Optimal Decoding and Performance Analysis of a Noisy Channel Network with Network Coding

Abstract

Abstract-We investigate sink decoding approaches and performance analysis for a network with intermediate node encoding (coded network). The network consists of statistically independent noisy channels. The sink bit error probability (BEP) is the performance measure. First, we investigate soft-decision decoding without statistical information on the upstream channels (the channels not directly connected to the sink). Numerical results show that the decoder cannot significantly improve the performance from a hard-decision decoder. We develop union bounds for analysis. The bounds show the asymptotic (regarding SNR: signal-to-noise ratio) performance of the decoder. Using statistical information about the upstream channels, we can find the error patterns of final hop channels (channels directly connected to sinks). With the error patterns, maximum-likelihood (ML) decoding can be performed, and a significant improvement in the BEP is obtained. To evaluate the union bound for the ML decoder, we use an equivalent point procedure. It is reduced to the least-squares problem with a linear constraint in the mediumto-high SNR region. With deterministic knowledge of the errors in the upstream channels, a genie-aided decoder can further improve the performance. We give the union bound for the genie decoder, which is straightforward to evaluate. By analyzing these decoders, we find that knowledge about the upstream channels is essential for good sink decoding.Index Terms-Network coding, noisy channel, optimal decoding, bit error probability, transmitted energy and analysis bounds.

Anti error propagation methods for wireless uplink using network coding

“…Consequently, the complex decision rule (16) is simplified to the threshold-based relaying strategy. We observe that the two source-relay channels have to meet the same SNR threshold, as the relay decoding error is bounded by the weaker channel as shown in (13). It is also observed that imposing any threshold having the form of log (λ T,k Γ) on γ k for some constant λ T,k > 0 and k = 1, 2 would lead to the same diversity performance, since log λ T,k Γ Γ→∞ ≈ log Γ.…”

“…However, global channel state information (CSI) needs to be known at the receiver, which greatly increases the signaling overhead. MLD based on local CSI is investigated in [13], but the channel fading effects are neglected to simplify the analysis. Another common weakness of the above work [11]- [13] is that only the receiver-side technique is considered.…”

“…MLD based on local CSI is investigated in [13], but the channel fading effects are neglected to simplify the analysis. Another common weakness of the above work [11]- [13] is that only the receiver-side technique is considered. In the cellular systems, the user devices generally have very limited power and processing capability.…”

On the energy efficiency in multi-user multi-relay coded network

“…Based on binary network coding, classical butterfly network and the two-way relay scheme have been widely studied [1]- [5]. Relay selection is conducted to maximize the energy efficiency (EE) [1], minimize the bit error rate [2], [4] and maximize the throughput [3], [5]. In [6], an approach with dynamic network coding has been applied.…”

Near-Capacity Network Coding for Cooperative Multi-User Communications

“…Network coding is a recently introduced paradigm conceived for efficiently disseminating data in multicast wireless networks, where the data flows arriving from multiple sources are combined to achieve compression and hence to increase the achievable throughput, as well as to reduce the delay imposed and to enhance the error-resilience [1]- [3]. The relay nodes store the incoming packets in their own buffer and then transmit the linear combinations of these packets.…”