Abelian codes over Eisenstein-Jacobi integers for MIMO systems

Abstract

In this work we present construction of Space Time Block Codes (STBC) from Abelian codes. A well known Eisenstein-Jacobi rank preserving map is applied to map the codeword matrix symbols to symbols in the complex plane. We then propose an N<inf>T</inf> X N<inf>R</inf> MIMO (multiple input, multiple output) communication system employing the constructed STBC. An analysis on the receiver (decoder) computational complexity and an upper bound on the average probability of error is presented. Performance of the proposed system is evaluated for a 4 X 2 MIMO system. Simulation results show that at an average bit error rate (ABER) of 10-4 the STBC over F<inf>7</inf> result in a coding gain of approximately 4 dB as compared to C(4; 2; 4) code. © 2017 IEEE.