Related papers: Capacity of Non-Malleable Codes
In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff, and compare…
In this paper, we discuss two-stage encoding algorithms capable of correcting a fraction of asymmetric errors. Suppose that the encoder transmits $n$ binary symbols $(x_1,\ldots,x_n)$ one-by-one over the Z-channel, in which a 1 is received…
The problem of mismatched decoding with an additive metric $q$ for a discrete memoryless channel $W$ is addressed. The "product-space" improvement of the random coding lower bound on the mismatch capacity, $C_q^{(\infty)}(W)$, was…
SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct…
Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial…
Consider the communication efficient secret sharing problem. A dealer wants to share a secret with $n$ parties such that any $k\leq n$ parties can reconstruct the secret and any $z<k$ parties eavesdropping on their shares obtain no…
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…
Recently, a novel variation of polar codes known as polarization-adjusted convolutional (PAC) codes has been introduced by Ar{\i}kan. These codes significantly outperform conventional polar and convolutional codes, particularly for short…
A binary code is called a superimposed cover-free $(s,\ell)$-code if the code is identified by the incidence matrix of a family of finite sets in which no intersection of $\ell$ sets is covered by the union of $s$ others. A binary code is…
In this work, we present a family of architectures for polar decoders using a reduced-complexity successive-cancellation decoding algorithm that employs unrolling to achieve extremely high throughput values while retaining moderate…
We consider channel coding for discrete memoryless channels (DMCs) with a novel cost constraint that constrains both the mean and the variance of the cost of the codewords. We show that the maximum (asymptotically) achievable rate under the…
We introduce the design of a set of code sequences $ \{ {\mathscr C}_{n}^{(m)} : n\geq 1, m \geq 1 \}$, with memory order $m$ and code-length $N=O(\phi^n)$, where $ \phi \in (1,2]$ is the largest real root of the polynomial equation…
Wireless network scheduling and control techniques (e.g., opportunistic scheduling) rely heavily on access to Channel State Information (CSI). However, obtaining this information is costly in terms of bandwidth, time, and power, and could…
We prove new upper bounds on the size of families of vectors in $\Z_m^n$ with restricted modular inner products, when $m$ is a large integer. More formally, if $\vec{u}_1,\ldots,\vec{u}_t \in \Z_m^n$ and $\vec{v}_1,\ldots,\vec{v}_t \in…
Moderate Density Parity Check (MDPC) codes are defined here as codes which have a parity-check matrix whose row weight is $O(\sqrt{n})$ where $n$ is the length $n$ of the code. They can be decoded like LDPC codes but they decode much less…
In this paper we give several new constructions of WOM codes. The novelty in our constructions is the use of the so called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction…
A pruned variant of polar coding is proposed for binary erasure channels. For sufficiently small $\varepsilon>0$, we construct a series of capacity achieving codes with block length $N=\varepsilon^{-5}$, code rate…
We address the problem of constructing a fast lossless code in the case when the source alphabet is large. The main idea of the new scheme may be described as follows. We group letters with small probabilities in subsets (acting as super…
In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is…
A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code…