Related papers: Codes That Achieve Capacity on Symmetric Channels
We prove two results on the universality of polar codes for source coding and channel communication. First, we show that for any polar code built for a source $P_{X,Z}$ there exists a slightly modified polar code - having the same rate, the…
We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in…
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…
Low-Density Parity-Check (LDPC) codes received much attention recently due to their capacity-approaching performance. The iterative message-passing algorithm is a widely adopted decoding algorithm for LDPC codes \cite{Kschischang01}. An…
We consider the problem of coded distributed computing using polar codes. The average execution time of a coded computing system is related to the error probability for transmission over the binary erasure channel in recent work by…
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…
This paper considers the achievable rates and decoding complexity of low-density parity-check (LDPC) codes over statistically independent parallel channels. The paper starts with the derivation of bounds on the conditional entropy of 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…
Polar codes have been gaining a lot of interest due to it being the first coding scheme to provably achieve the symmetric capacity of a binary memoryless channel with an explicit construction. However, the main drawback of polar codes is…
Polar codes have gained significant attention in channel coding for their ability to approach the capacity of binary input discrete memoryless channels (B-DMCs), thanks to their reliability and efficiency in transmission. However, existing…
In this paper, we consider quantized decoding of LDPC codes on the binary symmetric channel. The binary message passing algorithms, while allowing extremely fast hardware implementation, are not very attractive from the perspective of…
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…
Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic security is an important problem. By applying the two recently developed…
Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications.…
In this paper, we study codes with sparse generator matrices. More specifically, low-density generator matrix (LDGM) codes with a certain constraint on the weight of the columns in the generator matrix are considered. In this paper, it is…
In this paper, we propose a low-complexity, secrecy capacity achieving polar coding scheme for the cognitive interference channel with confidential messages (CICC) under the strong secrecy criterion. Existing polar coding schemes for…
We study the problem of strong coordination of the actions of two nodes $X$ and $Y$ that communicate over a discrete memoryless channel (DMC) such that the actions follow a prescribed joint probability distribution. We propose two novel…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
Polar codes are of great interest since they are the first provably capacity-achieving forward error correction codes. To improve throughput and to reduce decoding latency of polar decoders, maximum likelihood (ML) decoding units are used…