Related papers: A Packing Lemma for Polar Codes
An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the…
Consider the transmission of a polar code of block length $N$ and rate $R$ over a binary memoryless symmetric channel $W$ and let $P_e$ be the block error probability under successive cancellation decoding. In this paper, we develop new…
We investigate the packing and covering densities of linear and nonlinear binary codes, and establish a number of duality relationships between the packing and covering problems. Specifically, we prove that if almost all codes (in the class…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Partitions of the binary linear Hamming code into Preparata-like codes are known to induce line-parallelisms of PG$(n, 2)$. In this paper, we show that if $P$ is any Preparata-like code contained in the binary linear Hamming code $H$ of the…
We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known…
For a binary-input memoryless symmetric channel $W$, we consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over $W$. In particular, we study the asymptotics of the…
In coding theory, an error-correcting code can be encoded either systematically or non-systematically. In a systematic encode, the input data is embedded in the encoded output. Conversely, in a non-systematic code, the output does not…
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime…
The DNA storage channel is considered, in which a codeword is comprised of $M$ unordered DNA molecules. At reading time, $N$ molecules are sampled with replacement, and then each molecule is sequenced. A coded-index concatenated-coding…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
The statistical physics properties of low-density parity-check codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the…
Stopping sets and stopping set distribution of an low-density parity-check code are used to determine the performance of this code under iterative decoding over a binary erasure channel (BEC). Let $C$ be a binary $[n,k]$ linear code with…
This paper proposes a generic formulation that significantly expedites the training and deployment of image classification models, particularly under the scenarios of many image categories and high feature dimensions. As a defining…
Existing fixed-length feedback communication schemes are either specialized to particular channels (Schalkwijk--Kailath, Horstein), or apply to general channels but either have high coding complexity (block feedback schemes) or are…
We propose polar encoding, a representation of categorical and numerical $[0,1]$-valued attributes with missing values to be used in a classification context. We argue that this is a good baseline approach, because it can be used with any…
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…
We investigate dense coding by imposing various locality restrictions to our decoder by employing the resource theory of asymmetry framework. In this task, the sender Alice and the receiver Bob share an entangled state. She encodes the…
In this paper, we establish the list-decoding capacity theorem for sum-rank metric codes. This theorem implies the list-decodability theorem for random general sum-rank metric codes: Any random general sum-rank metric code with a rate not…