Minimum MSE relaying in coded networks

Abstract

In order to combine the advantages of Amplify-Forward (AF) and Decode-Forward (DF) in relay networks, several strategies have been developed making use of reliability information after decoding at the relay. The use of soft-output channel decoders enables forwarding reliability information for the decoded bits. This soft information can be forwarded in different ways, e.g. by transmission of the Log Likelihood Ratios (LLRs) normalized to the power constraint. In this paper transmitting expectation values after decoding, the so-called Decode-Estimate-Forward (DEF) scheme, will be shown to be the best choice in terms of the mean squared uncorrelated error at the receiver. Additionally, it will be shown that LLR combining is superior to maximum ratio combining at the receiver as the overall disturbance of the received signal is not Gaussian in the case of DEF. Furthermore, in the uncoded case LLR combing also improves the performance in terms of effective signal-to-noise ratio and bit error rate.

Distributed Soft Coding with a Soft Input Soft Output (SISO) Relay Encoder in Parallel Relay Channels

“…3 shows the proposed encoder structure at relay k. In the proposed DISC scheme, each relay exploits a rate-1 SISO encoder to encode the received analog signals based on its assigned constituent code. It has been shown in [6] and [31] that the soft bit estimate of source information symbol is the optimal input to the soft encoder in terms of maximizing the SNR of the SISO encoder output. Thus upon receiving signals, relay k first calculates the SBE of the source information symbol, denoted byx b k (n).…”

“…The SIR-LLR was first discussed in [5], where the relay calculates and forwards the LLR of received symbols. It was shown in [6,31] that the SIR-SBE is an optimal relaying protocol in terms of minimizing the mean square error (MSE) or maximizing the overall destination SNR. The Gaussian distribution has been used to approximate the probability distribution function (PDF) of both SBE and LLR.…”

“…In [29,37], a few error models have been proposed for distributed coding using DF protocol by taking into account the decoding errors in the destination decoding. In [4,7,8,23,29,31,36,38], distributed schemes with soft information encoding have been developed for a relaying system containing only one relay when imperfect decoding occurs at the relay. In these schemes, instead of making decisions on the transmitted information symbols at the relay as in other distributed coding schemes [14][15][16][17][18], the relay calculates and forwards the corresponding soft estimates.…”

Distributed Interleave-Division Multiplexing Space-Time Codes for coded relay networks

“…The idea of EF is the transmission of MMSE estimates conditioned on the received signal. This basic idea was recently extended to coded systems [6] and also to higher order modulation schemes [7]. This so-called Decode-Estimate-Forward (DEF) shows very good performance and is a reasonable choice in relay networks.…”

“…Transmission of Log-Likelihood Ratios (LLRs) is an alternative soft relay protocol called Decode-Amplify-Forward (DAF) and was investigated in combination with IDM-STC for an uncoded multi-user system in [8]. But as the DAF approach was already shown to be suboptimum in [6], we will not consider it here. In this paper a coded IDM-STC relay system with different relay schemes is investigated and the good performance of IDM-STC combined with DEF in realistic scenarios with small overhead and robustness against asynchronism is shown.…”