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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…
The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for…
Erasure codes offer an efficient way to decrease storage and communication costs while implementing atomic memory service in asynchronous distributed storage systems. In this paper, we provide erasure-code-based algorithms having the…
The conventional theory of linear network coding (LNC) is only over acyclic networks. Convolutional network coding (CNC) applies to all networks. It is also a form of LNC, but the linearity is w.r.t. the ring of rational power series rather…
We consider an \textit{Adaptive Random Convolutional Network Coding} (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
Supporting ultra-reliable and low-latency communication (URLLC) is a challenge in current wireless systems. Channel codes that generate large codewords improve reliability but necessitate the use of interleavers, which introduce undesirable…
The existence of quantum uncertainty relations is the essential reason that some classically impossible cryptographic primitives become possible when quantum communication is allowed. One direct operational manifestation of these…
We consider the problem of joint source-channel coding for semantic communication from a rateless perspective, the purpose of which is to settle the balance between reliability (distortion/perception) and effectiveness (rate) of…
Analog network coding (ANC) is a throughput increasing technique for the two-way relay channel (TWRC) whereby two end nodes transmit simultaneously to a relay at the same time and band, followed by the relay broadcasting the received sum of…
We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersect in the same small dimension. The theory is…
Codes in the projective space and codes in the Grassmannian over a finite field - referred to as subspace codes and constant-dimension codes (CDCs), respectively - have been proposed for error control in random linear network coding. For…
In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random…
We analyze whether the THz transmission distance can be extended with systematic linear network coding (sRLNC) and a low-bitrate additional channel. While various coding techniques have been proposed to mitigate issues of channel quality,…
We provide a novel framework to study subspace codes for non-coherent communications in wireless networks. To this end, an analog operator channel is defined with inputs and outputs being subspaces of $\mathbb{C}^n$. Then a certain distance…
Locally decodable channel codes form a special class of error-correcting codes with the property that the decoder is able to reconstruct any bit of the input message from querying only a few bits of a noisy codeword. It is well known that…
The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using…
Models for noncoherent error control in random linear network coding (RLNC) and store and forward (SAF) have been recently proposed. In this paper, we model different types of random network communications as the transmission of flats of…
Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its…
This paper revisits a classical scenario in communication theory: a waveform sampled at regular intervals is to be encoded so as to minimize distortion in its reconstruction, despite noise. This transformation must be online (causal), to…