Adaptive Linear Programming Decoding of Polar Codes

Polar codes are high density parity check codes and hence the sparse factor graph, instead of the parity check matrix, has been used to practically represent an LP polytope for LP decoding. Although LP decoding on this polytope has the ML-certificate property, it performs poorly over a BAWGN channel. In this paper, we propose modifications to adaptive cut generation based LP decoding techniques and apply the modified-adaptive LP decoder to short blocklength polar codes over a BAWGN channel. The proposed decoder provides significant FER performance gain compared to the previously proposed LP decoder and its performance approaches that of ML decoding at high SNRs. We also present an algorithm to obtain a smaller factor graph from the original sparse factor graph of a polar code. This reduced factor graph preserves the small check node degrees needed to represent the LP polytope in practice. We show that the fundamental polytope of the reduced factor graph can be obtained from the projection of the polytope represented by the original sparse factor graph and the frozen bit information. Thus, the LP decoding time complexity is decreased without changing the FER performance by using the reduced factor graph representation.Comment: 5 pages, 8 figures, to be presented at the IEEE Symposium on Information Theory (ISIT) 201

Performance of Joint Channel and Physical Network Coding Based on Alamouti STBC

This work considers the protograph-coded physical network coding (PNC) based on Alamouti space-time block coding (STBC) over Nakagami-fading two-way relay channels, in which both the two sources and relay possess two antennas. We first propose a novel precoding scheme at the two sources so as to implement the iterative decoder efficiently at the relay. We further address a simplified updating rule of the log-likelihood-ratio (LLR) in such a decoder. Based on the simplified LLR-updating rule and Gaussian approximation, we analyze the theoretical bit-error-rate (BER) of the system, which is shown to be consistent with the decoding thresholds and simulated results. Moreover, the theoretical analysis has lower computational complexity than the protograph extrinsic information transfer (PEXIT) algorithm. Consequently, the analysis not only provides a simple way to evaluate the error performance but also facilitates the design of the joint channel-and-PNC (JCNC) in wireless communication scenarios.Comment: 6 pages, 4 figures, accpete

Turbo receivers for interleave-division multiple-access systems

In this paper several turbo receivers for Interleave-Division Multiple-Access (IDMA) systems will be discussed. The multiple access system model is presented first. The optimal, Maximum A Posteriori (MAP) algorithm, is then presented. It will be shown that the use of a precoding technique at the emitter side is applicable to IDMA systems. Several low complexity Multi-User Detector (MUD), based on the Gaussian approximation, will be next discussed. It will be shown that the MUD with Probabilistic Data Association (PDA) algorithm provides faster convergence of the turbo receiver. The discussed turbo receivers will be evaluated by means of Bit Error Rate (BER) simulations and EXtrinsic Information Transfer (EXIT) charts

A Simplified Min-Sum Decoding Algorithm for Non-Binary LDPC Codes

Non-binary low-density parity-check codes are robust to various channel impairments. However, based on the existing decoding algorithms, the decoder implementations are expensive because of their excessive computational complexity and memory usage. Based on the combinatorial optimization, we present an approximation method for the check node processing. The simulation results demonstrate that our scheme has small performance loss over the additive white Gaussian noise channel and independent Rayleigh fading channel. Furthermore, the proposed reduced-complexity realization provides significant savings on hardware, so it yields a good performance-complexity tradeoff and can be efficiently implemented.Comment: Partially presented in ICNC 2012, International Conference on Computing, Networking and Communications. Accepted by IEEE Transactions on Communication

Network Code Design for Orthogonal Two-hop Network with Broadcasting Relay: A Joint Source-Channel-Network Coding Approach

This paper addresses network code design for robust transmission of sources over an orthogonal two-hop wireless network with a broadcasting relay. The network consists of multiple sources and destinations in which each destination, benefiting the relay signal, intends to decode a subset of the sources. Two special instances of this network are orthogonal broadcast relay channel and the orthogonal multiple access relay channel. The focus is on complexity constrained scenarios, e.g., for wireless sensor networks, where channel coding is practically imperfect. Taking a source-channel and network coding approach, we design the network code (mapping) at the relay such that the average reconstruction distortion at the destinations is minimized. To this end, by decomposing the distortion into its components, an efficient design algorithm is proposed. The resulting network code is nonlinear and substantially outperforms the best performing linear network code. A motivating formulation of a family of structured nonlinear network codes is also presented. Numerical results and comparison with linear network coding at the relay and the corresponding distortion-power bound demonstrate the effectiveness of the proposed schemes and a promising research direction.Comment: 27 pages, 9 figures, Submited to IEEE Transaction on Communicatio