Related papers: Modular Arithmetic Erasure Channels and Their Mult…
This paper considers the memoryless input-constrained binary erasure channel (BEC). The channel input constraint is the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of successive $1$s in the input sequence…
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…
Consider a single-user or multiple-access channel with a large output alphabet. A method to approximate the channel by an upgraded version having a smaller output alphabet is presented and analyzed. The original channel is not necessarily…
We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding…
A framework is proposed that allows for a joint description and optimization of both binary polar coding and $2^m$-ary digital pulse-amplitude modulation (PAM) schemes such as multilevel coding (MLC) and bit-interleaved coded modulation…
In this paper, we consider the problem of variable-length coding over the class of memoryless binary asymmetric channels (BACs) with noiseless feedback, including the binary symmetric channel (BSC) as a special case. In 2012, Naghshvar et…
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…
New algorithms for efficient decoding of polar codes (which may be CRC-augmented), transmitted over either a binary erasure channel (BEC) or an additive white Gaussian noise channel (AWGNC), are presented. We start by presenting a new…
A method of channel polarization, proposed by Arikan, allows us to construct efficient capacity-achieving channel codes. In the original work, binary input discrete memoryless channels are considered. A special case of $q$-ary channel…
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…
In next-generation communications, massive machine-type communications (mMTC) induce severe burden on base stations. To address such an issue, automatic modulation classification (AMC) can help to reduce signaling overhead by blindly…
Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect…
This paper introduces a quantitative generalization of the ``more capable'' comparison of broadcast channels, which is termed ``more capable with advantage''. Some basic properties are demonstrated (including tensorization on product…
In this paper, we introduce a new practical and general method for solving the main problem of designing the capacity approaching, optimal rate, irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC).…
The construction of polar codes for channels other than BECs requires sorting of all bit channels and then selecting the best $K$ of them for a block length $N=2^n$. In this paper, two types of partial orders (PO) of polar codes are…
Many imaging modalities involve reconstruction of unknown objects from collections of noisy projections related by random rotations. In one of these modalities, cryogenic electron microscopy (cryo-EM), the extremely low signal-to-noise…
Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless output-symmetric channel. One of the few drawbacks of the original polar code construction is that it is not universal. This means…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
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…
We introduce a new class of circuits for constructing efficiently decodable error-correction codes, based on a recently discovered contractible tensor network. We perform an in-depth study of a particular example that can be thought of as…