Performance analysis of iterative decoding algorithms with memory

Density evolution is often used to determine the performance of an ensemble of low-density parity-check (LDPC) codes under iterative message-passing algorithms. Conventional density evolution techniques over memoryless channels are based on the independence assumption amongst all the processed messa...

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Published in:2010 IEEE Information Theory Workshop on Information Theory pp. 1 - 5
Main Authors: Janulewicz, Emil, Banihashemi, Amir H
Format: Conference Proceeding
Language:English
Published: IEEE 01.01.2010
Subjects:
Algorithm design and analysis
Bayesian methods
Belief propagation
Iterative algorithms
Iterative decoding
Memoryless systems
Message passing
Parity check codes
Performance analysis
Strontium
ISBN:9781424463725, 1424463726
Online Access:Get full text
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Abstract Density evolution is often used to determine the performance of an ensemble of low-density parity-check (LDPC) codes under iterative message-passing algorithms. Conventional density evolution techniques over memoryless channels are based on the independence assumption amongst all the processed messages in variable and check nodes. This assumption is valid for many algorithms such as standard belief propagation (BP) and min-sum (MS) algorithms. However, there are other important iterative algorithms such as successive relaxation (SR) versions of BP and MS, and differential decoding with binary message passing (DD-BMP) algorithm of Mobini et. al., for which this assumption is not valid. The dependence created among messages for these algorithms is due to the introduction of memory in the iterative algorithm. In this work, we propose a model for iterative decoding algorithms with memory which covers SR and DD-BMP algorithms as special cases. Based on this model, we derive a Bayesian network for iterative algorithms with memory over memoryless channels and use this representation to analyze the algorithms using density evolution. The density evolution technique is developed based on truncating the memory of the decoding process and approximating it with a finite order Markov process, and can be implemented efficiently. As an example, we apply our technique to analyze the performance of DD-BMP on regular LDPC code ensembles, and make a number of interesting observations with regard to the performance/complexity trade off of DD-BMP in comparison with BP and MS algorithms.
AbstractList Density evolution is often used to determine the performance of an ensemble of low-density parity-check (LDPC) codes under iterative message-passing algorithms. Conventional density evolution techniques over memoryless channels are based on the independence assumption amongst all the processed messages in variable and check nodes. This assumption is valid for many algorithms such as standard belief propagation (BP) and min-sum (MS) algorithms. However, there are other important iterative algorithms such as successive relaxation (SR) versions of BP and MS, and differential decoding with binary message passing (DD-BMP) algorithm of Mobini et. al., for which this assumption is not valid. The dependence created among messages for these algorithms is due to the introduction of memory in the iterative algorithm. In this work, we propose a model for iterative decoding algorithms with memory which covers SR and DD-BMP algorithms as special cases. Based on this model, we derive a Bayesian network for iterative algorithms with memory over memoryless channels and use this representation to analyze the algorithms using density evolution. The density evolution technique is developed based on truncating the memory of the decoding process and approximating it with a finite order Markov process, and can be implemented efficiently. As an example, we apply our technique to analyze the performance of DD-BMP on regular LDPC code ensembles, and make a number of interesting observations with regard to the performance/complexity trade off of DD-BMP in comparison with BP and MS algorithms.
Author Janulewicz, Emil
Banihashemi, Amir H
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  givenname: Amir H
  surname: Banihashemi
  fullname: Banihashemi, Amir H
  organization: Dept. of Syst. & Comput. Eng., Carleton Univ., Ottawa, ON, Canada
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Snippet Density evolution is often used to determine the performance of an ensemble of low-density parity-check (LDPC) codes under iterative message-passing...
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SubjectTerms Algorithm design and analysis
Bayesian methods
Belief propagation
Iterative algorithms
Iterative decoding
Memoryless systems
Message passing
Parity check codes
Performance analysis
Strontium
Title Performance analysis of iterative decoding algorithms with memory
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