Related papers: Performance and Construction of Polar Codes on Sym…
Polar codes are a class of {\bf structured} channel codes proposed by Ar{\i}kan based on the principle of {\bf channel polarization}, and can {\bf achieve} the symmetric capacity of any Binary-input Discrete Memoryless Channel (B-DMC). The…
Achieving information-theoretic security using explicit coding scheme in which unlimited computational power for eavesdropper is assumed, is one of the main topics is security consideration. It is shown that polar codes are capacity…
A successive cancellation list (SCL) decoder with limited list size for polar codes can not be analyzed as a successive cancellation (SC) decoder, nor as a maximum likelihood (ML) decoder, due to the complicated decoding errors caused by…
We show that linear codes combined with rejection sampling can yield a capacity-achieving scheme for simulating additive exchangeable noise channels. Specifically, our scheme achieves an amount of communication within $\log e + 1$ bits from…
Long polar codes can achieve the capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancelation (SC) decoding algorithm. But for polar codes with short and moderate code length, the decoding…
Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an…
This paper presents a method for computing a finite-blocklength converse for the rate of fixed-length codes with feedback used on discrete memoryless channels (DMCs). The new converse is expressed in terms of a stochastic control problem…
Polar codes are the first class of channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels with efficient encoding and decoding algorithms. But the weight spectrum of Polar codes is relatively poor…
The min-sum approximation is widely used in the decoding of polar codes. Although it is a numerical approximation, hardly any penalties are incurred in practice. We give a theoretical justification for this. We consider the common case of a…
Being attracted by the property of classical polar code, researchers are trying to find its analogue in quantum fields, which is called quantum polar code. The first step and the key to design quantum polar code is to find out for the…
In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
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…
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…
In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made…
We consider the $2^n$ channels synthesized by the $n$-fold application of Ar\i{}kan's polar transform to a binary erasure channel (BEC). The synthetic channels are BECs themselves, and we show that, asymptotically for almost all these…
The problem of communication over binary dirty paper (DP) using nested polar codes is considered. An improved scheme, focusing on low delay, short to moderate blocklength communication is proposed. Successive cancellation list (SCL)…
A generalization of the polar coding scheme called mixed-kernels is introduced. This generalization exploits several homogeneous kernels over alphabets of different sizes. An asymptotic analysis of the proposed scheme shows that its…
Arikan's Polar codes attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper…
Synchronization channels, such as the well-known deletion channel, are surprisingly harder to analyze than memoryless channels, and they are a source of many fundamental problems in information theory and theoretical computer science. One…