Related papers: Multilevel Polarization of Polar Codes Over Arbitr…
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for…
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…
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…
Polar coding over a class of binary discrete memoryless channels with channel knowledge at the encoder is studied. It is shown that polar codes achieve the capacity of convex and one-sided classes of symmetric channels.
This study examines multilevel channel polarization for a certain class of erasure channels that the input alphabet size is an arbitrary composite number. We derive limiting proportions of partially noiseless channels for such a class. The…
Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and quantum outputs. Although they demonstrated…
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…
A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity $I(W)$ of any given binary-input discrete memoryless channel (B-DMC) $W$. The symmetric capacity is the highest rate…
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…
Ar{\i}kan's polar coding technique is based on the idea of synthesizing $n$ channels from the $n$ instances of the physical channel by a simple linear encoding transformation. Each synthesized channel corresponds to a particular input to…
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…
A multilevel coded modulation scheme is studied that uses solely binary polar codes and Honda-Yamamoto probabilistic shaping. The scheme is shown to achieve the capacity of discrete memoryless channels with input alphabets of cardinality a…
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…
Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input…
It is known that if an Abelian group operation is used in an Ar{\i}kan-style construction, we have multilevel polarization where synthetic channels can approach intermediate channels that are neither almost perfect nor almost useless. An…
Channel coding over arbitrarily-permuted parallel channels was first studied by Willems et al. (2008). This paper introduces capacity-achieving polar coding schemes for arbitrarily-permuted parallel channels where the component channels are…
A rateless coding scheme transmits incrementally more and more coded bits over an unknown channel until all the information bits are decoded reliably by the receiver. We propose a new rateless coding scheme based on polar codes, and we show…
It is shown that polar coding schemes achieve the known achievable rate regions for several multi-terminal communications problems including lossy distributed source coding, multiple access channels and multiple descriptions coding. The…