We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms of the generator matrix of the code. These lead to bounds on locality and notions of optimality. We then examine the locality properties of a family of nonbi...

This paper presents a novel approach for constructing structured regular QC-LDPC codes based on a special type of combinatorial designs,known as the balanced incomplete block design (BIBD).The code design approach based on the technology of block cyclic shift and dispertion (BCSD) for correcting erasure-bursts over the binary bursts erasure channel (BBEC). Furthermore, the Tanner graph of the c...

Shannon showed in [18] that the capacity of discrete memoryless channels (DMCs) does not increase even when a noiseless and delay free feedback link exists from receiver to transmitter. Moreover on symmetric DMCs the sphere packing bound is an upper bound for the error exponent of fixed-length block-codes, as shown by Dobrushin1 in [5]. Thus relaxations like error-and-erasure decoding or variab...

Data storage systems are more reliable than their individual components. In order to build highly reliable systems out of less reliable parts, systems introduce redundancy. In replicated systems, objects are simply copied several times with each copy residing on a different physical device. While such an approach is simple and direct, more elaborate approaches such as erasure coding can achieve...

The high repair cost of (n, k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. In this paper, we address bandwidth-optimal (n, k, d) Exact-Repair MDS codes, which allow for any failed node to be repaired exactly with access to arbitrary d survivor nodes, where k ≤ d...

The so-called Landauer-Bennett thesis says that logically irreversible operations (physically implemented) such as erasure necessarily involve dissipation by at least kln2 per bit of lost information. We identify the physical conditions that are necessary and sufficient for erasure and show that the thesis does not follow from the principles of classical mechanics. In particular, we show that e...

Fountain codes are a class of rateless codes well-suited for communication over erasure channels with unknown erasure parameter. We analyze the decoding of LT codes, the first instance of practical, universal Fountain codes. A set of interest during LT decoding is the set of output symbols of reduced degree one (the “ripple”). The evolution of the ripple size throughout the decoding process is ...

Multiple-description product codes, consisting of an erasure correction row code (e.g. Reed-Solomon code) and an error correction/detection column code (e.g. convolutional codes+CRC) have recently been introduced to protect progressive transmission of multimedia contents. The significance of this approach is its compatibility with and full use of the progressive nature of the rate-distortion sc...

We show that two-level languages are not only a good tool for describing code-generation algorithms, but a good tool for reasoning about them as well. Indeed, some general properties of two-level languages capture common proof obligations of code-generation algorithms in the form of twolevel programs. To prove that the generated code behaves as desired, we use an erasure property, which equatio...