Related papers: On the Optimal Achievable Rates for Linear Computa…
Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton bound. In this paper, following the…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…
Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
In coding schemes for the wire-tap channel or the broadcast channels with confidential messages, it is well known that the sender needs to use a stochastic encoding to avoid the information about the transmitted confidential message to be…
In this paper, a class of relay networks is considered. We assume that, at a node, outgoing channels to its neighbors are orthogonal, while incoming signals from neighbors can interfere with each other. We are interested in the multicast…
Marton's inner bound is the best known achievable region for a general discrete memoryless broadcast channel. To compute Marton's inner bound one has to solve an optimization problem over a set of joint distributions on the input and…
This paper is concerned with the ordered statistic decoding with local constraints (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly…
Achievable and converse bounds for general channels and mismatched decoding are derived. The direct (achievable) bound is derived using random coding and the analysis is tight up to factor 2. The converse is given in term of the achievable…
This paper investigates low-latency streaming codes for a three-node relay network. The source transmits a sequence of messages (streaming messages) to the destination through the relay between them, where the first-hop channel from the…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is…
The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals…
In this paper, we investigate problems of communication over physically degraded, state-dependent broadcast channels (BCs) with cooperating decoders. Two different setups are considered and their capacity regions are characterized. First,…
Coding over subsets (known as generations) rather than over all content blocks in P2P distribution networks and other applications is necessary for a number of practical reasons such as computational complexity. A penalty for coding only…
Mart{\'\i}nez-Pe{\~n}as and Kschischang (IEEE Trans.\ Inf.\ Theory, 2019) proposed lifted linearized Reed--Solomon codes as suitable codes for error control in multishot network coding. We show how to construct and decode \ac{LILRS} codes.…
A finite blocklenth analysis of the diversity-multiplexing tradeoff is presented, based on nonasymptotic bounds on the maximum channel coding rate of multiple-antenna block-memoryless Rayleigh-fading channels.The bounds in this paper allow…
Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…
This paper investigates a joint source-channel secrecy problem for the Shannon cipher broadcast system. We suppose list secrecy is applied, i.e., a wiretapper is allowed to produce a list of reconstruction sequences and the secrecy is…
Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain…