Miscorrection probability beyond the minimum distance

The miscorrection probability of a list decoder is the probability that the decoder will have at least one non-causal codeword in its decoding sphere. Evaluating this probability is important when using a list-decoder as a conventional decoder since in that case we require the list to contain at most one codeword for most of the errors. A lower bound on the miscorrection is the main result. The key ingredient in the proof is a new combinatorial upper bound on the list-size for a general q−ary block code. This bound is tighter than the best known on large alphabets, and it is shown to be very close to the algebraic bound for Reed-Solomon codes. Finally we discuss two known upper bounds on the miscorrection probability and unify them for linear MDS codes

Low-Complexity Codes for Random and Clustered High-Order Failures in Storage Arrays

RC (Random/Clustered) codes are a new efficient array-code family for recovering from 4-erasures. RC codes correct most 4-erasures, and essentially all 4-erasures that are clustered. Clustered erasures are introduced as a new erasure model for storage arrays. This model draws its motivation from correlated device failures, that are caused by physical proximity of devices, or by age proximity of endurance-limited solid-state drives. The reliability of storage arrays that employ RC codes is analyzed and compared to known codes. The new RC code is significantly more efficient, in all practical implementation factors, than the best known 4-erasure correcting MDS code. These factors include: small-write update-complexity, full-device update-complexity, decoding complexity and number of supported devices in the array

LDPC Codes with Local and Global Decoding

This paper presents a theoretical study of a new type of LDPC codes motivated by practical storage applications. LDPCL codes (suffix L represents locality) are LDPC codes that can be decoded either as usual over the full code block, or locally when a smaller sub-block is accessed (to reduce latency). LDPCL codes are designed to maximize the error-correction performance vs. rate in the usual (global) mode, while at the same time providing a certain performance in the local mode. We develop a theoretical framework for the design of LDPCL codes. Our results include a design tool to construct an LDPC code with two data-protection levels: local and global. We derive theoretical results supporting this tool and we show how to achieve capacity with it. A trade-off between the gap to capacity and the number of full-block accesses is studied, and a finite-length analysis of ML decoding is performed to exemplify a trade-off between the locality capability and the full-block error-correcting capability.Comment: 41 page

Network coding for non-uniform demands

Non-uniform demand networks are defined as a useful connection model, in between multicasts and general connections. In these networks, each sink demands a certain number of messages, without specifying their identities. We study the solvability of such networks and give a tight bound on the number of sinks for which the min cut condition is sufficient. This sufficiency result is unique to the non-uniform demand model and does not apply to general connection networks. We propose constructions to solve networks at, or slightly below capacity, and investigate the effect large alphabets have on the solvability of such networks. We also show that our efficient constructions are suboptimal when used in networks with more sinks, yet this comes with little surprise considering the fact that the general problem is shown to be NP-hard

A Combinatorial Bound on the List Size

In this paper we study the scenario in which a server sends dynamic data over a single broadcast channel to a number of passive clients. We consider the data to consist of discrete packets, where each update is sent in a separate packet. On demand, each client listens to the channel in order to obtain the most recent data packet. Such scenarios arise in many practical applications such as the distribution of weather and traffic updates to wireless mobile devices and broadcasting stock price information over the Internet. To satisfy a request, a client must listen to at least one packet from beginning to end. We thus consider the design of a broadcast schedule which minimizes the time that passes between a clients request and the time that it hears a new data packet, i.e., the waiting time of the client. Previous studies have addressed this objective, assuming that client requests are distributed uniformly over time. However, in the general setting, the clients behavior is difficult to predict and might not be known to the server. In this work we consider the design of universal schedules that guarantee a short waiting time for any possible client behavior. We define the model of dynamic broadcasting in the universal setting, and prove various results regarding the waiting time achievable in this framework

Cyclic lowest density MDS array codes

Three new families of lowest density maximum-distance separable (MDS) array codes are constructed, which are cyclic or quasi-cyclic. In addition to their optimal redundancy (MDS) and optimal update complexity (lowest density), the symmetry offered by the new codes can be utilized for simplified implementation in storage applications. The proof of the code properties has an indirect structure: first MDS codes that are not cyclic are constructed, and then transformed to cyclic codes by a minimum-distance preserving transformation