Related papers: Entropy Polarization-Based Data Compression Withou…
It is well known that to fulfill their full potential, the design of polar codes must be tailored to their intended decoding algorithm. While for successive cancellation (SC) decoding, information theoretically optimal constructions are…
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…
Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is…
The construction of polar codes for channels other than BECs requires sorting of all bit channels and then selecting the best $K$ of them for a block length $N=2^n$. In this paper, two types of partial orders (PO) of polar codes are…
We consider two problems related to polar codes. First is the problem of polar codes construction and analysis of their performance without Monte-Carlo method. The formulas proposed are the same as those in [Mori-Tanaka], yet we believe…
Achieving information-theoretic security using explicit coding scheme in which unlimited computational power for eavesdropper is assumed, is one of the main topics is security consideration. It is shown that polar codes are capacity…
We consider the problem of constructing an unconditionally secure cipher for the case when the key length is less than the length of the encrypted message. (Unconditional security means that a computationally unbounded adversary cannot…
We develop a low-complexity polar coding scheme for the discrete memoryless broadcast channel with confidential messages under strong secrecy and randomness constraints. Our scheme extends previous work by using an optimal rate of uniform…
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…
In this work, a novel data-driven methodology for designing polar codes for channels with and without memory is proposed. The methodology is suitable for the case where the channel is given as a "black-box" and the designer has access to…
A challenging problem related to the design of polar codes is "robustness against channel parameter variations" as stated in Ar{\i}kan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as…
In this paper, we propose a data-driven algorithm to design rate- and length-flexible polar codes. While the algorithm is very general, a particularly appealing use case is the design of codes for automorphism ensemble decoding (AED), a…
-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…
In this work, we address the low-complexity construction of shortened and punctured polar codes from a unified view. While several independent puncturing and shortening designs were attempted in the literature, our goal is a unique,…
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…
The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input…
We present a rate-compatible polar coding scheme that achieves the capacity of any family of channels. Our solution generalizes the previous results [1], [2] that provide capacity-achieving rate-compatible polar codes for a degraded family…
We consider explicit polar constructions of blocklength $n\rightarrow\infty$ for the two extreme cases of code rates $R\rightarrow1$ and $R\rightarrow0.$ For code rates $R\rightarrow1,$ we design codes with complexity order of $n\log n$ in…
In this paper, we present an efficient method to construct a good rate-compatible punctured polar (RCPP) code. One of the major challenges on the construction of a RCPP code is to design a common information set which is good for all the…
We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present…