Related papers: On the Polarizing Behavior and Scaling Exponent of…
In 2008 Arikan proposed polar coding [arXiv:0807.3917] which we summarize as follows: (a) From the root channel $W$ synthesize recursively a series of channels $W_N^{(1)},\dotsc,W_N^{(N)}$. (b) Select sophisticatedly a subset $A$ of…
Herein, we focus on explicit constructions of $\ell\times\ell$ binary kernels with small scaling exponent for $\ell \le 64$. In particular, we exhibit a sequence of binary linear codes that approaches capacity on the BEC with quasi-linear…
Polar codes were recently introduced by Ar\i kan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code…
This paper investigates the scaling exponent of polar codes for binary-input energy-harvesting (EH) channels with infinite-capacity batteries. The EH process is characterized by a sequence of i.i.d. random variables with finite variances.…
We consider the problem of coded distributed computing using polar codes. The average execution time of a coded computing system is related to the error probability for transmission over the binary erasure channel in recent work by…
Consider the transmission of a polar code of block length $N$ and rate $R$ over a binary memoryless symmetric channel $W$ and let $P_e$ be the block error probability under successive cancellation decoding. In this paper, we develop new…
A shortening method for large polarization kernels is presented, which results in shortened kernels with the highest error exponent if applied to kernels of size up to 32. It uses lower and upper bounds on partial distances for quick…
Polar code visibly approaches channel capacity in practice and is thereby a constituent code of the 5G standard. Compared to low-density parity-check code, however, the performance of short-length polar code has rooms for improvement that…
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…
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…
The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker…
Motivated by the significant performance gains which polar codes experience under successive cancellation list decoding, their scaling exponent is studied as a function of the list size. In particular, the error probability is fixed and the…
A decoding algorithm for polar codes with binary 16$\times$16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented. The proposed approach exploits the relationship of the considered kernels and the…
A family of polarizing kernels is presented together with polynomial-complexity algorithm for computing scaling exponent. The proposed convolutional polar kernels are based on convolutional polar codes, also known as b-MERA codes. For these…
Polar codes that approach capacity at a near-optimal speed, namely with scaling exponents close to $2$, have been shown possible for $q$-ary erasure channels (Pfister and Urbanke), the BEC (Fazeli, Hassani, Mondelli, and Vardy), all BMS…
In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. The proposed multi-kernel polar…
Progress in designing channel codes has been driven by human ingenuity and, fittingly, has been sporadic. Polar codes, developed on the foundation of Arikan's polarization kernel, represent the latest breakthrough in coding theory and have…
Constructing efficient low-rate error-correcting codes with low-complexity encoding and decoding have become increasingly important for applications involving ultra-low-power devices such as Internet-of-Things (IoT) networks. To this end,…
Consider a binary-input memoryless output-symmetric channel $W$. Such a channel has a capacity, call it $I(W)$, and for any $R<I(W)$ and strictly positive constant $P_{\rm e}$ we know that we can construct a coding scheme that allows…
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…