Jointly optimized multiple Reed-Muller codes for wireless half-duplex coded-cooperative network with joint decoding

Abstract

In this paper, we present a novel technique to use Reed-Muller (RM) codes for the wireless half-duplex coded-cooperative network. Plotkin's construction allows RM codes to be used in a coded-cooperative scheme. To improve the cooperation provided by the relay in a coded-cooperative scheme, a design criterion and an efficient algorithm to achieve the design objective are also suggested. Moreover, union bounds for average error probability are determined, for both the cooperative and the non-cooperative schemes based on RM codes in the Rayleigh fading channel. To generalize the proposed RM coded-cooperative scheme, we examined different RM codes at the source and at the relay. At the destination, soft decision maximum likelihood decoding (SD-MLD) and majority logic decoding are used. Theoretical analysis and Monte-Carlo simulations show that the proposed RM coded-cooperative scheme clearly outperforms the RM non-cooperative scheme.

Multiple relay‐based Reed–Muller network‐coded cooperation for wireless communication system

“…Store it in set Q. Now Q = 1 therefore, the optimum combination λ 0 = λ p = [1,3,4,5,6,7,9,10,11,13,15] corresponds to the least α 2 , i.e. 38, is selected and algorithm-1 is terminated at this stage.…”

“…The unique combination of ωg that yielded the lowest β 2 is 60 as shown in Table 2. This obtained unique combination is saved in set V. Now V = 1, therefore, the optimum combination ω 0 = ωg = 4, 6,7,9,11,12,13,15,17,19,20,21,22,23,24, 26 corresponds to minimum β 2 , i.e. 60, is selected and algorithm-2 is terminated at this stage.…”

“…The average bit-error probability bound for the proposed scheme is derived from the average bit-error probability bound of point-topoint RM coded (non-cooperative) scheme. The point-to-point RM coded scheme means that the RM code is not distributed among the multiple sources and among the multiple relays instead, the communication is directly taking place from source node (S) to destination node D. The probability of error for the R 5 coded noncooperative scheme for fast Rayleigh fading channels can be written by using the methods proposed in [7,23] as follows:…”

“…Υ R 1 D = Υ R 2 D = Υ S 1 D = Υ S 2 D over fast Rayleigh fading channel. The BER performance of the MR-RMNCC scheme is compared with RMNCC [14] and noncooperative scheme [7] under identical conditions, i.e. all the compared schemes have almost the same code rate, i.e.…”

“…The typical 5G communication scenario includes machine-type communication such as machine-to-machine communication that requires a short length message sequence rather than a long length message sequence [6]. The short length channel code such Reed-Muller (RM) code has been recently utilised in the coded-cooperative scenarios that not only yields better BER performance but also offered low complexity in both encoding and decoding processes [7]. Furthermore, another short length RM-coded cooperative scheme based on multiple relays is designed for vehicular ad hoc networks in the literature [8].…”