Food Communication System Evaluation of LDPC Codes Combined with Differential Space-time Block Codes

In this study, we propose a multi-antenna food communication system combined Low-Density ParityCheck (LDPC) codes with Differential Space-Time Block Codes (DSTBC), in which Channel State Information (CSI) is unknown to the transmitter and the receiver. The food communication system performance is given through computer simulation, we can see that the proposed food communication system not only provides transmit diversity gain but also coding gain.


INTRODUCTION
Multiple antenna schemes are promising technique in future communication food communication system which can improve the food communication system capacity and provide diversity gain. In multi-antenna systems, Differential Space-Time Block Coding (DSTBC) attracted the attention of many researchers because the channel state information is not needed not only at the transmitter side but also at the receiver side (Tarokh and Jafarkhani, 2000). It has been proved that there is 3 dB performance gap between differential detection and coherent detection, in order to provide coding gain besides of diversity gain, it is necessary to use them together with suitable channel codes. Teimouri and Shiva (2008) analyses the error probability bounds of concatenated DSTBC and Trellis Coded Modulation (TCM). Muayyadi et al. (2014) analyses the performance of multiuser WCDMA food communication system using DSTBC in Rayleigh fading channel. They didn't consider the most powerful error correcting codes-Low Density Parity Check codes (LDPC) (Gallager, 1962;MacKay, 1999). Suzuki et al. (2009) and Wang and Li (2007), concatenation scheme of LDPC codes and Quasi orthogonal STBC is studied. But LDPC codes have not been considered in DSTBC as far as we know. This observation motivates us to propose the DSTBC food communication system based on LDPC codes. Fig. 1, our food communication system model consists of a channel code concatenated with DSTBC.

Food communication system model: As shown in
Information bits are firstly sent to the LDPC encoder, the coded bits are sent to the DSTBC encoder after modulation and then transmitted on a frame-byframe basis through MIMO fading channels after differential space-time block coding. There is an interleaver in the food communication system model of, but in our system, due to the fact that LDPC codes are employed, whose low density characteristic enables them to act as interleaver as well. It follows that there is no need to use interleaver and thereby the food communication system overhead can be significantly reduced.
We assume that there are N T transmit antennas and N R receive antennas, then the diversity order is defined as K = N T N R . The MIMO fading channel can be expressed as a matrix H = [h ij ] (i = 1,…N R , j = 1…N T ), where, h ij is the channel coefficient between the jth transmit antenna and the i th receive antenna. Under the assumption of independent Rayleigh fading, the channel coefficients h ij are modeled as independent and identically distributed (i.i.d.) complex circular Gaussian random variables with zero mean and unit variance. The received signal can be expressed as: where, Y is a N R ×T matrix of received symbols with T representing the number of symbols per antenna, X is a N T ×T matrix of transmitted symbols and N is a N R ×T noise matrix with elements modeled as i.i.d. complex circular Gaussian random variables having zero mean and unit variance.

Low
where, λ i (ρ i ) is nonnegative and λ (1) (ρ (1)) equals one, λ i (ρ i ) specifies the variable (check) node degree distribution when the pair is associated to a sequence of code ensembles C n (λ, ρ). More precisely, λ i (ρ i ) represents the fraction of edges emanating from variable (check) nodes of degree i. The maximum variable degree and check degree are denoted by d v and d c respectively. When it comes to degree i in a paritycheck matrix, it means the same as column weight i, which is defined as the number of nonzero elements in that column of the parity-check matrix. The decoding scheme is performed as follows. The first step: Initialize: The second step: Operation on check nodes: The third step: Operation on variable nodes: where, the constants K ij are chosen to ensure q ij (0) + q ij (1) = 1. The forth step: Compute: where, the constants K i are chosen to ensure Q i (0) + Q i (1) = 0. The fifth step: make decision according to Q i : If HI = 0 or the max-iterations is reached, the decoding process is ended, otherwise go to the step one.

DIFFERENTIAL SPACE-TIME BLOCK CODES
In this section, we will briefly introduce the encoder and decoder of DSTBC. After LDPC encoding and DSTBC encoding, s 1 and s 2 are transmitted at time 1, -s 2 * and s 1 * are transmitted at time 2 from two antennas, which do not carry any information. Suppose s 2t-1 and s 2t are sent respectively from transmit antennas one and two at time 2t-1 and that -s * 2t , s * 2t-1 are sent, respectively from antennas one and two at time 2t, we use the following matrix to denote the orthogonal basis which act as the reference to calculate the next transmitted symbols: Then s 2t+1 and s 2t+2 can be calculated as: where, M 2t-1 = (M 1 2t-1 M 2 2t-1 ) is the differential coefficient vector. The differential encoding process as (8) is inductively repeated until the end of the frame.
We demonstrate the above differential encoding scheme by an example. Assume that the constellation is BPSK consisting of the points 1/ 2 and -1/ 2, then the mapping M maps two bits onto BPSK constellation is given by (Tarokh and Jafarkhani, 2000): Decoding scheme: For notational simplicity, we will first present the results for one receive antenna. For example, there are four signals r 2t-1 , r 2t , r 2t+1 , r 2t+2 are received: where, H is channel coefficients matrix redefined by: After differential detection, we get a vector of (R 1 , R 2 ): The receiver computes the closest vector to (R 1 R 2 ), which is

RESULTS AND DISCUSSION
The frame design of the early warning system of food safety: In this section, we present simulation results for both the performance of the DSTBC and LDPC-DSTBC, BPSK, QPSK and 8PSK constellations are considered. The fading is assumed to be constant over frame and vary from one frame to another. As shown in Fig. 2. We construct the mother code by using the Progressive Edge Growth (PEG) method, which has been proven to be able to produce the best LDPC codes with moderate code length and can generate a Weight-Increasing Parity-Check (WIPC) matrix. We employ LDPC codes with rate 1/2 (504, 252) in our simulation, the maximum iterations is eight. The variable node degree distribution of irregular LDPC codes is as follows:

∑
It has been proved that the performance of the DSTBC is 3 dB worse than the STBC scheme which employs coherent detection). Our scheme can significantly compensate this gap. As shown in Fig. 3 and 4.

CONCLUSION
In this study, we propose a food communication system diagram concatenated LDPC and Differential Space-time Block Codes. It can not only provide diversity gain but also coding gain, which no channel state information is needed. The food communication system performance will be improved further if LDPC codes with longer code length are employed.