相关论文: Capacity achieving multiwrite WOM codes

We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $ P $ and $ N $…

The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with {\em bounded complexity}, per information bit, of encoding and decoding. It also…

We address the maximum attainable rate of fingerprinting codes under the marking assumption, studying lower and upper bounds on the value of the rate for various sizes of the attacker coalition. Lower bounds are obtained by considering…

We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…

Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…

We present a family of additive quantum error-correcting codes whose capacities exceeds that of quantum random coding (hashing) for very noisy channels. These codes provide non-zero capacity in a depolarizing channel for fidelity parameters…

Batch codes serve as critical tools for load balancing in distributed storage systems. While numerous constructions exist for specific batch sizes t, current methodologies predominantly rely on code dimension parameters, limiting their…

This paper concerns with the construction of codes over $GF(2)$ which reach the max-flow for single source multicast acyclic networks with delay. The coding is always a bitwise XOR of packets with equal lengths, and is based on highly…

We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded…

This paper gives a construction of group divisible designs on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which is motivated from the decoding of binary quadratic residue codes. A conjecture is proposed for…

Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. Fundamental bounds, some explicit or…

In this paper, wireless systems operating under queueing constraints in the form of limitations on the buffer violation probabilities are considered. The throughput under such constraints is captured by the effective capacity formulation.…

Non-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes…

This paper presents an analysis of spinal codes, a class of rateless codes proposed recently. We prove that spinal codes achieve Shannon capacity for the binary symmetric channel (BSC) and the additive white Gaussian noise (AWGN) channel…

Designs for Order-of-Addition (OofA) experiments have received growing attention due to their impact on responses based on the sequence of component addition. In certain cases, these experiments involve heterogeneous groups of units, which…

It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…

This note is a stripped down version of a published paper on the Potts partition function, where we concentrate solely on the linear coding aspect of our approach. It is meant as a resource for people interested in coding theory but who do…

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…

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…

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…