Related papers: Coding for Combined Block-Symbol Error Correction
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
We discuss how subspace codes can be used to simultaneously correct errors and erasures when the network performs random linear network coding and the edges are noisy channels. This is done by combining the subspace code with a classical…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
For communication systems with heavy burst noise, an optimal Forward Error Correction (FEC) scheme is expected to have a large burst error correction capacity while simultaneously owning moderate random error correction capability. This…
Motivated by modern network communication applications which require low latency, we study codes that correct erasures with low decoding delay. We provide a simple explicit construction that yields convolutional codes that can correct both…
We study segmented burst-deletion channels motivated by the observation that synchronization errors commonly occur in a bursty manner in real-world settings. In this channel model, transmitted sequences are implicitly divided into…
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…
Secure quantum networks are a bedrock requirement for developing a future quantum internet. However, quantum channels are susceptible to channel noise that introduce errors in the transmitted data. The traditional approach to providing…
In random-access networks, such as the IEEE 802.11 network, different users may transmit their packets simultaneously, resulting in packet collisions. Traditionally, the collided packets are simply discarded. To improve performance,…
A new approach to the problem of error correction in communication channels is proposed, in which the input sequence is transformed in such a way that the interdependence of symbols is significantly increased. Then, after the sequence is…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
Error and erasure exponents for the broadcast channel with degraded message sets are analyzed. The focus of our error probability analysis is on the main receiver where, nominally, both messages are to be decoded. A two-step decoding…
Phased burst errors (PBEs) are bursts of errors occurring at one or more known locations. The correction of PBEs is a classical topic in coding theory, with prominent applications such as the design of array codes for memory systems or…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum…
We consider a simple network, where a source and destination node are connected with a line of erasure channels. It is well known that in order to achieve the min-cut capacity, the intermediate nodes are required to process the information.…