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In this paper, we first propose an universal polar coding scheme for parallel Gaussian channels with non-binary inputs. It is assumed that the encoder knows only the sum capacity of M parallel channels instead of the capacity of any single…
Polar codes have been shown to approach capacity of symmetric binary erasure channels and also have low encoding and decoding complexity. Wireless channels are bursty in nature and a method to apply polar codes over wireless channels is…
Given a probability distribution $\mathcal{D}$ over the non-negative integers, a $\mathcal{D}$-repeat channel acts on an input symbol by repeating it a number of times distributed as $\mathcal{D}$. For example, the binary deletion channel…
This work investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless…
While long polar codes can achieve the capacity of arbitrary binary-input discrete memoryless channels when decoded by a low complexity successive cancelation (SC) algorithm, the error performance of the SC algorithm is inferior for polar…
Using a generating function approach, a computationally tractable expression is derived to predict the frame error rate arising at the output of the binary symmetric channel when a number of outer Reed--Solomon codes are concatenated with a…
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…
We consider a communication system where two transmitters wish to exchange information through a half-duplex relay in the middle. The channels between the transmitters and the relay have asymmetric channel gains. More specifically, the…
This paper proposes the design of polar and convolutional coset codes for the unequal message protection (UMP) in the short blocklength regime, to overcome the rate loss introduced by preamble-based solutions. After providing conditions to…
We show that successive cancellation list decoding can be formulated exclusively using log-likelihood ratios. In addition to numerical stability, the log-likelihood ratio based formulation has useful properties which simplify the sorting…
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…
A general method of coding over expansion is proposed,which allows one to reduce the highly non-trivial problems of coding over analog channels and compressing analog sources to a set of much simpler subproblems, coding over discrete…
Polar codes are high density parity check codes and hence the sparse factor graph, instead of the parity check matrix, has been used to practically represent an LP polytope for LP decoding. Although LP decoding on this polytope has the…
We consider network coding for a noiseless broadcast channel where each receiver demands a subset of messages available at the transmitter and is equipped with noisy side information in the form an erroneous version of the message symbols…
This paper presents a polarization-driven (PD) shortening technique for the design of rate-compatible polar codes. The proposed shortening strategy consists of reducing the generator matrix by relating its row index with the channel…
Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
We study channel simulation under common randomness assistance in the finite-blocklength regime and identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance.…
Compression refers to encoding data using bits, so that the representation uses as few bits as possible. Compression could be lossless: i.e. encoded data can be recovered exactly from its representation) or lossy where the data is…
We consider practical hardware implementation of Polar decoders. To reduce latency due to the serial nature of successive cancellation (SC), existing optimizations improve parallelism with two approaches, i.e., multi-bit decision or reduced…