Related papers: On Systematic Polarization-Adjusted Convolutional …
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…
Using a mild variant of polar codes we design linear compression schemes compressing Hidden Markov sources (where the source is a Markov chain, but whose state is not necessarily observable from its output), and to decode from Hidden Markov…
It has been observed that particular rate-1/2 partially systematic parallel concatenated convolutional codes (PCCCs) can achieve a lower error floor than that of their rate-1/3 parent codes. Nevertheless, good puncturing patterns can only…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite…
Developing computationally-efficient codes that approach the Shannon-theoretic limits for communication and compression has long been one of the major goals of information and coding theory. There have been significant advances towards this…
Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…
We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…
Polar codes are a family of capacity-achieving error-correcting codes, and they have been selected as part of the next generation wireless communication standard. Each polar code bit-channel is assigned a reliability value, used to…
We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…
The quantum hashing bound guarantees that rates up to $1-H(p_I, p_X, p_Y, p_Z)$ are achievable for memoryless Pauli channels, but it is not generally tight. A known way to improve achievable rates for certain asymmetric Pauli channels is to…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
The structure of polar codes inherently requires block lengths to be powers of two. In this paper, we investigate how different block lengths can be realized by coupling of several short-length polar codes. For this, we first analyze "code…
Among error-correcting codes, polar codes are the first to provably achieve channel capacity with an explicit construction. In this work, we present software implementations of a polar decoder that leverage the capabilities of modern…
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…
In this paper, we provide a new approach to the analytical estimation of the bit-error rate (BER) for convolutional codes for Viterbi decoding in the binary symmetric channel (BSC). The expressions we obtained for lower and upper BER bounds…
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for…
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed…
We consider error-correction coding schemes for adversarial wiretap channels (AWTCs) in which the channel can a) read a fraction of the codeword bits up to a bound $r$ and b) flip a fraction of the bits up to a bound $p$. The channel can…
We present a comparative study of the performance of various polar code constructions in an additive white Gaussian noise (AWGN) channel. A polar code construction is any algorithm that selects $K$ best among $N$ possible polar bit-channels…