On encoding symbol degrees of array BP-XOR codes

Low density parity check (LDPC) codes, LT codes and digital fountain techniques have received significant attention from both academics and industry in the past few years. By employing the underlying ideas of efficient Belief Propagation (BP) decoding process (also called iterative message passing decoding process) on binary erasure channels (BEC) in LDPC codes, Wang has recently introduced the concept of array BP-XOR codes and showed the necessary and sufficient conditions for MDS [k + 2,k] and [n,2] array BP-XOR codes. In this paper, we analyze the encoding symbol degree requirements for array BP-XOR codes and present new necessary conditions for array BP-XOR codes. These new necessary conditions are used as a guideline for constructing several array BP-XOR codes and for presenting a complete characterization (necessary and sufficient conditions) of degree two array BP-XOR codes and for designing new edge-colored graphs. Meanwhile, these new necessary conditions are used to show that the codes by Feng, Deng, Bao, and Shen in IEEE Transactions on Computers are incorrect

Asymptotically MDS Array BP-XOR Codes

Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process. Recently, array XOR codes have attracted attention for storage systems due to their burst error recovery performance and easy arithmetic based on Exclusive OR (XOR)-only logic operations. Array BP-XOR codes are a subclass of array XOR codes that can be decoded using BP under BEC. Requiring the capability of BP-decodability in addition to Maximum Distance Separability (MDS) constraint on the code construction process is observed to put an upper bound on the maximum achievable code block length, which leads to the code construction process to become a harder problem. In this study, we introduce asymptotically MDS array BP-XOR codes that are alternative to exact MDS array BP-XOR codes to pave the way for easier code constructions while keeping the decoding complexity low with an asymptotically vanishing coding overhead. We finally provide and analyze a simple code construction method that is based on discrete geometry to fulfill the requirements of the class of asymptotically MDS array BP-XOR codes.Comment: 8 pages, 4 figures, to be submitte

Asymptotically MDS Array BP-XOR Codes

Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process. Recently, array XOR codes have attracted attention for storage systems due to their burst error recovery performance and easy arithmetic based on Exclusive OR (XOR)-only logic operations. Array BP-XOR codes are a subclass of array XOR codes that can be decoded using BP under BEC. Requiring the capability of BP-decodability in addition to Maximum Distance Separability (MDS) constraint on the code construction process is observed to put an upper bound on the maximum achievable code block length, which leads to the code construction process to become a harder problem. In this study, we introduce asymptotically MDS array BP-XOR codes that are alternative to exact MDS array BP-XOR codes to pave the way for easier code constructions while keeping the decoding complexity low with an asymptotically vanishing coding overhead. We finally provide and analyze a simple code construction method that is based on discrete geometry to fulfill the requirements of the class of asymptotically MDS array BP-XOR codes.Comment: 8 pages, 4 figures, to be submitte

EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures

We present a novel method, that we call EVENODD, for tolerating up to two disk failures in RAID architectures. EVENODD employs the addition of only two redundant disks and consists of simple exclusive-OR computations. This redundant storage is optimal, in the sense that two failed disks cannot be retrieved with less than two redundant disks. A major advantage of EVENODD is that it only requires parity hardware, which is typically present in standard RAID-5 controllers. Hence, EVENODD can be implemented on standard RAID-5 controllers without any hardware changes. The most commonly used scheme that employes optimal redundant storage (i.e., two extra disks) is based on Reed-Solomon (RS) error-correcting codes. This scheme requires computation over finite fields and results in a more complex implementation. For example, we show that the complexity of implementing EVENODD in a disk array with 15 disks is about 50% of the one required when using the RS scheme. The new scheme is not limited to RAID architectures: it can be used in any system requiring large symbols and relatively short codes, for instance, in multitrack magnetic recording. To this end, we also present a decoding algorithm for one column (track) in error

