A Note on the Injection Distance

Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory, {54(8), 2008] that the network coding counterpart of Gabidulin codes performs asymptotically optimal with respect to the subspace distance. Recently, Silva and Kschischang introduced in [D. Silva and F.R. Kschischang, "On Metrics for Error Correction in Network Coding," To appear in IEEE Trans. Inform. Theory, ArXiv: 0805.3824v4[cs.IT], 2009] the injection distance to give a detailed picture of what happens in noncoherent network coding. We show that the above codes are also asymptotically optimal with respect to this distance

Coding for Security and Reliability in Distributed Systems

This dissertation studies the use of coding techniques to improve the reliability and security of distributed systems. The first three parts focus on distributed storage systems, and study schemes that encode a message into n shares, assigned to n nodes, such that any n - r nodes can decode the message (reliability) and any colluding z nodes cannot infer any information about the message (security). The objective is to optimize the computational, implementation, communication and access complexity of the schemes during the process of encoding, decoding and repair. These are the key metrics of the schemes so that when they are applied in practical distributed storage systems, the systems are not only reliable and secure, but also fast and cost-effective. Schemes with highly efficient computation and implementation are studied in Part I. For the practical high rate case of r ≤ 3 and z ≤ 3, we construct schemes that require only r + z XORs to encode and z XORs to decode each message bit, based on practical erasure codes including the B, EVENODD and STAR codes. This encoding and decoding complexity is shown to be optimal. For general r and z, we design schemes over a special ring from Cauchy matrices and Vandermonde matrices. Both schemes can be efficiently encoded and decoded due to the structure of the ring. We also discuss methods to shorten the proposed schemes. Part II studies schemes that are efficient in terms of communication and access complexity. We derive a lower bound on the decoding bandwidth, and design schemes achieving the optimal decoding bandwidth and access. We then design schemes that achieve the optimal bandwidth and access not only for decoding, but also for repair. Furthermore, we present a family of Shamir's schemes with asymptotically optimal decoding bandwidth. Part III studies the problem of secure repair, i.e., reconstructing the share of a (failed) node without leaking any information about the message. We present generic secure repair protocols that can securely repair any linear schemes. We derive a lower bound on the secure repair bandwidth and show that the proposed protocols are essentially optimal in terms of bandwidth. In the final part of the dissertation, we study the use of coding techniques to improve the reliability and security of network communication. Specifically, in Part IV we draw connections between several important problems in network coding. We present reductions that map an arbitrary multiple-unicast network coding instance to a unicast secure network coding instance in which at most one link is eavesdropped, or a unicast network error correction instance in which at most one link is erroneous, such that a rate tuple is achievable in the multiple-unicast network coding instance if and only if a corresponding rate is achievable in the unicast secure network coding instance, or in the unicast network error correction instance. Conversely, we show that an arbitrary unicast secure network coding instance in which at most one link is eavesdropped can be reduced back to a multiple-unicast network coding instance. Additionally, we show that the capacity of a unicast network error correction instance in general is not (exactly) achievable. We derive upper bounds on the secrecy capacity for the secure network coding problem, based on cut-sets and the connectivity of links. Finally, we study optimal coding schemes for the network error correction problem, in the setting that the network and adversary parameters are not known a priori.</p

S-PRAC: Fast Partial Packet Recovery with Network Coding in Very Noisy Wireless Channels

Well-known error detection and correction solutions in wireless communications are slow or incur high transmission overhead. Recently, notable solutions like PRAC and DAPRAC, implementing partial packet recovery with network coding, could address these problems. However, they perform slowly when there are many errors. We propose S-PRAC, a fast scheme for partial packet recovery, particularly designed for very noisy wireless channels. S-PRAC improves on DAPRAC. It divides each packet into segments consisting of a fixed number of small RLNC encoded symbols and then attaches a CRC code to each segment and one to each coded packet. Extensive simulations show that S-PRAC can detect and correct errors quickly. It also outperforms DAPRAC significantly when the number of errors is high

Lifelong Neural Predictive Coding: Learning Cumulatively Online without Forgetting

In lifelong learning systems, especially those based on artificial neural networks, one of the biggest obstacles is the severe inability to retain old knowledge as new information is encountered. This phenomenon is known as catastrophic forgetting. In this article, we propose a new kind of connectionist architecture, the Sequential Neural Coding Network, that is robust to forgetting when learning from streams of data points and, unlike networks of today, does not learn via the immensely popular back-propagation of errors. Grounded in the neurocognitive theory of predictive processing, our model adapts its synapses in a biologically-plausible fashion, while another, complementary neural system rapidly learns to direct and control this cortex-like structure by mimicking the task-executive control functionality of the basal ganglia. In our experiments, we demonstrate that our self-organizing system experiences significantly less forgetting as compared to standard neural models and outperforms a wide swath of previously proposed methods even though it is trained across task datasets in a stream-like fashion. The promising performance of our complementary system on benchmarks, e.g., SplitMNIST, Split Fashion MNIST, and Split NotMNIST, offers evidence that by incorporating mechanisms prominent in real neuronal systems, such as competition, sparse activation patterns, and iterative input processing, a new possibility for tackling the grand challenge of lifelong machine learning opens up.Comment: Key updates including results on standard benchmarks, e.g., split mnist/fmnist/not-mnist. Task selection/basal ganglia model has been integrate

Underwater acoustic communications and adaptive signal processing

This dissertation proposes three new algorithms for underwater acoustic wireless communications. One is a new tail-biting circular MAP decoder for full tail-biting convolution (FTBC) codes for very short data blocks intended for Internet of Underwater Things (IoUT). The proposed algorithm was evaluated by ocean experiments and computer simulations on both Physical (PHY) and Media access control (MAC) layers. The ocean experimental results show that without channel equalization, the full tail-biting convolution (FTBC) codes with short packet lengths not only can perform similarly to zero-tailing convolution (ZTC) codes in terms of bit error rate (BER) in the PHY layer. Computer simulation results show that the FTBC codes outperform the ZTC codes in terms of MAC layer metrics, such as collision rate and bandwidth utilization, in a massive network of battery powered IoUT devices. Second, this dissertation also proposes a new approach to utilizing the underwater acoustic (UWA) wireless communication signals acquired in a real-world experiment as a tool for evaluating new coding and modulation schemes in realistic doubly spread UWA channels. This new approach, called passband data reuse, provides detailed procedures for testing the signals under test (SUT) that change or add error correction coding, change bit to symbol mapping (baseband modulation) schemes from a set of original experimental data --Abstract, page iv