📝 Abstract

Physical-layer Network Coding (PNC) can significantly improve the throughput of wireless two way relay channel (TWRC) by allowing the two end nodes to transmit messages to the relay simultaneously. To achieve reliable communication, channel coding could be applied on top of PNC. This paper investigates link-by-link channel-coded PNC, in which a critical process at the relay is to transform the superimposed channel-coded packets received from the two end nodes plus noise, Y3=X1+X2+W3, to the network-coded combination of the source packets, S1 XOR S2 . This is in distinct to the traditional multiple-access problem, in which the goal is to obtain S1 and S2 separately. The transformation from Y3 to (S1 XOR S2) is referred to as the Channel-decoding-Network-Coding process (CNC) in that it involves both channel decoding and network coding operations. A contribution of this paper is the insight that in designing CNC, we should first (i) channel-decode Y3 to the superimposed source symbols S1+S2 before (ii) transforming S1+S2 to the network-coded packets (S1 XOR S2) . Compared with previously proposed strategies for CNC, this strategy reduces the channel-coding network-coding mismatch. It is not obvious, however, that an efficient decoder for step (i) exists. A second contribution of this paper is to provide an explicit construction of such a decoder based on the use of the Repeat Accumulate (RA) code. Specifically, we redesign the belief propagation algorithm of the RA code for traditional point-to-point channel to suit the need of the PNC multiple-access channel. Simulation results show that our new scheme outperforms the previously proposed schemes significantly in terms of BER without added complexity.

💡 Analysis

Physical-layer Network Coding (PNC) can significantly improve the throughput of wireless two way relay channel (TWRC) by allowing the two end nodes to transmit messages to the relay simultaneously. To achieve reliable communication, channel coding could be applied on top of PNC. This paper investigates link-by-link channel-coded PNC, in which a critical process at the relay is to transform the superimposed channel-coded packets received from the two end nodes plus noise, Y3=X1+X2+W3, to the network-coded combination of the source packets, S1 XOR S2 . This is in distinct to the traditional multiple-access problem, in which the goal is to obtain S1 and S2 separately. The transformation from Y3 to (S1 XOR S2) is referred to as the Channel-decoding-Network-Coding process (CNC) in that it involves both channel decoding and network coding operations. A contribution of this paper is the insight that in designing CNC, we should first (i) channel-decode Y3 to the superimposed source symbols S1+S2 before (ii) transforming S1+S2 to the network-coded packets (S1 XOR S2) . Compared with previously proposed strategies for CNC, this strategy reduces the channel-coding network-coding mismatch. It is not obvious, however, that an efficient decoder for step (i) exists. A second contribution of this paper is to provide an explicit construction of such a decoder based on the use of the Repeat Accumulate (RA) code. Specifically, we redesign the belief propagation algorithm of the RA code for traditional point-to-point channel to suit the need of the PNC multiple-access channel. Simulation results show that our new scheme outperforms the previously proposed schemes significantly in terms of BER without added complexity.

📄 Content

1 Channel Coding and Decoding in a Relay System Operated with Physical-layer Network Coding

Shengli Zhang, Soung Chang Liew Department of Information Engineering The Chinese University of Hong Kong New Territories, Hong Kong

Abstract:
This paper investigates link-by-link channel-coded PNC (Physical layer Network Coding), in which a critical process at the relay is to transform the superimposed channel-coded packets received from the two end nodes (plus noise), 3 1 2 3 Y X X W

, to the network-coded combination of the source packets, 1 2 S S ⊕ . This is in contrast to the traditional multiple-access problem, in which the goal is to obtain both 1S and 2 S explicitly at the relay node. Trying to obtain 1S and 2 S explicitly is an overkill if we are only interested in 1 2 S S ⊕ . In this paper, we refer to the transformation 3 1 2 Y S S → ⊕ as the Channel-decoding-Network-Coding process (CNC) in that it involves both channel decoding and network coding operations. This paper shows that if we adopt the Repeat Accumulate (RA) channel code at the two end nodes, then there is a compatible decoder at the relay that can perform the transformation 3 1 2 Y S S → ⊕ efficiently. Specifically, we redesign the belief propagation decoding algorithm of the RA code for traditional point-to-point channel to suit the need of the PNC multiple-access channel. Simulation results show that our new scheme outperforms the previously proposed schemes significantly in terms of BER without added complexity.

Key Words: physical layer network coding, channel coding, repeat accumulate code I. Introduction The two-way relay channel (TWRC) is a fundamental network structure of much interest to the wireless communications research community. Application of network coding in TWRC, in 2 particular, has attracted intense interest recently. The first proposal of network coding for TWRC can be traced to [1], in which network coding is applied at the relay node to exploit the broadcast nature of the wireless medium. With respect to Fig. 1, the scheme works as follows. Node N1 sends node N3 its packet. Through another orthogonal channel, node N2 sends node N3 its packet. Then N3 mixes the information of N1 and N2 to form a network-coded packet and broadcasts it to N1 and N2. In this way, the number of time slots needed to exchange one packet is three. The scheme in [1] regards network coding as an upper layer technique, and separates it from other lower-layer processes such as modulation and channel coding. In [2, 3], this scheme was further extended to combine with channel coding. In [4], we proposed a new network coding scheme called Physical-layer Network Coding (PNC). PNC was originally inspired by the observation that the relay node N3 does not need to know the individual contents of the source packets, S1 and S2, to form the network-coded packet 1 2 S S ⊕ , and that the needed information 1 2 S S ⊕ could be obtained even if the two end nodes were to transmit simultaneously to the relay in the same time slot. In particular, N3 in PNC directly transforms the superimposed packets received to the network-coded packet 1 2 S S ⊕ for broadcast to N1 and N2. In this way, the number of time slots needed to exchange one packet is reduced from three to two with respect to the scheme in [1]. At the same time, the bit-error rate (BER) is also decreased [4].
An issue left open by [4] is the use of channel coding to achieve reliable communication. There are two ways to apply channel coding in PNC. First, channel coding could be applied on an end-by-end basis, in which only the end nodes, but not the relay node, perform channel encoding and decoding. We refer to this set-up as end-to-end coded PNC. Second, channel coding could be applied on a link-by-link basis, in which the end nodes as well as relay node perform channel encoding and decoding. In particular, the relay will first transform the superimposed channel-coded signals 3 1 2 3 Y X X W

(W3 is the noise at N3) received from the end nodes to unchannel-coded but network-coded information 1 2 S S ⊕ , and then channel-encode 1 2 S S ⊕ for broadcast to the end nodes. We refer to this set-up as link-by-link coded PNC. This paper investigates link-by-link coded 3 PNC schemes, focusing on the critical transformation process 3 1 2 Y S S → ⊕ therein. Note that the process of channel-encoding 1 2 S S ⊕ is the same as that for ordinary point-to-point channel, whereas the transformation 3 1 2 Y S S → ⊕ can be quite intricate and its implementation can affect the system performance significantly, as will be demonstrated in this paper. We refer to the process of 3 1 2 Y S S → ⊕ as the Channel-decoding-Network-Coding process (CNC).
Two straightforward link-by-link coded PNC schemes with different implementations of CNC can be found in the literature [5, 6]. Throughout this paper, lowercase letters will be used t

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