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

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2018

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Akdoğan, Şükrü Can

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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

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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.