Related papers: On the Error Probability of Short Concatenated Pol…
Subcode-ensemble decoders improve iterative decoding by running multiple decoders in parallel over carefully chosen subcodes, increasing the likelihood that at least one decoder avoids the dominant trapping structures. Achieving strong…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
We address the error floor problem of low-density parity check (LDPC) codes on the binary-input additive white Gaussian noise (AWGN) channel, by constructing a serially concatenated code consisting of two systematic irregular repeat…
Convolutional precoding in polarization-adjusted convolutional (PAC) codes is a recently introduced variant of polar codes. It has demonstrated an effective reduction in the number of minimum weight codewords (a.k.a error coefficient) of…
Unrolling a decoding algorithm allows to achieve extremely high throughput at the cost of increased area. Look-up tables (LUTs) can be used to replace functions otherwise implemented as circuits. In this work, we show the impact of…
-We develop a polar coding scheme for empirical coordination in a two-node network with a noisy link in which the input and output signals have to be coordinated with the source and the reconstruction. In the case of non-causal encoding and…
The structure and size of the interleaver used in a turbo code critically affect the distance spectrum and the covariance property of a component decoder's information input and soft output. This paper introduces a new class of…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
In this work we propose an encoding and decoding framework for staircase codes based on non-systematic polar codes as component codes. The staircase structure allows for efficient parallelized decoding, while the polar component codes allow…
Two concatenated coding schemes incorporating algebraic Reed-Solomon (RS) codes and polarization-adjusted convolutional (PAC) codes are proposed. Simulation results show that at a bit error rate of $10^{-5}$, a concatenated scheme using RS…
The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $\left\{W_i\right\}_{i=1}^{N}$ is considered. The sequence of channels is assumed to be completely known to both the…
In the Shannon lecture at the 2019 International Symposium on Information Theory (ISIT), Ar{\i}kan proposed to employ a one-to-one convolutional transform as a pre-coding step before the polar transform. The resulting codes of this…
A novel construction of polar codes with dynamic frozen symbols is proposed. The proposed codes are subcodes of extended BCH codes, which ensure sufficiently high minimum distance. Furthermore, a decoding algorithm is proposed, which…
Product codes are widely used in data-storage, optical and wireless applications. Their analytical performance evaluation usually relies on the truncated union bound, which provides a low error rate approximation based on the minimum…
We prove that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within $\epsilon > 0$ of the Shannon capacity with a block length, construction complexity, and decoding complexity all…
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…
Polar codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming 5G standard. As such, a lot of attention has been devoted to the development of…
Research on polar codes has been constantly gaining attention over the last decade, by academia and industry alike, thanks to their capacity-achieving error-correction performance and low-complexity decoding algorithms. Recently, they have…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…