LDPC Coded Soft Forwarding with Network Coding for System Model - PowerPoint PPT Presentation

Motivation LDPC Coded Soft Forwarding with Network Coding for System Model Two-Way Relay Channel Soft For- warding Calculation of LLR Nalin K. Jayakody 1 ,Vitaly Skachek 1 , Mark Flanagan 2 Soft Error Variance 1 Institute of Computer Science, University of Tartu, ESTONIA. Analysis 2School of Electrical and Communications Engineering Simulation University College Dublin, IRELAND. Results Summary Design and Application of Random Network Codes (DARNEC) COST Action IC1104 Istanbul, 5th Nov 2015 DARNEC 2015 1/24

Overview Motivation Motivation System Model System Model Soft For- warding Calculation Soft Forwarding of LLR Soft Error Calculation of LLR Variance Analysis Simulation Soft Error Variance Analysis Results Summary Simulation Results Summary DARNEC 2015 2/24

Why soft information relaying? ◮ The Amplify and Forward (AF) and Decode and Forward (DF) protocols suffer from noise amplification and error propagation, respectively ◮ In order to combine the advantages of both AF and DF in relay networks, many Motivation strategies have been proposed in which soft (reliability) information is transmitted System Model to the destination; this idea is known as soft information relaying (SIR) Soft For- ◮ SIR has been shown to be an effective solution which mitigates the propagation warding of relay decoding errors to the destination Calculation of LLR Soft Error Variance Relay Relay Analysis Simulation Results Second Time Slot Summary Destination Destination Source Source First Time Slot DARNEC 2015 3/24

What is "Soft Information"? Motivation System ◮ Soft information indicates the reliabilities or probabilities of the underlying Model source symbols Soft For- warding Calculation ◮ Soft information is often expressed in the form of log-likelihood ratios (LLRs) or of LLR soft bits Soft Error Variance ◮ As the destination decoder works in the probabilistic domain, the soft Analysis information relaying (SIR) protocol complies with the decoder’s requirements Simulation Results ◮ It also gives an idea regarding the reliability of the relay received signal to the Summary destination DARNEC 2015 4/24

Contributions Motivation ◮ We investigate a soft network coded two way relay channel (TWRC) scheme over System Model Rayleigh fading channels with LDPC coding. Soft For- warding ◮ We introduce a model for the effective noise experienced by the soft network Calculation coded symbols called the soft scalar model. This model is then used to compute of LLR the log-likelihood ratios (LLRs) at the destination. Soft Error Variance ◮ For this purpose, an analytical expression is derived for the soft error variance. Analysis Simulation ◮ We also introduce a simplified model to calculate the soft error variance which is Results very easy to compute and adapt on-the-fly. Summary ◮ Finally, we provide an upper bound of the soft error variance. DARNEC 2015 5/24

The multiple access relay system in half-duplex mode Motivation System Relay Model Soft For- warding x R x R Calculation of LLR Soft Error Variance Analysis Simulation x A x B Results x B Summary x A User B User A DARNEC 2015 6/24

Detailed System Model Destination B Motivation Joint LDPC Network Soft Channel Decoder Decoder Demodulator System Model Relay Soft For- Channel Source A warding Calculation LDPC Decoder Soft LDPC of LLR Modulator Channel Demodulator Encoder Soft Error Soft Network Power Scaling Variance Encoder Source B Analysis Simulation Soft LDPC Channel LDPC Decoder Results Modulator Demodulator Encoder Summary Channel Destination A Soft Joint LDPC Network Channel Decoder Decoder Demodulator DARNEC 2015 7/24

System Model Motivation System ◮ The received signals at each of the nodes in the first and second time slots are Model Soft For- � warding y iR = P i h iR x i + n iR , Calculation of LLR and � y i ¯ i = P i h i ¯ i x i + n i ¯ Soft i , Error Variance where n iR and n i ¯ i are vectors having i.i.d. real Gaussian (noise) entries with zero Analysis mean and variance σ 2 iR and σ 2 i , respectively. i , ¯ i ∈ { A , B } with i � = ¯ i . i ¯ Simulation ◮ In the third time slot, the relay employs an LDPC decoder (regular) for decoding Results (using the parity-check matrix H ) the noisy codewords received via the user-relay Summary links. DARNEC 2015 8/24

SDF at the relay LLR computation � P ( x j � Motivation i =+ 1 | y iR ) λ iR ( x j i | y iR ) = log , P ( x j System i = − 1 | y iR ) Model where i ∈ { A , B } .This computation can be easily performed using an LDPC decoder Soft For- warding Soft network coding operation Calculation The network coding operation can be approximately implemented in the soft domain of LLR using the computed a posteriori LLR values as Soft Error Variance x j x j x j � x j x j � ˜ R ≈ sign (˜ A ˜ B ) min | ˜ A | , | ˜ B | Analysis , Simulation Results where x j A = λ AR ( x j Summary ˜ A | y AR ) and x j B = λ BR ( x j ˜ B | y BR ) . This can be viewed as the hard decision of the network coded BPSK symbol multiplied by a reliability measurement based on the a posteriori LLRs. DARNEC 2015 9/24

