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Performance Evaluation of Integer Optimization Decoding

柿沼, 美希, 祐一 高野

Published Mar 1, 2018• 0 citations
Publisher

Abstract

This paper explores a mathematical optimization approach to error correction. Tanatmis et al. [2010] proposed an integer optimization formulation for the maximum likelihood decoding of binary linear codes. They developed a cutting plane algorithm in which valid inequalities for cutting off non-integral solutions are iteratively added to the continuous relaxation problem. By contrast, we focus on the integer optimization decoding; that is, we solve the integer optimization problem directly by using mathematical optimization software. We evaluate the computational performance of the integer optimization decoding and suggest its potential for practical use. The computational results demonstrate that in a lownoise condition, the integer optimization decoding achieved higher bit error rate performance than did the common sum-product decoding for low-density parity-check codes.

DOI
10.34360/00007876

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This paper explores a mathematical optimization approach to error correction. Tanatmis et al. [2010] proposed an integer optimization formulation for the maximum likelihood decoding of binary linear codes. They developed a cutting plane algorithm in which valid inequalities for cutting off non-integral solutions are iteratively added to the continuous relaxation problem. By contrast, we focus on the integer optimization decoding; that is, we solve the integer optimization problem directly by using mathematical optimization software. We evaluate the computational performance of the integer optimization decoding and suggest its potential for practical use. The computational results demonstrate that in a lownoise condition, the integer optimization decoding achieved higher bit error rate performance than did the common sum-product decoding for low-density parity-check codes.
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We study an integer programming (IP) based separation approach to find the maximum likelihood (ML) codeword for binary linear codes. An algorithm introduced in Tanatmis et al. is extended and improved with respect to decoding performance without increasing the worst case complexity. This is demonstrated on the LDPC and the BCH code classes. Moreover, we propose an integer programming formulation to calculate the minimum distance of a binary linear code. We exemplarily compute the minimum distance of the (204, 102) LDPC code and the (576, 288) WIMAX code. Using the minimum distance of a code, a new class of valid inequalities is introduced.