Related papers: Decoding Network Codes using the Sum-Product Algor…
We study the theoretical performance of a combined approach to demodulation and decoding of binary continuous-phase modulated signals under repetition-like codes. This technique is motivated by a need to transmit packetized or framed data…
To reduce computational complexity and delay in randomized network coded content distribution (and for some other practical reasons), coding is not performed simultaneously over all content blocks but over much smaller subsets known as…
The sum-rank metric generalizes the Hamming and rank metric by partitioning vectors into blocks and defining the total weight as the sum of the rank weights of these blocks, based on their matrix representation. In this work, we explore…
Due to the sequential nature of the successive-cancellation (SC) algorithm, the decoding of polar codes suffers from significant decoding latencies. Fast SC decoding is able to speed up the SC decoding process, by implementing parallel…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
In this article we focus on the problem of channel decoding in presence of a-priori information. In particular, assuming that the a-priori information reliability is not perfectly estimated at the receiver, we derive a novel analytical…
Sparse coding provides a versatile framework for efficiently capturing and representing crucial data (information) concisely, which plays an essential role in various computer science fields, including data compression, feature extraction,…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate…
We examine the issue of separation and code design for networks that operate over finite fields. We demonstrate that source-channel (or source-network) separation holds for several canonical network examples like the noisy multiple access…
Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…
This paper investigates the problem of decomposition with respect to outputs for Boolean control networks (BCNs). First, with the linear expression of BCNs and the matrix semi-tensor product, some algebraic equivalent conditions for the…
Research on polar codes has been constantly gaining attention over the last decade, by academia and industry alike, thanks to their capacity-achieving error-correction performance and low-complexity decoding algorithms. Recently, they have…
It is already known that in multicast (single source, multiple sinks) network, random linear network coding can achieve the maximum flow upper bound. In this paper, we investigate how random linear network coding behaves in general…
We give a polynomial time algorithm to decode multivariate polynomial codes of degree $d$ up to half their minimum distance, when the evaluation points are an arbitrary product set $S^m$, for every $d < |S|$. Previously known algorithms can…
We consider the problem of minimizing the number of broadcasts for collecting all sensor measurements at a sink node in a noisy broadcast sensor network. Focusing first on arbitrary network topologies, we provide (i) fundamental limits on…
We describe message-passing and decimation approaches for lossy source coding using low-density generator matrix (LDGM) codes. In particular, this paper addresses the problem of encoding a Bernoulli(0.5) source: for randomly generated LDGM…
There has been a rise in decoding quantum error correction codes with neural network based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger…
The NP-hard problem of decoding random linear codes is crucial to both coding theory and cryptography. In particular, this problem underpins the security of many code based post-quantum cryptographic schemes. The state-of-art algorithms for…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…