protocols, and channel coding or forward error correction (FEC). Choosing one of these error control strategies or a suitable hybrid of both of them is a critical design decision for any communication system.