Pairwise Check Decoding for LDPC Coded Two-Way Relay Block Fading Channels

Partial decoding has the potential to achieve a larger capacity region than full decoding in two-way relay (TWR) channels. Existing partial decoding realizations are however designed for Gaussian channels and with a static physical layer network coding (PLNC). In this paper, we propose a new solution for joint network coding and channel decoding at the relay, called pairwise check decoding (PCD), for low-density parity-check (LDPC) coded TWR system over block fading channels. The main idea is to form a check relationship table (check-relation-tab) for the superimposed LDPC coded packet pair in the multiple access (MA) phase in conjunction with an adaptive PLNC mapping in the broadcast (BC) phase. Using PCD, we then present a partial decoding method, two-stage closest-neighbor clustering with PCD (TS-CNC-PCD), with the aim of minimizing the worst pairwise error probability. Moreover, we propose the minimum correlation optimization (MCO) for selecting the better check-relation-tabs. Simulation results confirm that the proposed TS-CNC-PCD offers a sizable gain over the conventional XOR with belief propagation (BP) in fading channels.Comment: to appear in IEEE Trans. on Communications, 201

Asymptotic Analysis on Spatial Coupling Coding for Two-Way Relay Channels

Compute-and-forward relaying is effective to increase bandwidth efficiency of wireless two-way relay channels. In a compute-and-forward scheme, a relay tries to decode a linear combination composed of transmitted messages from other terminals or relays. Design for error correcting codes and its decoding algorithms suitable for compute-and-forward relaying schemes are still important issue to be studied. In this paper, we will present an asymptotic performance analysis on LDPC codes over two-way relay channels based on density evolution (DE). Because of the asymmetric nature of the channel, we employ the population dynamics DE combined with DE formulas for asymmetric channels to obtain BP thresholds. In addition, we also evaluate the asymptotic performance of spatially coupled LDPC codes for two-way relay channels. The results indicate that the spatial coupling codes yield improvements in the BP threshold compared with corresponding uncoupled codes for two-way relay channels.Comment: 5 page

Joint Compute and Forward for the Two Way Relay Channel with Spatially Coupled LDPC Codes

We consider the design and analysis of coding schemes for the binary input two way relay channel with erasure noise. We are particularly interested in reliable physical layer network coding in which the relay performs perfect error correction prior to forwarding messages. The best known achievable rates for this problem can be achieved through either decode and forward or compute and forward relaying. We consider a decoding paradigm called joint compute and forward which we numerically show can achieve the best of these rates with a single encoder and decoder. This is accomplished by deriving the exact performance of a message passing decoder based on joint compute and forward for spatially coupled LDPC ensembles.Comment: This paper was submitted to IEEE Global Communications Conference 201

Multilevel Coding Schemes for Compute-and-Forward with Flexible Decoding

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits computation (or, decoding) of a class of functions at the relay. The function to be computed (or, decoded) is then chosen depending on the channel realization. We define such a class of functions which can be decoded at the relay using the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using the QPSK constellation. Numerical results with QPSK show that the flexibility afforded by our proposed scheme results in substantially higher rates than those achievable by always using a fixed function or by adapting the function at the relay but coding over GF(4).Comment: This paper was submitted to IEEE Transactions on Information Theory in July 2011. A shorter version also appeared in the proceedings of the International Symposium on Information Theory in August 2011 without the proof of the main theore