Decoding of Convolutional Codes over the Erasure Channel

In this paper we study the decoding capabilities of convolutional codes over the erasure channel. Of special interest will be maximum distance profile (MDP) convolutional codes. These are codes which have a maximum possible column distance increase. We show how this strong minimum distance condition of MDP convolutional codes help us to solve error situations that maximum distance separable (MDS) block codes fail to solve. Towards this goal, we define two subclasses of MDP codes: reverse-MDP convolutional codes and complete-MDP convolutional codes. Reverse-MDP codes have the capability to recover a maximum number of erasures using an algorithm which runs backward in time. Complete-MDP convolutional codes are both MDP and reverse-MDP codes. They are capable to recover the state of the decoder under the mildest condition. We show that complete-MDP convolutional codes perform in certain sense better than MDS block codes of the same rate over the erasure channel.Comment: 18 pages, 3 figures, to appear on IEEE Transactions on Information Theor

Network Coding Meets TCP: Theory and Implementation

The theory of network coding promises significant benefits in network performance, especially in lossy networks and in multicast and multipath scenarios. To realize these benefits in practice, we need to understand how coding across packets interacts with the acknowledgment (ACK)-based flow control mechanism that forms a central part of today's Internet protocols such as transmission control protocol (TCP). Current approaches such as rateless codes and batch-based coding are not compatible with TCP's retransmission and sliding-window mechanisms. In this paper, we propose a new mechanism called TCP/NC that incorporates network coding into TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in the congestion window. At the heart of our scheme is a new interpretation of ACKs-the sink acknowledges every degree of freedom (i.e., a linear combination that reveals one unit of new information) even if it does not reveal an original packet immediately. Thus, our new TCP ACK rule takes into account the network coding operations in the lower layer and enables a TCP-compatible sliding-window approach to network coding. Coding essentially masks losses from the congestion control algorithm and allows TCP/NC to react smoothly to losses, resulting in a novel and effective approach for congestion control over lossy networks such as wireless networks. An important feature of our solution is that it allows intermediate nodes to perform re-encoding of packets, which is known to provide significant throughput gains in lossy networks and multicast scenarios. Simulations show that our scheme, with or without re-encoding inside the network, achieves much higher throughput compared to TCP over lossy wireless links. We present a real-world implementation of this protocol that addresses the practical aspects of incorporating network coding and decoding with TCP's wind ow management mechanism. We work with TCP-Reno, which is a widespread and practical variant of TCP. Our implementation significantly advances the goal of designing a deployable, general, TCP-compatible protocol that provides the benefits of network coding.National Science Foundation (U.S.) (Grant CNS-0627021)National Science Foundation (U.S.) (Grant CNS-0721491)National Science Foundation (U.S.) (Grant CCF-0915922)United States. Defense Advanced Research Projects Agency (Subcontract 18870740-37362-C)United States. Defense Advanced Research Projects Agency (Subcontract 060786)United States. Defense Advanced Research Projects Agency (Subcontract 069145)United States. Defense Advanced Research Projects Agency (Contract N66001-06-C-2020)Space and Naval Warfare Systems Center San Diego (U.S.) (Contract N66001- 08-C-2013

Robust and efficient video/image transmission

The Internet has become a primary medium for information transmission. The unreliability of channel conditions, limited channel bandwidth and explosive growth of information transmission requests, however, hinder its further development. Hence, research on robust and efficient delivery of video/image content is demanding nowadays. Three aspects of this task, error burst correction, efficient rate allocation and random error protection are investigated in this dissertation. A novel technique, called successive packing, is proposed for combating multi-dimensional (M-D) bursts of errors. A new concept of basis interleaving array is introduced. By combining different basis arrays, effective M-D interleaving can be realized. It has been shown that this algorithm can be implemented only once and yet optimal for a set of error bursts having different sizes for a given two-dimensional (2-D) array. To adapt to variable channel conditions, a novel rate allocation technique is proposed for FineGranular Scalability (FGS) coded video, in which real data based rate-distortion modeling is developed, constant quality constraint is adopted and sliding window approach is proposed to adapt to the variable channel conditions. By using the proposed technique, constant quality is realized among frames by solving a set of linear functions. Thus, significant computational simplification is achieved compared with the state-of-the-art techniques. The reduction of the overall distortion is obtained at the same time. To combat the random error during the transmission, an unequal error protection (UEP) method and a robust error-concealment strategy are proposed for scalable coded video bitstreams