Abstract
This paper proposes distributed Reed-Muller coded spatial modulation (DRMC-SM) scheme based on Kronecker product (KP) construction. This special construction enabled an effective distribution of classical Reed-Muller (RM) code along source and relay nodes. The proposed DRMC-SM scheme not only offers resilience in bit error rate (BER) performance but also enhances the spectral efficiency due to additional antenna index transmission inculcated by spatial modulation (SM). The usefulness of KP construction over classical Plotkin (CP) construction in coded-cooperation is analysed with and without incorporating SM. An efficient criteria for selecting the optimum bits is adopted at relay node which eventually results in better weight distribution of the mutually constructed (source and relay) RM code. The numerical results show that proposed KP construction outperforms CP construction by 1 dB in signal to noise ratio (SNR) at bit error rate (BER) of $$\,7\times 10^{-7}$$ . Moreover, the proposed DRMC-SM scheme outperforms its non-cooperative Reed-Muller coded spatial modulation scheme as well as distributed turbo coded spatial modulation scheme. This prominent gain in SNR is evident due to the path diversity, efficient selection of bits at the relay node and joint soft-in-soft-out (SISO) RM decoding employed at the destination node.
Highlights
Over a past decade, the multiple input multiple output (MIMO) techniques are widely deployed in wireless communication system to attain higher spectral efficiency [1, 2] and ameliorate link reliability [3, 4]
Distributed Reed-Muller coded spatial modulation (DRMC-SM) scheme has been proposed in this manuscript
If relay is given an extra gain of 2 dB in signal to noise ratio (SNR) over source node, i.e. ΓRD = ΓSD + 2 dB, the bit error rate performance of coded cooperative distributed Reed-Muller coded spatial modulation (DRMC-SM) scheme is further enhanced as it yields 2.5 dB performance gain over non cooperative RMC-SM scheme at BER= 4.5 × 10−6
Summary
Classical Reed Muller codes belonged to a class of linear block codes whose rich structural properties and simple construction make it distinct over other block codes. The dimension and minimum hamming distance of RM code R(r, n) is defined by u =. The RM codes are rich in structural properties which allow them to be decomposed into component RM codes. A3(N3, u3, d3) is decomposed into two short length RM codes A1(N1, u1, d1) and A2(N2, u2, d2), where Nk,uk and dk(k = 1, 2, 3) that defines code length, information sequence length and code’s minimum hamming distance. The obtained generator matrix through KP construction is given as GA3 =. Where GA1 , GA2 and GA3 are the generator matrices of Reed Muller codes i.e., A1, A2 and A3, respectively. The dimension and minimum hamming distance [20] of RM code A3 are given by u3 = u1 + u2 and d3 = min{2d1, d2}, respectively. Better codes in terms of BER can be constructed by exploiting its construction in coded-cooperation
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