An Error Event Sensitive Tradeoff Between Rate and Coding Gain in MIMO MAC

Toni Ernvall*, Jyrki Lahtonen, Hsiao Feng Lu, Roope Vehkalahti

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

This paper investigates the design of codes for multiple-input multiple-output (MIMO) multiple access channel (MAC). If a joint maximum-likelihood decoding is to be performed at the receiver, then every MIMO-MAC code can be regarded as a single-user code, where the minimum determinant criterion proposed by Tarokh et al. is useful for designing such codes and for upper bounding the maximum pairwise error probability (PEP), whenever the codes are of finite rate and operate in finite signal-to-noise ratio range. Unlike the case of single-user codes where the minimum determinant can be lower bounded by a fixed constant as code-rate grows, it was proved by Lahtonen et al. that the minimum determinant of MIMO-MAC codes decays as a function of the rates. This decay phenomenon is further investigated in this paper, and upper bounds for the decays of minimum determinant corresponding to each error event are provided. Lower bounds for the optimal decay are established and are based on an explicit construction of codes using algebraic number theory and Diophantine approximation. For some error profiles, the constructed codes are shown to meet the aforementioned upper bounds, hence they are optimal finite-rate codes in terms of PEPs associated with such error events. An asymptotic diversity-multiplexing gain tradeoff (DMT) analysis of the proposed codes is also given. It is shown that these codes are DMT optimal when the values of multiplexing gains are small.

Original languageEnglish
Article number7271098
Pages (from-to)5931-5947
Number of pages17
JournalIEEE Transactions on Information Theory
Volume61
Issue number11
DOIs
Publication statusPublished - 1 Nov 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • algebra
  • fading
  • MIMO
  • Multiuser channels
  • space-time codes

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