Related papers: Polar Codes with exponentially small error at fini…
We analyze the practical performance of quantum polar codes, by computing rigorous bounds on block error probability and by numerically simulating them. We evaluate our bounds for quantum erasure channels with coding block lengths between…
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…
Polarization-adjusted convolutional (PAC) codes are a new family of linear block codes that can perform close to the theoretical bounds in the short block-length regime. These codes combine polar coding and convolutional coding. In this…
Recently, Ar{\i}kan introduced the method of channel polarization on which one can construct efficient capacity-achieving codes, called polar codes, for any binary discrete memoryless channel. In the thesis, we show that decoding algorithm…
This paper investigates the impact of puncturing on finite-length polar codes in which a puncturing pattern $\pv^{N}=(p_0,...,p_N)$ is applied to a length-$N$ polar code.. We first introduce two virtual channels to stochastically model the…
A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…
Polar codes are a class of linear block codes that provably achieves channel capacity. They have been selected as a coding scheme for the control channel of enhanced mobile broadband (eMBB) scenario for $5^{\text{th}}$ generation wireless…
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…
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…
Polar codes are the first error-correcting codes to provably achieve the channel capacity but with infinite codelengths. For finite codelengths the existing decoder architectures are limited in working frequency by the partial sums…
Arikan has shown that systematic polar codes (SPC) outperform nonsystematic polar codes (NSPC). However, the performance gain comes at the price of elevated encoding complexity, i.e., compared to NSPC, the available encoding methods for SPC…
In this letter, we explore the performance limits of short polar codes and find that the maximum likelihood (ML) performance of a simple CRC-polar concatenated scheme can approach the finite blocklength capacity. Then, in order to approach…
This paper investigates properties of concatenated polar codes and their potential applications. We start with reviewing previous work on stopping set analysis for conventional polar codes, which we extend in this paper to concatenated…
Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this…
This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis…
This paper presents polar coding schemes for the 2-user discrete memoryless broadcast channel (DM-BC) which achieve Marton's region with both common and private messages. This is the best achievable rate region known to date, and it is…
ABS polar codes were recently proposed to speed up polarization by swapping certain pairs of adjacent bits after each layer of polar transform. In this paper, we observe that applying the Arikan transform $(U_i, U_{i+1}) \mapsto…
This paper investigates polar codes for the additive white Gaussian noise (AWGN) channel. The scaling exponent $\mu$ of polar codes for a memoryless channel $q_{Y|X}$ with capacity $I(q_{Y|X})$ characterizes the closest gap between the…
Improved bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is…
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…