A note on the linear programming decoding of binary linear codes for multiple-access channel

Shunsuke Horii*, Toshiyasu Matsushima, Shigeichi Hirasawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we develop linear-programming (LP) decoding for multiple-access channels with binary linear codes. For single-user channels, LP decoding has attracted much attention in recent years as a good approximation to maximum-likelihood (ML) decoding. We demonstrate how the ML decoding problem for multiple-access channels with binary linear codes can be formulated as an LP problem. This is not straightforward, because the objective function of the problem is generally a nonlinear function of the codeword symbols. We introduce auxiliary variables such that the objective function is a linear function of these variables. The ML decoding problem then reduces to the LP problem. As in the case for single-user channels, we formulate the relaxed LP problem to reduce the complexity for practical implementation, and as a result propose a decoder that has the desirable property known as the ML certificate property (i.e., if the decoder outputs an integer solution, the solution is guaranteed to be the ML codeword). Although the computational complexity of the proposed algorithm is exponential in the number of users, we can reduce this complexity for Gaussian multiple-access channels. Furthermore, we compare the performance of the proposed decoder with a decoder based on the sum-product algorithm.

Original languageEnglish
Pages (from-to)1230-1237
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number6
Publication statusPublished - 2011 Jun


  • Linear-programming decoding
  • Maximum likelihood decoding
  • Multiple-access channel

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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