Doped Fountain Coding for Minimum Delay Data Collection in Circular Networks

This paper studies decentralized, Fountain and network-coding based strategies for facilitating data collection in circular wireless sensor networks, which rely on the stochastic diversity of data storage. The goal is to allow for a reduced delay collection by a data collector who accesses the network at a random position and random time. Data dissemination is performed by a set of relays which form a circular route to exchange source packets. The storage nodes within the transmission range of the route's relays linearly combine and store overheard relay transmissions using random decentralized strategies. An intelligent data collector first collects a minimum set of coded packets from a subset of storage nodes in its proximity, which might be sufficient for recovering the original packets and, by using a message-passing decoder, attempts recovering all original source packets from this set. Whenever the decoder stalls, the source packet which restarts decoding is polled/doped from its original source node. The random-walk-based analysis of the decoding/doping process furnishes the collection delay analysis with a prediction on the number of required doped packets. The number of doped packets can be surprisingly small when employed with an Ideal Soliton code degree distribution and, hence, the doping strategy may have the least collection delay when the density of source nodes is sufficiently large. Furthermore, we demonstrate that network coding makes dissemination more efficient at the expense of a larger collection delay. Not surprisingly, a circular network allows for a significantly more (analytically and otherwise) tractable strategies relative to a network whose model is a random geometric graph

Efficient and Effective Schemes for Streaming Media Delivery

The rapid expansion of the Internet and the increasingly wide deployment of wireless networks provide opportunities to deliver streaming media content to users at anywhere, anytime. To ensure good user experience, it is important to battle adversary effects, such as delay, loss and jitter. In this thesis, we first study efficient loss recovery schemes, which require pure XOR operations. In particular, we propose a novel scheme capable of recovering up to 3 packet losses, and it has the lowest complexity among all known schemes. We also propose an efficient algorithm for array codes decoding, which achieves significant throughput gain and energy savings over conventional codes. We believe these schemes are applicable to streaming applications, especially in wireless environments. We then study quality adaptation schemes for client buffer management. Our control-theoretic approach results in an efficient online rate control algorithm with analytically tractable performance. Extensive experimental results show that three goals are achieved: fast startup, continuous playback in the face of severe congestion, and maximal quality and smoothness over the entire streaming session. The scheme is later extended to streaming with limited quality levels, which is then directly applicable to existing systems

Embracing corruption burstiness: Fast error recovery for ZigBee under wi-Fi interference

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.The ZigBee communication can be easily and severely interfered by Wi-Fi traffic. Error recovery, as an important means for ZigBee to survive Wi-Fi interference, has been extensively studied in recent years. The existing works add upfront redundancy to in-packet blocks for recovering a certain number of random corruptions. Therefore the bursty nature of ZigBee in-packet corruptions under Wi-Fi interference is often considered harmful, since some blocks are full of errors which cannot be recovered and some blocks have no errors but still requiring redundancy. As a result, they often use interleaving to reshape the bursty errors, before applying complex FEC codes to recover the re-shaped random distributed errors. In this paper, we take a different view that burstiness may be helpful. With burstiness, the in-packet corruptions are often consecutive and the requirement for error recovery is reduced as ”recovering any k consecutive errors” instead of ”recovering any random k errors”. This lowered requirement allows us to design far more efficient code than the existing FEC codes. Motivated by this implication, we exploit the corruption burstiness to design a simple yet effective error recovery code using XOR operations (called ZiXOR). ZiXOR uses XOR code and the delay is significantly reduced. More, ZiXOR uses RSSI-hinted approach to detect in packet corruptions without CRC, incurring almost no extra transmission overhead. The testbed evaluation results show that ZiXOR outperforms the state-of-the-art works in terms of the throughput (by 47%) and latency (by 22%)This work was supported by the National Natural Science Foundation of China (No. 61602095 and No. 61472360), the Fundamental Research Funds for the Central Universities (No. ZYGX2016KYQD098 and No. 2016FZA5010), National Key Technology R&D Program (Grant No. 2014BAK15B02), CCFIntel Young Faculty Researcher Program, CCF-Tencent Open Research Fund, China Ministry of Education—China Mobile Joint Project under Grant No. MCM20150401 and the EU FP7 CLIMBER project under Grant Agreement No. PIRSES-GA- 2012-318939. Wei Dong is the corresponding author