# Error Bounds For Decode-and-forward Relaying

## Contents |

**Sel. **In fact, the error vectore = xr⊕ xs∈C (2)is also a valid codeword from the code C. For the relay channel,Cover and El Gamal [3] described two fundamental cod-ing strategies where the relay either decodes (decode-and-forward), or compresses (compress-and-forward) the receivedsource tran smission befo re forwarding it to Its labelling isdeﬁned by (12). http://megavoid.net/error-bounds/error-bounds.html

CitationsCitations4ReferencesReferences25Bounds of the probability of error for decode-and-forward relaying with two sources"In this case, no information about the channels s j r-ch is used at the decoder. Inform. Correspondinglywe can use the union bound to upper-bound the error proba-bility. MAP decoderThe MAP decoder for the relay channel with decode-and-forward has not yet b een analyzed in detail in literature.

## Error Bounds For Decode-and-forward Relaying

Thecorresponding MAP decoding rule is[ˆxs, ˆxr]=argmax[xs,xr]∈C×Cp(xs= xs, xr= xr|ysd, yrd) (7)=argmax[xs,xr]∈C×Cp(ysd, yrd|xs, xr) · p(xs, xr)/p(ysd, yrd)=argmax[xs,xr]∈C×Cp(ysd|xs) · p(yrd|xr) · p(xr|xs) · c0(8)=argmax[xs,xr]∈C×C12Ni=1˜xs,iLs,i+12Ni=1˜xr,iLr,i+lnp(xr= xr|xs= xs), (9)where C×Cdenotes the Cartesian product of A good match between the simulations andthe bounds is observed. Workshop, (San Diego, USA), Feb. 2010.[20] S. Symp.

Commun. (ICC),(Istanbul, Turkey), June 2006.[21] A. Here are the instructions how to enable JavaScript in your web browser. Generated Mon, 10 Oct 2016 14:35:39 GMT by s_ac15 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.7/ Connection NOTATIONThroughout the paper, we write vectors in boldface letters,and the i-th element of a vector a as ai.

Asilo-mar Conf. Nosratinia, “Coded coopera-tion in wireless communications: space-time transmission and iterativ edecoding,” IEEE Trans. The SNR value γ ′ rd can be optimised to minimise the bound to the error probability as explained in [11, 12] for the onesource case. https://www.researchgate.net/publication/224145042_Error_bounds_for_decode-and-forward_relaying The mean values of Lr,i,however,depend on the codeword xrtransmitted by th e relay.Consider ﬁrst the case that the relay d ecodes error-free, i.e.that xr= xs= 0.ThenallLr,ihave positive mean, andp(e|¯er) corresponds to

IMPLEMENTATION OF THE MAP DE CODERThe ML decoder in (5) can easily and in a straightforwardfashion be implemented using the trellis of the code C.Therefore we omit the details here.A direct Roy **and T.** Generated Mon, 10 Oct 2016 14:35:39 GMT by s_ac15 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.6/ Connection The ML de-coder estimates only the codeword transmitted by the source,whereas the MAP decoder estimates in add ition to that, in ajoint fashion, the codeword transmitted by the relay.

The signal-to-noise ratio (SNR) of an AWGNchannel is denoted by γ = Es/N0,whereEsis the receivedsignal energy and N0is the single-sided noise power density.We use the complementary error function erfc(z)=2/√π ·∞ze−s2ds.Consider a Please try the request again. Error Bounds For Decode-and-forward Relaying We speciﬁcally focus on decode-and-forward,which has been shown to p erform well when the relay islocated close to the source. with p(ue,i=0)=1 − q and p(ue,i=1)=q, where the probability q is small.Notice in particular that ue,iis not uniform.In th is way, we obtainp(w(e)=0)=(1− q)Kp(w(e)=dmin)=Kq(1 − q)K−1(11)...where we assume that the minimum

the probability that therelay decodes ysrto e).As the s-r channel is an AWGN channel, the zero-weight er-ror word occurs with the highest probability. navigate here N. Yates, “Cooperativ e communications,”FNT in Networking, vol. 1, no. 3-4, pp. 271–425, 2006.[2] E. Based on the two noisy observations ysdand yrd, the destination node estimates the codeword xsthatwas transmitted by the source node; this estimate is denotedbyˆxs.The source-to-destination (s-d) channel, the source-to-relay(s-r) channel and

Acoust., Speech, and Signal Processing,(LasVegas,USA),pp. 3213–3216, Apr. 2008.[19] A. Downloaded on August 05,2010 at 08:03:27 UTC from IEEE Xplore. The proposed errormodel, enabling the im plementation of the MAP decoder, alsoallows us to take into account the decoding errors at the relayin the derivation of MAP performance bounds.The reminder of http://megavoid.net/error-bounds/error-bounds-statistics.html The bounds are expressed with a union-bound approach and weight enumerators.

