Optimal Streaming Codes for Channels with Burst and Arbitrary Erasures

Abstract

This paper considers transmitting a sequence of messages (a streaming source) over a packet erasure channel.In each time slot, the source constructs a packet based on the current and the previous messages and transmits the packet, which may be erased when the packet travels from the source to the destination. Every source message must be recovered perfectly at the destination subject to a fixed decoding delay. We assume that the channel loss model introduces either one burst erasure or multiple arbitrary erasures in any fixed-sized sliding window. Under this channel loss assumption, we fully characterize the maximum achievable rate by constructing streaming codes that achieve the optimal rate. In addition, our construction of optimal streaming codes implies the full characterization of the maximum achievable rate for convolutional codes with any given column distance, column span and decoding delay.Numerical results demonstrate that the optimal streaming codes outperform existing streaming codes of comparable complexity over some instances of the Gilbert-Elliott channel and the Fritchman channel. I. INTRODUCTIONLow-latency video conferencing has been a cornerstone for communication and collaboration for individuals and enterprises. The advent of 5G networks promises to make high-throughput at low-latency ubiquitous. This enables new applications such as high-quality video conferencing, virtual reality (VR) and Internet-of-things (IoT) applications including vehicle-to-vehicle communication and mission-critical machine-type communication [1]. At the core of these important applications is the need to reliably deliver packets with low latency. Packet losses at the physical layer and the network layer are inevitable, which may be caused by unreliable wireless links or congestion at network bottlenecks. In order to alleviate the effect of packet losses on applications that are run over the Internet, two main error control schemes have been implemented at the data link and transport layers: Automatic repeat request (ARQ) and forward error correction (FEC).For long-distance low-latency communication, it is not suitable to use ARQ schemes for error control because each retransmission incurs an extra round-trip delay. More specifically, correcting an erasure using ARQ results in a 3-way delay (forward + backward + forward), and this aggregate (3-way) delay including transmission, propagation and processing delays is required to be lower than 150 ms for interactive applications such as voice and video This paper was presented in part at 2018 IEEE International Symposium on Information Theory.

Low-Latency Network-Adaptive Error Control for Interactive Streaming

“…We will leverage the following lemma to construct optimal streaming codes based on optimal block codes. The lemma is a direct consequence of [16,Lemma 1] with the identification W = T + 1. The proof is standard and is based on periodic interleaving (cf.…”

“…Recently, several systematic studies have been carried out to characterize the fundamental limits of streaming codes (i.e., low-latency FEC schemes) that correct burst and arbitrary (isolated) erasures [15]- [17], where the former is usually due to network congestion and the latter can be caused by unreliable wireless links. In particular, the authors in [16,17] have provided a high-complexity construction of a class of FEC streaming codes that possess the following two properties:…”

“…However, in order to achieve the optimal tradeoff between the capability of correcting arbitrary losses and the capability of correcting burst losses subject to a decoding delay constraint, we have to carefully choose the parity frames. The existence of such optimal parity frames has been recently proved in [16,17]. More precisely, given a decoding delay constraint of T frames and any coding parameters (B, N ) such that T ≥ B ≥ N ≥ 1, there exists an optimal choice for the parity frames which leads to a capacity-achieving streaming code that can correct length-B burst erasures and N arbitrary erasures.…”

“…Although the existence of optimal streaming codes has been proved in [16,17], no explicit construction over practical field size was given. Motivated by the fact that finite fields with characteristic 2 allow very efficient computation, we provide the first explicit construction of optimal streaming codes over GF(256) when T ≤ 11.…”

An Explicit Rate-Optimal Streaming Code for Channels with Burst and Arbitrary Erasures

“…The sliding-window burst erasure model, considered in this paper, was proposed by Badr et al in [4] along with upper and lower bounds on the capacity of the channel. The exact capacity in this setup was determined in independent works by Fong et al [5] and Krishnan and Kumar [6]. The proof of Fong et al is existential in nature and involves a recursive construction for computing coefficients in the generator matrix however, the field size requirements are large (O T N ).…”