Related papers: Polar Coded Computing: The Role of the Scaling Exp…
Polar codes were introduced in 2009 by Arikan as the first efficient encoding and decoding scheme that is capacity achieving for symmetric binary-input memoryless channels. Recently, this code family was extended by replacing the…
Monotone chain polar codes generalize classical polar codes to multivariate settings, offering a flexible approach for achieving the entire admissible rate region in the distributed lossless coding problem. However, this flexibility also…
We show that the performance of iterative belief propagation (BP) decoding of polar codes can be enhanced by decoding over different carefully chosen factor graph realizations. With a genie-aided stopping condition, it can achieve the…
Study of polar codes in fading channels is of great importance when applying polar codes in wireless communications. Channel estimation is a fundamental step for communication to be possible in fading channels. For both systematic and…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
Multilevel coding (MLC) is a coded modulation technique which can achieve excellent performance over a range of communication channels. Polar codes have been shown to be quite compatible with communication systems using MLC, as the rate…
Polar codes are designed for parallel binary-input additive white Gaussian noise (BiAWGN) channels with an average power constraint. The two main design choices are: the mapping between codeword bits and channels of different quality, and…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is…
We construct a joint coordination-channel polar coding scheme for strong coordination of actions between two agents $\mathsf X$ and $\mathsf Y$, which communicate over a discrete memoryless channel (DMC) such that the joint distribution of…
We consider lossy source compression of a binary symmetric source using polar codes and the low-complexity successive encoding algorithm. It was recently shown by Arikan that polar codes achieve the capacity of arbitrary symmetric…
Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5th generation (5G) wireless standard. Most polar code research examines the original Arikan polar…
We consider the joint design of polar coding and higher-order modulation schemes for ever increased spectral efficiency. The close connection between the polar code construction and the multi-level coding approach is described in detail.…
We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…
We consider the one helper source coding problem posed and investigated by Ahlswede, K\"orner and Wyner. In this system, the error probability of decoding goes to one as the source block length $n$ goes to infinity. This implies that we…
Polar codes are recursive general concatenated codes. This property motivates a recursive formalization of the known decoding algorithms: Successive Cancellation, Successive Cancellation with Lists and Belief Propagation. Using such…
We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…
We study the application of polar codes in deletion channels by analyzing the cascade of a binary erasure channel (BEC) and a deletion channel. We show how polar codes can be used effectively on a BEC with a single deletion, and propose a…
Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors, the cost for managing a single…
This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It is shown that, unlike conventional successive cancellation decoding, where latency…
Polar codes have promising error-correction capabilities. Yet, decoding polar codes is often challenging, particularly with large blocks, with recently proposed decoders based on list-decoding or neural-decoding. The former applies multiple…