相关论文: Polar Codes With Higher-Order Memory
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
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…
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 general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
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…
Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the analysis and construction of polar codes involve the complex iterative-calculation. In…
A pruned variant of polar coding is proposed for binary erasure channels. For sufficiently small $\varepsilon>0$, we construct a series of capacity achieving codes with block length $N=\varepsilon^{-5}$, code rate…
Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect…
We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM…
It is shown that polar codes achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two levels so that the…
Polar codes, introduced recently by Ar\i kan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation,…
We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a joint successive cancellation decoder is deployed at the…
Reed-Muller (RM) codes and polar codes are generated by the same matrix $G_m= \bigl[\begin{smallmatrix}1 & 0 \\ 1 & 1 \\ \end{smallmatrix}\bigr]^{\otimes m}$ but using different subset of rows. RM codes select simply rows having largest…
When a neural network (NN) is used to decode a polar code, its training complexity scales exponentially as the code block size (or to be precise, as a number of message bits) increases. Therefore, existing solutions that use a neural…
In this paper, we establish the partial order (POs) for both the binary erasure channel (BEC) and the binary memoryless symmetric channel (BMSC) under any block rate-matched polar codes. Firstly, we define the POs in the sense of…
Polar codes were introduced in 2009 and proven to achieve the symmetric capacity of any binary-input discrete memoryless channel under low-complexity successive cancellation decoding. In this thesis, we construct cyclic polar codes based on…
Polar codes under successive cancellation decoding proposed by Ar{\i}kan provably achieve the symmetric capacity of any given binary-input discrete memoryless channel. The successive cancellation list decoder for polar codes was described…
Polar codes are the first provable capacity-achieving forward error correction (FEC) codes. In general polar codes can be decoded via either successive cancellation (SC) or belief propagation (BP) decoding algorithm. However, to date…
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…
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…