### 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 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 language | English |
---|---|

Pages (from-to) | 1230-1237 |

Number of pages | 8 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E94-A |

Issue number | 6 |

DOIs | |

Publication status | Published - 2011 Jun |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

**A note on the linear programming decoding of binary linear codes for multiple-access channel.** / Horii, Shunsuke; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E94-A, no. 6, pp. 1230-1237. https://doi.org/10.1587/transfun.E94.A.1230

}

TY - JOUR

T1 - A note on the linear programming decoding of binary linear codes for multiple-access channel

AU - Horii, Shunsuke

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 2011/6

Y1 - 2011/6

N2 - 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.

AB - 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.

KW - Linear-programming decoding

KW - Maximum likelihood decoding

KW - Multiple-access channel

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UR - http://www.scopus.com/inward/citedby.url?scp=79957973641&partnerID=8YFLogxK

U2 - 10.1587/transfun.E94.A.1230

DO - 10.1587/transfun.E94.A.1230

M3 - Article

AN - SCOPUS:79957973641

VL - E94-A

SP - 1230

EP - 1237

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 6

ER -