Low-density Parity-check Codes for Wireless Relay Networks

In wireless networks, it has always been a challenge to satisfy high traffic throughput demands, due to limited spectrum resources. In past decades, various techniques, including cooperative communications, have been developed to achieve higher communication rates. This thesis addresses the challenges imposed by cooperative wireless networks, in particular focusing on practical code constructions and designs for wireless relay networks. The thesis is divided into the following four topics: 1) constructing and designing low-density parity-check (LDPC) codes for half-duplex three-phase two-way relay channels, 2) extending LDPC code constructions to half-duplex three-way relay channels, 3) proposing maximum-rate relay selection algorithms and LDPC code constructions for the broadcast problem in wireless relay networks, and 4) proposing an iterative hard interference cancellation decoder for LDPC codes in 2-user multiple-access channels. Under the first topic, we construct codes for half-duplex three-phase two-way relay channels where two terminal nodes exchange information with the help of a relay node. Constructing codes for such channels is challenging, especially when messages are encoded into multiple streams and a destination node receives signals from multiple nodes. We first prove an achievable rate region by random coding. Next, a systematic LDPC code is constructed at the relay node where relay bits are generated from two source codewords. At the terminal nodes, messages are decoded from signals of the source node and the relay node. To analyze the performance of the codes, discretized density evolution is derived. Based on the discretized density evolution, degree distributions are optimized by iterative linear programming in three steps. The optimized codes obtained are 26% longer than the theoretic ones. For the second topic, we extend LDPC code constructions from half-duplex three-phase two-way relay channels to half-duplex three-way relay channels. An achievable rate region of half-duplex three-way relay channels is first proved. Next, LDPC codes for each sub-region of the achievable rate region are constructed, where relay bits can be generated only from a received codeword or from both the source codeword and received codewords. Under the third topic, we study relay selection and code constructions for the broadcast problem in wireless relay networks. We start with the system model, followed by a theorem stating that a node can decode a message by jointly decoding multiple blocks of received signals. Next, the maximum rate is given when a message is decoded hop-by-hop or decoded by a set of nodes in a transmission phase. Furthermore, optimal relay selection algorithms are proposed for the two relay schemes. Finally, LDPC codes are constructed for the broadcast problem in wireless relay networks. For the fourth topic, an iterative hard interference cancellation decoder for LDPC codes in 2-user multiple-access channels is proposed. The decoder is based on log-likelihood ratios (LLRs). Interference is estimated, quantized and subtracted from channel outputs. To analyze the codes, density evolution is derived. We show that the required signal-to-noise ratio (SNR) for the proposed low-complexity decoder is 0.2 dB higher than that for an existing sub-optimal belief propagation decoder at code rate 1/3.4 month

Bilayer Protograph Codes for Half-Duplex Relay Channels

Despite encouraging advances in the design of relay codes, several important challenges remain. Many of the existing LDPC relay codes are tightly optimized for fixed channel conditions and not easily adapted without extensive re-optimization of the code. Some have high encoding complexity and some need long block lengths to approach capacity. This paper presents a high-performance protograph-based LDPC coding scheme for the half-duplex relay channel that addresses simultaneously several important issues: structured coding that permits easy design, low encoding complexity, embedded structure for convenient adaptation to various channel conditions, and performance close to capacity with a reasonable block length. The application of the coding structure to multi-relay networks is demonstrated. Finally, a simple new methodology for evaluating the end-to-end error performance of relay coding systems is developed and used to highlight the performance of the proposed codes.Comment: Accepted in IEEE Trans. Wireless Com

Bilayer Low-Density Parity-Check Codes for Decode-and-Forward in Relay Channels

This paper describes an efficient implementation of binning for the relay channel using low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying strategy by incorporating relay-generated information bits in specially designed bilayer graphical code structures. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC codes are capable of working at two different channel parameters and two different rates: that at the relay and at the destination. To analyze the performance of bilayer LDPC codes, bilayer density evolution is devised as an extension of the standard density evolution algorithm. Based on bilayer density evolution, a design methodology is developed for the bilayer codes in which the degree distribution is iteratively improved using linear programming. Further, in order to approach the theoretical decode-and-forward rate for a wide range of channel parameters, this paper proposes two different forms bilayer codes, the bilayer-expurgated and bilayer-lengthened codes. It is demonstrated that a properly designed bilayer LDPC code can achieve an asymptotic infinite-length threshold within 0.24 dB gap to the Shannon limits of two different channels simultaneously for a wide range of channel parameters. By practical code construction, finite-length bilayer codes are shown to be able to approach within a 0.6 dB gap to the theoretical decode-and-forward rate of the relay channel at a block length of $10^5$ and a bit-error probability (BER) of $10^{-4}$. Finally, it is demonstrated that a generalized version of the proposed bilayer code construction is applicable to relay networks with multiple relays.Comment: Submitted to IEEE Trans. Info. Theor

Self-concatenated code design and its application in power-efficient cooperative communications

In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions

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

A Deterministic Construction for Jointly Designed Quasicyclic LDPC Coded-Relay Cooperation

This correspondence presents a jointly designed quasicyclic (QC) low-density parity-check (LDPC) coded-relay cooperation with joint-iterative decoding in the destination node. Firstly, a design-theoretic construction of QC-LDPC codes based on a combinatoric design approach known as optical orthogonal codes (OOC) is presented. Proposed OOC-based construction gives three classes of binary QC-LDPC codes with no length-4 cycles by utilizing some known ingredients including binary matrix dispersion of elements of finite field, incidence matrices, and circulant decomposition. Secondly, the proposed OOC-based construction gives an effective method to jointly design length-4 cycles free QC-LDPC codes for coded-relay cooperation, where sum-product algorithm- (SPA-) based joint-iterative decoding is used to decode the corrupted sequences coming from the source or relay nodes in different time frames over constituent Rayleigh fading channels. Based on the theoretical analysis and simulation results, proposed QC-LDPC coded-relay cooperations outperform their competitors under same conditions over the Rayleigh fading channel with additive white Gaussian noise