Related papers: Interpolation of Quantum Polar Codes and Quantum R…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
Quantum cryptography via key distribution mechanisms that utilize quantum entanglement between sender-receiver pairs will form the basis of future large-scale quantum networks. A key engineering challenge in such networks will be the…
Reed-Muller (RM) codes and polar codes are generated by the same matrix $G_m= \bigl[\begin{smallmatrix}1 & 0 \\ 1 & 1 \\ \end{smallmatrix}\bigr]^{\otimes m}$ but using different subset of rows. RM codes select simply rows having largest…
Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal…
Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from…
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…
Constructing efficient low-rate error-correcting codes with low-complexity encoding and decoding have become increasingly important for applications involving ultra-low-power devices such as Internet-of-Things (IoT) networks. To this end,…
A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the…
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…
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…
The use of quantum computation for wireless network applications is emerging as a promising paradigm to bridge the performance gap between in-practice and optimal wireless algorithms. While today's quantum technology offers limited number…
In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density…
Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our…
Reed-Muller (RM) codes have undergone significant analytical advancements over the past decade, particularly for binary memoryless symmetric (BMS) channels. We extend the scope of RM codes development and analysis to multiple-access…
Deep polar codes are pre-transformed polar codes that employ a multi-layered polar kernel transformation strategy to enhance code performance in short blocklength regimes. However, like conventional polar codes, their block length is…
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and quantum outputs. Although they demonstrated…
We construct concatenated capacity-achieving quantum codes for noisy optical quantum channels. We demonstrate that the error-probability of capacity-achieving quantum polar encoding can be reduced by the proposed low-complexity…
Among error-correcting codes, polar codes are the first to provably achieve channel capacity with an explicit construction. In this work, we present software implementations of a polar decoder that leverage the capabilities of modern…
Recently, a new class of error-control codes, the polar codes, have attracted much attention. The polar codes are the first known class of capacity-achieving codes for many important communication channels. In addition, polar codes have…
The Reed-Muller (RM) code encoding $n$-variate degree-$d$ polynomials over ${\mathbb F}_q$ for $d < q$, with its evaluation on ${\mathbb F}_q^n$, has relative distance $1-d/q$ and can be list decoded from a $1-O(\sqrt{d/q})$ fraction of…