SYSTEM MODELWe consider the wireless relay channel d epicted in Fig. 1:source s communicates with destination d with the help ofrelay r, which uses the decode-and-forward strategy. Valenti and B. Of course, the resulting probability distributioncannot be identical to the actual one for all the weights as ithas only the single p arameter q.

## Section IIoutlines some notation used in this paper.

Sneessens and L. Louveaux, and L. Subscribe Enter Search Term First Name / Given Name Family Name / Last Name / Surname Publication Title Volume Issue Start Page Search Basic Search Author Search Publication Search Advanced Search Kramer, I.

We consider the scenario where the SNRsγsrand γrdare ﬁxed, and γsdvaries.In Fig. 3 we plot the bounds on the frame error rate underML and MAP decoding together with the corresponding simu-lation FER bounds (empty markers) and simulations (solid markers) forthe relay network of Fig. 1. The system returned: (22) Invalid argument The remote host or network may be down. this contact form Aazhang, “Lowdensity parity check codes for the relay channel,” IEEE J.

More precisely, for each triplet (γ sd , γ sr , γ rd ), we determine numerically the value of γ ′ rd which minimises the lower bound on the probability Fundamental limits for this scenario havebeen considered in [6]-[9]. Schemes based on turbo codes, e.g.,[10, 12, 14, 16, 17, 20], and low-density parity-check (LDPC)codes, e.g., [21, 22], are most proliﬁc.Code design and performance analysis have been proposedbased on decoding thresholds This is discussed in more detail in Section V-A.IV.

Theory, vol. 51,pp. 1815–1817, May 2005.[9] Y. i =1, 2,...,N,whereyidenotes the i-th element of vector y.For the analysis later on, we need the conditional distributionsof these L-values. Downloaded on August 05,2010 at 08:03:27 UTC from IEEE Xplore. Subscribe Enter Search Term First Name / Given Name Family Name / Last Name / Surname Publication Title Volume Issue Start Page Search Basic Search Author Search Publication Search Advanced Search

van der Meulen, “Three-terminal communication channels,” Adv.Appl. Use of this web site signifies your agreement to the terms and conditions. Restrictions apply. ••••••••••••••••••••••••••••••••••••Fig. 3. The complement of eris denoted by ¯er.Theprobability of error at the destination can be written asp(e)=p(e|er)p(er)+p(e|¯er)p(¯er), (14)where we d istinguish between the case that the relay m akesan erro r and

Inthese schemes multiple-access interference is assumed at thedestination, and full duplex operation is assumed at the relay.Due to practical constraints, it is considered a challengeto provide full duplex operation at the For convenience, instead ofestimating [xs, xr], we estimate [xs, e], i.e. Inform. Skip to MainContent IEEE.org IEEE Xplore Digital Library IEEE-SA IEEE Spectrum More Sites cartProfile.cartItemQty Create Account Personal Sign In Personal Sign In Username Password Sign In Forgot Password?

Wireless Commun., vol. 6, pp. 3384–3394,Sept. 2007.1010Authorized licensed use limited to: KTH THE ROYAL INSTITUTE OF TECHNOLOGY. M. The advantage of this error model is that it providesa reasonable approximation of the true distribution of errorvectors, and th at it allows a trellis-based implementation ofthe MAP decoder, as shown This decoder uses twoassumptions:A1 The s-d ch an n el SNR γsdis known at the destination.A2 The observation yrdis the output of a (virtual) memo-ryless AWGN channel with input xsand SNR

IEEE Vehicular Technolo gy Conference(VTC), pp. 322–326, Oct. 2003.[11] M. Please try the request again. Furthermore we present analytical expressions for the error rates for both ML and MAP decoding.Discover the world's research10+ million members100+ million publications100k+ research projectsJoin for free Error Bounds for Decode-and-Forward RelayingAlexandre