A study on the set choice of multiple factor graph belief propagation decoders for polar codes

Download

index.pdf

Date

2018

Author

Akdoğan, Şükrü Can

Metadata

Show full item record

Item Usage Stats

207
views

108
downloads

Polar codes are linear block codes with low encoding and decoding complexity that are proven to achieve the channel capacity for any given binary-input discrete memoryless channel as the codeword length {u1D441} goes to infinity. The main idea of polar codes is about channel polarization. Special factor graphs are used to represent the encoding and decoding structure of polar codes. These factor graphs consist of {u1D45B} stages for ({u1D441},{u1D43E}) codes, where {u1D45B} = {u1D459}{u1D45C}{u1D454}2{u1D441}. Each stage contains {u1D441}/2 many Z-shaped connections between specific input-output pairs. Defining the height of a Z connection as the node distance between its input (or output) nodes; Stage-{u1D456} that occurs only once in a factor graph for each {u1D456} = 1, … , {u1D45B}, contains Z-shapes of height 2 ({u1D456}−1) . Encoding is done with a specific factor graph, whose Z connections are ordered from the largest to the smallest, that we refer to as the “reference factor graph, {u1D45B}…321”. However, belief propagation decoding can be implemented with one of the {u1D45B}! different factor graphs, by permuting the stages of the reference factor graph. In this thesis, we study on belief propagation decoding of rate ½ polar codes over a binary erasure channel, using single or multiple factor graphs within the decoder. In order to classify the factor graphs, we propose the “stage order number”, in addition to the “number of frozen variables” and “capacity sum” parameters considered by [Doğan, 2015] and [Peker, 2018]. For {u1D45B} = 6, single factor graph decoding performances of {u1D45B}! factor graphs are demonstrated and related to the mentioned three parameters. Construction of compatible factor graph sets, in order to get better performance in multiple-factor graph decoding is studied and their performance is found for {u1D45B} = 6, 7, … , 11 by simulations. Since the sets, consisting of factor graphs with parameters varying in wide ranges seem to have better performance, we propose the “Set Choice” algorithm to compose factor graph sets with ensured variety. Multiple decoders using sets of ⌈{u1D45B}/2⌉ factor graphs obtained by this algorithm can achieve similar performance to that of the cyclic set of {u1D45B} factor graphs.

Subject Keywords

Decoders (Electronics)., Signal processing.

URI

http://etd.lib.metu.edu.tr/upload/12622344/index.pdf
https://hdl.handle.net/11511/27401

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

An Investigation on belief propagation decoding of polar codes Doğan, Orkun; Diker Yücel, Melek; Department of Electrical and Electronics Engineering (2015) Polar codes are provably symmetric capacity achieving codes for any given binary input discrete memoryless channel, with low encoding and decoding complexities. Polar codes introduced by Erdal Arıkan in 2009 are based on the channel polarization. N binary channels are synthesized out of N copies of binary input discrete memoryless channels, such that as N goes to infinity each of the synthesized channel’s capacity goes to either 0 or 1; i.e., the channels are seen purely as noisy or noiseless channels. Thes...
A novel two-step pseudo-response based adaptive harmonic balance method for dynamic analysis of nonlinear structures Sert, Onur; Ciğeroğlu, Ender (Elsevier BV, 2019-09-01) Harmonic balance method (HBM) is one of the most popular and powerful methods, which is used to obtain response of nonlinear vibratory systems in frequency domain. The main idea of the method is to express the response of the system in Fourier series and converting the nonlinear differential equations of motion into a set of nonlinear algebraic equations. System response can be obtained by solving this nonlinear equation set in terms of the unknown Fourier coefficients. The accuracy of the solution is great...
A Distributed Fault-Tolerant Topology Control Algorithm for Heterogeneous Wireless Sensor Networks Bagci, Hakki; KÖRPEOĞLU, İBRAHİM; Yazıcı, Adnan (Institute of Electrical and Electronics Engineers (IEEE), 2015-04-01) This paper introduces a distributed fault-tolerant topology control algorithm, called the Disjoint Path Vector (DPV), for heterogeneous wireless sensor networks composed of a large number of sensor nodes with limited energy and computing capability and several supernodes with unlimited energy resources. The DPV algorithm addresses the k-degree Anycast Topology Control problem where the main objective is to assign each sensor's transmission range such that each has at least k-vertex-disjoint paths to superno...
Belief propagation decoding of polar codes under factor graph permutations Peker, Ahmet Gökhan; Yücel, Melek Diker; Department of Electrical and Electronics Engineering (2018) Polar codes, introduced by Arıkan, are linear block codes that can achieve the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. Polar codes of block length N are constructed by channel polarization method, which consists of channel combining and splitting operations to obtain N polarized subchannels from N copies of binary-input discrete memoryless channels. As N grows, symmetric channel capacities of the polarized subchannels converge to either 0 or...
On higher order approximations for hermite-gaussian functions and discrete fractional Fourier transforms Candan, Çağatay (Institute of Electrical and Electronics Engineers (IEEE), 2007-10-01) Discrete equivalents of Hermite-Gaussian functions play a critical role in the definition of a discrete fractional Fourier transform. The discrete equivalents are typically calculated through the eigendecomposition of a commutator matrix. In this letter, we first characterize the space of DFT-commuting matrices and then construct matrices approximating the Hermite-Gaussian generating differential equation and use the matrices to accurately generate the discrete equivalents of Hermite-Gaussians.

Citation Formats

Ş. C. Akdoğan, “A study on the set choice of multiple factor graph belief propagation decoders for polar codes,” M.S. - Master of Science, Middle East Technical University, 2018.