Related papers: Relaxed Polar Codes
The min-sum approximation is widely used in the decoding of polar codes. Although it is a numerical approximation, hardly any penalties are incurred in practice. We give a theoretical justification for this. We consider the common case of a…
Transmission of information reliably and efficiently across channels is one of the fundamental goals of coding and information theory. In this respect, efficiently decodable deterministic coding schemes which achieve capacity provably have…
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…
Wyner's work on wiretap channels and the recent works on information theoretic security are based on random codes. Achieving information theoretical security with practical coding schemes is of definite interest. In this note, the attempt…
Polar codes were originally specified for codelengths that are powers of two. In many applications, it is desired to have a code that is not restricted to such lengths. Two common strategies of modifying the length of a code are shortening…
This paper first presents a new approach to evaluating the descriptive complexity of finite-length binary sequences. Specifically, we investigate the sequence-wise recovery behavior induced by polar compression and successive cancellation…
Polar codes have received increasing attention in the past decade, and have been selected for the next generation of wireless communication standard. Most research on polar codes has focused on codes constructed from a $2\times2$…
Polar codes are the first proven capacity-achieving codes. Recently, they are adopted as the channel coding scheme for 5G due to their superior performance.A polar code for encoding length-K information bits in length-N codeword could be…
Polar codes are the first codes with a proven capacity-achieving capability, but their decoding faces several challenges, especially under long code lengths. In this paper, we target algorithmic improvements and analyses to enable the…
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…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
For any prime power $q$, Mori and Tanaka introduced a family of $q$-ary polar codes based on $q$~by~$q$ Reed-Solomon polarization kernels. For transmission over a $q$-ary erasure channel, they also derived a closed-form recursion for the…
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 introduce a new family of polar-like codes, called Partially Polarized Polar (PPP) codes. PPP codes are constructed from conventional polar codes by selectively pruning polarization kernels, thereby modifying the synthesized bit-channel…
A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation…
A coding scheme for write once memory (WOM) using polar codes is presented. It is shown that the scheme achieves the capacity region of noiseless WOMs when an arbitrary number of multiple writes is permitted. The encoding and decoding…
In this paper, we leverage polar codes and the well-established channel polarization to design capacity-achieving codes with a certain constraint on the weights of all the columns in the generator matrix (GM) while having a low-complexity…
A list decoding scheme for universal polar codes is presented. Our scheme applies to the universal polar codes first introduced by Sasoglu and Wang, and generalized to processes with memory by the authors. These codes are based on the…
Polar codes are a recently proposed class of block codes that provably achieve the capacity of various communication channels. They received a lot of attention as they can do so with low-complexity encoding and decoding algorithms, and they…