Soft forwarding Motivation System Model ◮ The signal transmitted from the relay can be written as Soft For- warding x R = β ˜ ˇ x R . Calculation of LLR ◮ The factor β is chosen to satisfy the transmit power constraint at the relay, i.e., Soft x j Error R ) 2 ] = 1. E [(ˇ Variance Analysis ◮ Thus, the received signal at source i in the third time slot can be written as Simulation Results � y Ri = P R h Ri β ˜ x R + n Ri . Summary DARNEC 2015 10/24

Soft scalar model Motivation We modify the model first introduced in [Jayakody et al.] for the relationship between System the correct symbols x j R = x j A x j x j B and the soft symbols (LLRs) ˜ R , but here the model is Model applied to the LLRs and not to the “soft modulated” symbols: Soft For- warding x j R = η x j n j , ˜ R + ˜ Calculation of LLR n j is called the soft error variable, Soft ◮ where ˜ Error Variance ◮ The constant η is called the soft scalar (its effect similar to that of a fading Analysis coefficient), Simulation ◮ we choose the value of η which minimizes the mean-square value of the soft Results error, i.e., Summary η = E [ x R ˜ x R ] . DARNEC 2015 11/24

LLR computation at the destination Motivation ◮ Assuming the soft scalar model, the received signal at each source i in the third System Model time slot can be written as Soft For- √ warding y Ri = P R h Ri βη x R + ˆ n Ri , Calculation of LLR where � n Ri = n Ri + ˆ P R h Ri β ˜ n . Soft Error Variance ◮ The LLR corresponding to the third time slot transmission is given by Analysis √ Simulation � P ( x j � R = + 1 | y Ri ) = 2 P R h Ri βη Results λ Ri ( x j y j R | y Ri ) = log P ( x j σ 2 Ri . ˆ R = − 1 | y Ri ) Summary Ri σ 2 Ri = σ 2 Ri + P R h 2 Ri β 2 σ 2 where ˆ ˜ n . DARNEC 2015 12/24

Motivation ◮ Note that the a priori LLR at source i corresponding to the source ¯ i is easily System calculated as Model � ii ) = 2 P ¯ i h ¯ ii ( x j ii y j λ ¯ i | y ¯ Soft For- ¯ σ 2 ¯ ii . warding ¯ ii Calculation of LLR ◮ Next, the network decoded soft symbols at source i are computed via Soft Error ¯ λ Ri ( x j i | y Ri ) = λ Ri ( x j R | y Ri ) · x j Variance ¯ i . Analysis Simulation ◮ At each source i , the parity bit ( p ) LLRs derived from the relay transmission will Results be combined with the parity bit LLRs derived from the transmission from source ¯ i Summary ( p ) λ ( p ) i ) = λ ( p ) ii )+ ¯ ( x ¯ ii ( x ¯ i | y ¯ λ Ri ( x ¯ i | y Ri ) . ¯ i DARNEC 2015 13/24

Analysis of the soft error Motivation System ◮ First, we note that since the symbols x R are equidistributed in {− 1 , + 1 } , we have Model Soft For- E ( x R ) = 0. warding Calculation ◮ By invoking symmetry of the channel, BPSK modulation, and LDPC decoding of LLR process we also have E (˜ x R ) = 0; it follows that E (˜ n ) = 0. Soft Error Variance ◮ We assume [ten Brink] Analysis Simulation x R (Λ | x R = 1 ) = p ˜ x R ( − Λ | x R = − 1 ) , p ˜ Results Summary where Λ indicates the network coded LLR at the relay. DARNEC 2015 14/24

Analysis of the soft error Lemma 1 Motivation The PDF of the soft error variable conditioned on the network-coded relay symbol System satisfies Model p ˜ n (Λ | x R = 1 ) = p ˜ n ( − Λ | x R = − 1 ) Soft For- warding for all Λ ∈ R . Calculation of LLR Corollary 1 Soft The PDF of the soft error variable possesses even symmetry, i.e. Error Variance Analysis p ˜ n (Λ) = p ˜ n ( − Λ) Simulation Results for all Λ ∈ R . Summary Lemma 2 This lemma proves that the soft scalar η is independent of conditioning on x R ,i.e. E (˜ x R | x R = + 1 ) = − E (˜ x R | x R = − 1 ) = η . DARNEC 2015 15/24