arXiv subjects

Sinan Kahraman

Publications and source records attributed to Sinan Kahraman.

4 recordsLinked to original sources

arXiv2019

Equidistant Polarizing Transforms

We consider non-binary polarization transform problem of polar codes. The focus of this work is on finding equidistant (or almost equidistant) polarizing transforms to maximize the minimum distance and to approach the equidistant distant spectrum bound as a function of signal set. This bound is an ultimate limit and tight for additive white Gaussian channels. In this way, polarization of error probability for the good channel is improved while the bad channel is almost the same for a given signal set. Our main result is that the polarization speed is increased by using polarizing transform with an improved distance profile. A non-binary polarization transform for q = 5 is found that can provide the equidistant distant spectrum bound. Almost equidistant polarization transforms for q = 4, 6, 7 and 8 are introduced for PSK signal sets. As a private solution, we provided new geometries for the signal set design to define the equidistant transform for q = 3 and q = 4 for one and two dimensional signalings. We proposed a procedure to design transforms that have better distance profiles for q-ary signal sets. Finally, we show improvements in frame error rates.

cs.IT↗

arXiv2019

Non Binary Polar Codes with Equidistant Transform for Transmission over the AWGN Channel

Finding fast polarizing transforms is an important problem as polar codes suffer from slow finitelength performance. This paper considers non binary polar codes for transmission over the AWGN channel and designs polarizing transforms with better distance characteristics using a simple procedure for signal sets. The main idea of the paper is to define Equidistant Polarizing Transforms and show that they achieve the best distance spectrum bound. We provides an example of such transform for q = 5. In this case PSK-type signal set is used. Finally, we show performance gains and some comparison with other methods.

cs.IT↗

arXiv2019

Strange Attractor in Density Evolution

The strange attractor represents a complex pattern of behavior in dynamic systems. This paper introduces a strange attractor for synthetic channels in polar coding as a result of a geometric property of density evolution that is a polar code construction technique. First, we define a subset of synthetic channels that are universally less reliable than the original channel. Here, the cardinality of the attractor set is (n+2)-th Fibonacci number for the block length N = 2n. This can be seen as a significantly large number for very long codes. On the other hand, strange attractor can provide new achievable rates for the finite block lengths. Secondly, it is known that polar codes can be constructed with sub-linear complexity by the use of partial orderings. In this study, we additionally define 1 + log2(log2 N) universal operators to reduce the complexity. Then, these universal operators can be applied on the attractor set to increase the number of synthetic channels that are universally less reliable than the natural channel.

cs.IT↗

arXiv2017

Strange Attractor for Efficient Polar Code Design

This paper presents a definition of a construction for long polar codes. Recently, we know that partial order is a universal property of the construction with a sublinear complexity for polar codes. In order to describe the partial order, addition and left-swap operators are only defined as universal up to now. In this study, we first propose $1+\log_2 \log_2 N$ universal operators to describe multiple partial order for the block length $N=2^n$. By using these operators, some known antichains can be universally ordered. Furthermore, by using a simple geometric property of Gaussian approximation, we define an attractor that is a pre-defined subset of synthetic channels. They are universally less reliable than the natural channel $W$. Then, we show that the cardinality of this attractor is $(n+2)$-th Fibonacci number which is a significantly large number of channels for long codes. The main contribution is that there are significant number of synthetic channels explicitly defined as almost useless by the help of attractor and multiple partial order. As a result, proposed attractor with multiple partial order can be seen as an efficient tool to investigate and design extremely long codes.

cs.IT↗