A Note on the Linear Programming Decoding of Binary Linear Codes for Multiple-Access Channel

• HORII Shunsuke

  Department of Applied Mathematics, Waseda University

• MATSUSHIMA Toshiyasu

  Department of Applied Mathematics, Waseda University

• HIRASAWA Shigeichi

  Waseda Research Institute for Science and Engineering, Waseda University and Cyber University

Abstract

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 non-linear 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.

Journal

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A (6), 1230-1237, 2011

  The Institute of Electronics, Information and Communication Engineers

Keywords

• multiple-access channel
• maximum likelihood decoding
• linear-programming decoding

Details

• CRID: 1390282681286999680
• NII Article ID: 10029802169
• NII Book ID: AA10826239
• DOI: 10.1587/transfun.e94.a.1230
• ISSN: 17451337
• ISSN: 09168508
• Web Site: http://www.jstage.jst.go.jp/article/transfun/E94.A/6/E94.A_6_1230/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed