Related papers: On the degradations of Binary-Input Discrete Memor…
Monomial codes were recently equipped with partial order relations, fact that allowed researchers to discover structural properties and efficient algorithm for constructing polar codes. Here, we refine the existing order relations in the…
Given a family of binary-input memoryless output-symmetric (BMS) channels having a fixed capacity, we derive the BMS channel having the highest (resp. lowest) capacity among all channels that are degraded (resp. upgraded) with respect to…
A method for efficiently constructing polar codes is presented and analyzed. Although polar codes are explicitly defined, straightforward construction is intractable since the resulting polar bit-channels have an output alphabet that grows…
A pruned variant of polar coding is reinvented for all binary erasure channels. For small $\varepsilon>0$, we construct codes with block length $\varepsilon^{-5}$, code rate $\text{Capacity}-\varepsilon$, error probability $\varepsilon$,…
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…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
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…
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…
The polar transformation of a binary erasure channel (BEC) can be exactly approximated by other BECs. Ar{\i}kan proposed that polar codes for a BEC can be efficiently constructed by using its useful property. This study proposes a new class…
A generalization of Ar\i kan's polar code construction using transformations of the form $G^{\otimes n}$ where $G$ is an $\ell \times \ell$ matrix is considered. Necessary and sufficient conditions are given for these transformations to…
The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for…
Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an…
Polar codes with memory (PCM) are proposed in this paper: a pair of consecutive code blocks containing a controlled number of mutual information bits. The shared mutual information bits of the succeeded block can help the failed block to…
As the first error correction codes provably achieving the symmetric capacity of binary-input discrete memory-less channels (B-DMCs), polar codes have been recently chosen by 3GPP for eMBB control channel. Among existing algorithms,…
The goal of a denoising algorithm is to recover a signal from its noise-corrupted observations. Perfect recovery is seldom possible and performance is measured under a given single-letter fidelity criterion. For discrete signals corrupted…
We present a method of constructing rate-compatible polar codes that are capacity-achieving with low-complexity sequential decoders. The proposed code construction allows for incremental retransmissions at different rates in order to adapt…
Sphere decoding (SD) of polar codes is an efficient method to achieve the error performance of maximum likelihood (ML) decoding. But the complexity of the conventional sphere decoder is still high, where the candidates in a target sphere…
A decoding algorithm for polar codes with binary 16$\times$16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented. The proposed approach exploits the relationship of the considered kernels and the…
This paper investigates properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief…
Polar codes have emerged as the most favorable channel codes for their unique capacity-achieving property. To date, numerous works have been reported for efficient design of polar codes decoder. However, these prior efforts focused on…