Related papers: Capacity achieving multiwrite WOM codes
We wish to generate list-decodable codes over small alphabets using as little randomness as possible. Specifically, we hope to generate codes achieving what we term the Elias bound, which means that they are $(\rho,L)$-list-decodable with…
We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…
A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for…
Efficient block encoding of many-body Hamiltonians is a central requirement for quantum algorithms in scientific computing, particularly in the early fault-tolerant era. In this work, we introduce new explicit constructions for block…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
Combinatorial designs are closely related to linear codes. In recent year, there are a lot of $t$-designs constructed from certain linear codes. In this paper, we aim to construct $2$-designs from binary three-weight codes. For any binary…
Transmission of information reliably and efficiently across channels is one of the fundamental goals of coding and information theory. In this respect, efficiently decodable deterministic coding schemes which achieve capacity provably have…
Non-malleable codes, introduced by Dziembowski, Pietrzak and Wichs (ICS 2010), encode messages $s$ in a manner so that tampering the codeword causes the decoder to either output $s$ or a message that is independent of $s$. While this is an…
In this paper upper and lower bounds on the probability of decoding failure under maximum likelihood decoding are derived for different (nonbinary) Raptor code constructions. In particular four different constructions are considered; (i)…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…
In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity…
We derive the coding capacity for duplication-correcting codes capable of correcting any number of duplications. We do so both for reverse-complement duplications, as well as palindromic (reverse) duplications. We show that except for…
While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum error-correcting codes the cost of implementing the non-Clifford…
Recently it was proved that if a linear code is invariant under the action of a doubly transitive permutation group, it achieves the capacity of erasure channel. Therefore, it is of sufficient interest to classify all codes, invariant under…
Polar codes are the first proven capacity-achieving codes. Recently, they are adopted as the channel coding scheme for 5G due to their superior performance.A polar code for encoding length-K information bits in length-N codeword could be…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…
This paper shows that, with high probability, randomly punctured Reed-Solomon codes over fields of polynomial size achieve the list decoding capacity. More specifically, we prove that for any $\epsilon>0$ and $R\in (0,1)$, with high…