Effective Delay Control in Online Network Coding
📝 Abstract
Motivated by streaming applications with stringent delay constraints, we consider the design of online network coding algorithms with timely delivery guarantees. Assuming that the sender is providing the same data to multiple receivers over independent packet erasure channels, we focus on the case of perfect feedback and heterogeneous erasure probabilities. Based on a general analytical framework for evaluating the decoding delay, we show that existing ARQ schemes fail to ensure that receivers with weak channels are able to recover from packet losses within reasonable time. To overcome this problem, we re-define the encoding rules in order to break the chains of linear combinations that cannot be decoded after one of the packets is lost. Our results show that sending uncoded packets at key times ensures that all the receivers are able to meet specific delay requirements with very high probability.
💡 Analysis
Motivated by streaming applications with stringent delay constraints, we consider the design of online network coding algorithms with timely delivery guarantees. Assuming that the sender is providing the same data to multiple receivers over independent packet erasure channels, we focus on the case of perfect feedback and heterogeneous erasure probabilities. Based on a general analytical framework for evaluating the decoding delay, we show that existing ARQ schemes fail to ensure that receivers with weak channels are able to recover from packet losses within reasonable time. To overcome this problem, we re-define the encoding rules in order to break the chains of linear combinations that cannot be decoded after one of the packets is lost. Our results show that sending uncoded packets at key times ensures that all the receivers are able to meet specific delay requirements with very high probability.
📄 Content
arXiv:0901.4898v1 [cs.IT] 30 Jan 2009 1 Effective Delay Control in Online Network Coding Jo˜ao Barros∗ Rui A. Costa† Daniele Munaretto‡ Joerg Widmer‡ ∗Instituto de Telecomunicac¸˜oes, Faculdade de Engenharia da Universidade do Porto, jbarros@fe.up.pt †Instituto de Telecomunicac¸˜oes, Faculdade de Ciˆencias da Universidade do Porto, ruicosta@dcc.fc.up.pt ‡DoCoMo Euro-Labs, Munich, Germany, lastname@docomolab-euro.com Abstract—Motivated by streaming applications with stringent delay constraints, we consider the design of online network coding algorithms with timely delivery guarantees. Assuming that the sender is providing the same data to multiple receivers over independent packet erasure channels, we focus on the case of perfect feedback and heterogeneous erasure probabilities. Based on a general analytical framework for evaluating the decoding delay, we show that existing ARQ schemes fail to ensure that receivers with weak channels are able to recover from packet losses within reasonable time. To overcome this problem, we re- define the encoding rules in order to break the chains of linear combinations that cannot be decoded after one of the packets is lost. Our results show that sending uncoded packets at key times ensures that all the receivers are able to meet specific delay requirements with very high probability. I. INTRODUCTION The issue of delay between data transmission and successful delivery to the receiving application is arguably one of the key concerns when applying coding ideas to networking problems. This is particularly true for network coding, where nodes combine multiple packets by means of algebraic operations and perform computationally heavy Gaussian elimination al- gorithms to recover the sent data. Although there is growing consensus that both in wireless broadcast scenarios [1], [2] network coding can bring benefits in terms of throughput and robustness, the fact that a receiver may have to wait for a considerable number of packets, before it can decode the data, justifies the question whether and how network coding can be used in scenarios with stringent end-to-end delays. In the seminal paper of Ahlswede, Cai, Li, and Yeung [3], which shows that network coding is required to achieve the multicast capacity of a general network, the problem is formulated in an information-theoretic setting, where delay and complexity are not taken into account. Delay is also not a primary concern of the algebraic framework in [4] and of the random linear network coding method [5], [6], in which each node in the network selects independently and randomly a set of coefficients and uses them to form linear combinations of the data symbols (or packets) it receives. When intermediate nodes cannot perform coding operations and applications are able to tolerate some delay, fountain codes (e.g., Raptor codes [7]) emerge as a viable solution offering low coding overhead as well as near-optimal throughput over packet erasure channels. Clearly, in all of these instances, coding is performed in a feedforward fashion. The encoders upstream are oblivious to packet loss downstream and their coding decisions do not exploit any feedback information. In contrast, the property that transmitted packets are linear combinations of subsets of pack- ets available at the sender buffer suggests that network coding protocols could be enhanced by modifying the content of the acknowledgments typically provided by transport protocols. Instead of acknowledging specific packets, each destination node of a unicast or multicast session can send back requests for degrees of freedom that increase the dimension of its vector space and allow for faster decoding. Recent contributions that pursue this idea (e.g., [8], [9]) focus mostly on end-to-end reliability with perfect feedback, i.e., complete and immediate knowledge of the packets stored at each receiver. The source node reacts by sending the most innovative linear combination that is useful to most destination nodes. Throughput optimal network coding protocols follow- ing this concept appear in [10], [11], which introduce the useful notion of seen packet as an abstraction for the case in which a packet cannot yet be decoded but can be safely removed from the sender buffer. Removing packets in a timely fashion has obvious benefits in terms of queue length. By using the feedback information to move a coding window along the sender buffer instead of mixing fixed sets of packets (also called generations [6]), these protocols perform online network coding in the sense that they adapt their coding decisions based on the erasure patterns observed in the network. Realizing that existing solutions do not yet cover the full range of trade-offs between throughput and delay, in particular when users experience different packet loss probabilities, we set out to provide end-to-end delay control for online network coding with feedback. Our main contributions are as follows: • Delay Analysis: We provide
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