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We investigate the reasons behind the superior performance of belief propagation decoding of non-binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over…
Spatially-coupled low-density parity-check codes attract much attention due to their capacity-achieving performance and a memory-efficient sliding-window decoding algorithm. On the other hand, the encoder needs to solve large linear…
Existence of quantum low-density parity-check (LDPC) codes whose minimal distance scales linearly with the number of qubits is a major open problem in quantum information. Its practical interest stems from the need to protect information in…
Local certification is a distributed mechanism enabling the nodes of a network to check the correctness of the current configuration, thanks to small pieces of information called certificates. For many classic global properties, like…
A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization, i.e., a cycle-free realization of the code on the…
Distributed networks are prone to errors so verifying their output is critical. Hence, we develop LOCAL certification protocols for graph properties in which nodes are given certificates that allow them to check whether their network as a…
We consider the problem of decentralized detection in a network consisting of a large number of nodes arranged as a tree of bounded height, under the assumption of conditionally independent, identically distributed observations. We…
An efficient decoding algorithm for horizontally u-interleaved LRPC codes is proposed and analyzed. Upper bounds on the decoding failure rate and the computational complexity of the algorithm are derived. It is shown that interleaving…
In this study, an optimization model for offline scheduling policy of low-density parity-check (LDPC) codes is proposed to improve the decoding efficiency of the belief propagation (BP). The optimization model uses the number of messages…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the method which we apply shows that in order to achieve capacity…
When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…
We introduce Decision Tree Decoders (DTDs), which rely only on the sparsity of the binary check matrix, making them broadly applicable for decoding any quantum low-density parity-check (qLDPC) code and fault-tolerant quantum circuits. DTDs…
We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in…
In this paper we present a new algorithm, denoted as TEP, to decode low-density parity-check (LDPC) codes over the Binary Erasure Channel (BEC). The TEP decoder is derived applying the expectation propagation (EP) algorithm with a tree-…
We study the {\em verification} problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would like to verify whether $H$ has some…
We consider the effect of LLR saturation on belief propagation decoding of low-density parity-check codes. Saturation occurs universally in practice and is known to have a significant effect on error floor performance. Our focus is on…
Motivated by applications to distributed storage, Gopalan \textit{et al} recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check…
Density evolution for protograph Low-Density Parity-Check (LDPC) codes is considered, and it is shown that the message-error rate falls double-exponentially with iterations whenever the degree-2 subgraph of the protograph is cycle-free and…
Recent developments in decoding of Tanner codes with maximum-likelihood certificates are based on a sufficient condition called local-optimality. We define hierarchies of locally-optimal codewords with respect to two parameters. One…