An erasure code is said to be a code with sequential recovery with parameters r and t, if for any s ≤ t erased code symbols, there is an s-step recovery process in which at each step we recover exactly one erased code symbol by contacting at most r other code symbols. In earlier work by the same authors, presented at ISIT 2017, we had given a construction for binary codes with sequential recove...

In this paper we present a couple of tools developed by the author on FreeBSD and available from the author s Web page in source format The rst one called dummynet is a tool designed for the perfor mance evaluation of network protocols and appli cations Despite its original design goal there has been a lot of interest on using dummynet as a band width manager in network servers dummynet sim ula...

Spatially-Coupled LDPC (SC-LDPC) ensembles have gained significant interest since they were shown to universally achieve the capacity of binary memoryless channels under low-complexity belief-propagation decoding. In this work, we focus on the performance of these ensembles over binary erasure channels affected additionally by bursts. We assume that the burst can erase either a complete spatial...

The problem of fast evaluation of a matrix-vector product over GF (2) is considered. The problem is reduced to erasure decoding of a linear error-correcting code. A large set of redundant parity check equations for this code is generated. The multiplication algorithm is derived by tracking the execution of the message-passing algorithm on the obtained set of parity check equations. The obtained...

We introduce a new family of concatenated codes with an outer low-density parity-check (LDPC) code and an inner low-density generator matrix (LDGM) code, and prove that these codes can achieve capacity under any memoryless binaryinput output-symmetric (MBIOS) channel using maximum-likelihood (ML) decoding with bounded graphical complexity, i.e., the number of edges per information bit in their ...

A generic (r,m)-erasure correcting set generates for each binary linear code of codimension r a collection of parity check equations that enables iterative decoding of all potentially correctable erasure patterns of size at most m. As we have shown earlier, such a set essentially is just a parity check collection with this property for the Hamming code of codimension r . We prove non-constructi...

The performance of low-density parity-check (LDPC) codes over the binary erasure channel for a low erasure probability is limited by small stopping sets. The frame error rate over the additive white Gaussian noise (AWGN) channel for a high signal-to-noise ratio is limited by small trapping sets and by the minimum distance of the LDPC code, which is equal to the codeword with the minimal Hamming...

We consider in this paper a network that consists of two senders and two receivers. We further assume that each sender could act as a relay for other communications. All channels connecting these nodes are supposed to be erasure channels where symbols are received correctly (error-free), or lost. This model is realistic for many practical scenarios in the context of wireless and sensor networks...

In this paper we consider the orthogonal cooperative broadcast channel with a common message. The downlink and cooperation channels are modelled by erasure channels and assumed to be orthogonal. We derive an achievable rate for this channel by using a combination of decode-and-forward and estimate-and-forward and considering both symmetric and asymmetric cooperation. These schemes are based on ...

We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and the column erasure channel model. For both models we derive the symbol erasure correction capabilities of spread codes and compare them to other known codes ...