Optimal Streaming Codes for Channels with Burst and Arbitrary Erasures

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.Comment: 36 pages, 3 figures, 2 table

Online Versus Offline Rate in Streaming Codes for Variable-Size Messages

Providing high quality-of-service for live communication is a pervasive challenge which is plagued by packet losses during transmission. Streaming codes are a class of erasure codes specifically designed for such low-latency streaming communication settings. We consider the recently proposed setting of streaming codes under variable-size messages which reflects the requirements of applications such as live video streaming. In practice, streaming codes often need to operate in an "online" setting where the sizes of the future messages are unknown. Yet, previously studied upper bounds on the rate apply to "offline" coding schemes with access to all (including future) message sizes. In this paper, we evaluate whether the optimal offline rate is a feasible goal for online streaming codes when communicating over a burst-only packet loss channel. We identify two broad parameter regimes where, perhaps surprisingly, online streaming codes can, in fact, match the optimal offline rate. For both of these settings, we present rate-optimal online code constructions. For all remaining parameter settings, we establish that it is impossible for online coding schemes to attain the optimal offline rate.Comment: 16 pages, 2 figures, this is an extended version of the IEEE ISIT 2020 paper with the same titl

Rate-Optimal Streaming Codes for Channels with Burst and Isolated Erasures

Recovery of data packets from packet erasures in a timely manner is critical for many streaming applications. An early paper by Martinian and Sundberg introduced a framework for streaming codes and designed rate-optimal codes that permit delay-constrained recovery from an erasure burst of length up to $B$. A recent work by Badr et al. extended this result and introduced a sliding-window channel model $\mathcal{C}(N,B,W)$. Under this model, in a sliding-window of width $W$, one of the following erasure patterns are possible (i) a burst of length at most $B$ or (ii) at most $N$ (possibly non-contiguous) arbitrary erasures. Badr et al. obtained a rate upper bound for streaming codes that can recover with a time delay $T$, from any erasure patterns permissible under the $\mathcal{C}(N,B,W)$ model. However, constructions matching the bound were absent, except for a few parameter sets. In this paper, we present an explicit family of codes that achieves the rate upper bound for all feasible parameters $N$, $B$, $W$ and $T$.Comment: shorter version submitted to ISIT 201

Error Propagation Mitigation in Sliding Window Decoding of Braided Convolutional Codes

We investigate error propagation in sliding window decoding of braided convolutional codes (BCCs). Previous studies of BCCs have focused on iterative decoding thresholds, minimum distance properties, and their bit error rate (BER) performance at small to moderate frame length. Here, we consider a sliding window decoder in the context of large frame length or one that continuously outputs blocks in a streaming fashion. In this case, decoder error propagation, due to the feedback inherent in BCCs, can be a serious problem.In order to mitigate the effects of error propagation, we propose several schemes: a \emph{window extension algorithm} where the decoder window size can be extended adaptively, a resynchronization mechanism where we reset the encoder to the initial state, and a retransmission strategy where erroneously decoded blocks are retransmitted. In addition, we introduce a soft BER stopping rule to reduce computational complexity, and the tradeoff between performance and complexity is examined. Simulation results show that, using the proposed window extension algorithm, resynchronization mechanism, and retransmission strategy, the BER performance of BCCs can be improved by up to four orders of magnitude in the signal-to-noise ratio operating range of interest, and in addition the soft BER stopping rule can be employed to reduce computational complexity.Comment: arXiv admin note: text overlap with arXiv:1801.0323

Optimal Multiplexed Erasure Codes for Streaming Messages with Different Decoding Delays

This paper considers multiplexing two sequences of messages with two different decoding delays over a packet erasure channel. In each time slot, the source constructs a packet based on the current and previous messages and transmits the packet, which may be erased when the packet travels from the source to the destination. The destination must perfectly recover every source message in the first sequence subject to a decoding delay $T_\mathrm{v}$ and every source message in the second sequence subject to a shorter decoding delay $T_\mathrm{u}\le T_\mathrm{v}$. We assume that the channel loss model introduces a burst erasure of a fixed length $B$ on the discrete timeline. Under this channel loss assumption, the capacity region for the case where $T_\mathrm{v}\le T_\mathrm{u}+B$ was previously solved. In this paper, we fully characterize the capacity region for the remaining case $T_\mathrm{v}> T_\mathrm{u}+B$. The key step in the achievability proof is achieving the non-trivial corner point of the capacity region through using a multiplexed streaming code constructed by superimposing two single-stream codes. The main idea in the converse proof is obtaining a genie-aided bound when the channel is subject to a periodic erasure pattern where each period consists of a length-$B$ burst erasure followed by a length-$T_\mathrm{u}$ noiseless duration.Comment: 20 pages, 1 figure, 1 table, presented in part at 2019 IEEE ISI