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Progress in designing channel codes has been driven by human ingenuity and, fittingly, has been sporadic. Polar codes, developed on the foundation of Arikan's polarization kernel, represent the latest breakthrough in coding theory and have…
A challenging problem related to the design of polar codes is "robustness against channel parameter variations" as stated in Ar{\i}kan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as…
A fundamental question in information theory is to quantify the loss of information under a noisy channel. Partial orders are typical tools to that end, however, they are often also challenging to evaluate. For the special class of binary…
For every p in (0,1/2), we give an explicit construction of binary codes of rate approaching "capacity" 1-H(p) that enable reliable communication in the presence of worst-case additive errors}, caused by a channel oblivious to the codeword…
We analyze the practical performance of quantum polar codes, by computing rigorous bounds on block error probability and by numerically simulating them. We evaluate our bounds for quantum erasure channels with coding block lengths between…
As sensing and instrumentation play an increasingly important role in systems controlled over wired and wireless networks, the need to better understand delay-sensitive communication becomes a prime issue. Along these lines, this article…
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…
We consider a new formulation of a class of synchronization error channels and derive analytical bounds and numerical estimates for the capacity of these channels. For the binary channel with only deletions, we obtain an expression for the…
Motivated by applications such as recommendation systems, we consider the estimation of a binary random field X obtained by row and column permutations of a block constant random matrix. The estimation of X is based on observations Y, which…
In this letter, we consider the proof of non-stationary channel polarization theory. First we construct a multi-channel stochastic process for the non-stationary channel polarization operation. Then based on this stochastic process, we…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
Polar codes were recently introduced by Ar\i kan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code…
Developing reliable interatomic potential models with quantified predictive accuracy is crucial for atomistic simulations. Commonly used potentials, such as those constructed through the embedded atom method (EAM), are derived from…
In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties of optimal solutions. In this work we…
The paper introduces new bounds on the asymptotic density of parity-check matrices and the achievable rates under ML decoding of binary linear block codes transmitted over memoryless binary-input output-symmetric channels. The lower bounds…
This paper investigates the belief propagation decoding of spatially-coupled MacKay-Neal (SC-MN) codes over erasure channels with memory. We show that SC-MN codes with bounded degree universally achieve the symmetric information rate (SIR)…
In this paper, we shed light on how an adaptive, efficient error coding in the transport layer helps ensure the application requirements. We recap the use of MDS codes and show that binary coding can significantly reduce the complexity and…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…