On LDPC Codes for Gaussian Interference Channels

In this paper, we focus on the two-user Gaussian interference channel (GIC), and study the Han-Kobayashi (HK) coding/decoding strategy with the objective of designing low-density parity-check (LDPC) codes. A code optimization algorithm is proposed which adopts a random perturbation technique via tracking the average mutual information. The degree distribution optimization and convergence threshold computation are carried out for strong and weak interference channels, employing binary phase-shift keying (BPSK). Under strong interference, it is observed that optimized codes operate close to the capacity boundary. For the case of weak interference, it is shown that via the newly designed codes, a nontrivial rate pair is achievable, which is not attainable by single user codes with time-sharing. Performance of the designed LDPC codes are also studied for finite block lengths through simulations of specific codes picked from the optimized degree distributions.Comment: ISIT 201

Joint Channel-Network Coding Strategies for Networks with Low Complexity Relays

We investigate joint network and channel coding schemes for networks when relay nodes are not capable of performing channel coding operations. Rather, channel encoding is performed at the source node while channel decoding is done only at the destination nodes. We examine three different decoding strategies: independent network-then-channel decoding, serial network and channel decoding, and joint network and channel decoding. Furthermore, we describe how to implement such joint network and channel decoding using iteratively decodable error correction codes. Using simple networks as a model, we derive achievable rate regions and use simulations to demonstrate the effectiveness of the three decoders.Comment: accepted and to appear in European Transactions on Telecommunication

Cooperative Punctured Polar Coding (CPPC) Scheme Based on Plotkin’s Construction

A new cooperative punctured polar coding (CPPC) scheme with multi joint successive cancellation (MJSC) decoding at the destination is proposed, which may be obtained by applying puncturing algorithm to cooperative polar coding scenario. In this proposed algorithm we generate a cooperative scheme for punctured polar codes with various code lengths by employing the reduction of the general polarizing matrix combined with the cooperative construction to match the multilevel characteristics of polar codes. Punctured polar codes which are a class of polar codes can support a wide range of lengths for a given rate. Hence in our CPPC scheme, the punctured polar codes can be first constructed by eliminating some of the frozen bits such that the values of the punctured bits are known to the decoder. Then the proposed coded cooperative construction is employed to match the Plotkin’s construction between the two relay nodes. This scheme has low encoding and decoding complexity since it can be encoded and decoded in a similar way as a classical polar code. The CPPC scheme offers a cooperative coding which not only improves the data rate of the cooperative system, but also improves the overall bit error rate performance. Numerical results show that cooperative punctured polar codes constructed by our approach perform much better than those by the conventional direct approach

Distributed Soft Coding with a Soft Input Soft Output (SISO) Relay Encoder in Parallel Relay Channels

In this paper, we propose a new distributed coding structure with a soft input soft output (SISO) relay encoder for error-prone parallel relay channels. We refer to it as the distributed soft coding (DISC). In the proposed scheme, each relay first uses the received noisy signals to calculate the soft bit estimate (SBE) of the source symbols. A simple SISO encoder is developed to encode the SBEs of source symbols based on a constituent code generator matrix. The SISO encoder outputs at different relays are then forwarded to the destination and form a distributed codeword. The performance of the proposed scheme is analyzed. It is shown that its performance is determined by the generator sequence weight (GSW) of the relay constituent codes, where the GSW of a constituent code is defined as the number of ones in its generator sequence. A new coding design criterion for optimally assigning the constituent codes to all the relays is proposed based on the analysis. Results show that the proposed DISC can effectively circumvent the error propagation due to the decoding errors in the conventional detect and forward (DF) with relay re-encoding and bring considerable coding gains, compared to the conventional soft information relaying.Comment: to appear on IEEE Transactions on Communication

Decode-and-Forward Relaying via Standard AWGN Coding and Decoding

A framework is developed for decode-and-forward based relaying using standard coding and decoding that are good for the single-input single-output (SISO) additive white Gaussian noise channel. The framework is applicable to various scenarios and demonstrated for several important cases. Each of these scenarios is transformed into an equivalent Gaussian multiple-input multiple-output (MIMO) common-message broadcast problem, which proves useful even when all links are SISO ones. Over the effective MIMO broadcast channel, a recently developed Gaussian MIMO common-message broadcast scheme is applied. This scheme transforms the MIMO links into a set of parallel SISO channels with no loss of mutual information, using linear pre- and post-processing combined with successive decoding. Over these resulting SISO channels, “off-the-shelf” scalar codes may be used

Low-Density Graph Codes for slow fading Relay Channels

We study Low-Density Parity-Check (LDPC) codes with iterative decoding on block-fading (BF) Relay Channels. We consider two users that employ coded cooperation, a variant of decode-and-forward with a smaller outage probability than the latter. An outage probability analysis for discrete constellations shows that full diversity can be achieved only when the coding rate does not exceed a maximum value that depends on the level of cooperation. We derive a new code structure by extending the previously published full-diversity root-LDPC code, designed for the BF point-to-point channel, to exhibit a rate-compatibility property which is necessary for coded cooperation. We estimate the asymptotic performance through a new density evolution analysis and the word error rate performance is determined for finite length codes. We show that our code construction exhibits near-outage limit performance for all block lengths and for a range of coding rates up to 0.5, which is the highest possible coding rate for two cooperating users.Comment: Accepted for publication in IEEE Transactions on Information Theor

Asymmetric Turbo Code for Coded-Cooperative Wireless Communication Based on Matched Interleaver with Channel Estimation and Multi-Receive Antennas at the Destination

This paper investigates the multiple relay coded-cooperation scheme based on asymmetric turbo code (ATC) with multiple receive antennas over Rayleigh block fading channels. An encoding scheme based on ATC is proposed for coded-cooperation i.e. distributed asymmetric turbo code (DATC). The code matched interleaver (CMI) is selected by a rigorous comparison with a uniform-random interleaver (URI). This optimum choice of interleaver at the relay nodes provides maximum benefit from DATC coded-cooperation scheme. Practically in any wireless communication system, the channel side information (CSI) is usually unknown at the receiver. Therefore, spatial normalized least mean square (NLMS) adaptive transversal filters are employed to estimate the CSI at the destination node. Moreover, in coded-cooperation scheme, the effectiveness and validation of spatial NLMS adaptive transversal filters is also verified by simulation results. Quadrature phase shift keying (QPSK) is used in coded-cooperation scheme and corresponding soft-demodulators are employed along with joint iterative soft-input soft-output (SISO) decoder at the destination node. Monte Carlo simulations shows that the proposed scheme incorporates coding gain, diversity gain and cooperation gain successfully, which eventually results in net gain of 2.7 to 3.5 dBs over non-cooperation ATC counterpart

Design of low-density parity-check codes in relay channels

Recent breakthroughs in forward error correction, in the form of low-density parity-check (LDPC) and turbo codes, have seen near Shannon limit performances especially for pointto- point channels. The construction of capacity-achieving codes in relay channels, for LDPC codes in particular, is currently the subject of intense interest in the research and development community. This thesis adds to this field, developing methods and supporting theory in designing capacity-achieving LDPC codes for decode-and-forward (DF) schemes in relay channels. In the first part of the thesis, new theoretical results toward optimizing the achievable rate of DF scheme in half-duplex relay channels under simplified and pragmatic conditions (equal power or equal time allocation) are developed. We derive the closed-form solutions for the optimum parameters (time or power) that maximize the achievable rates of the DF scheme in the half-duplex relay channel. We also derive the closed-form expression for the DF achievable rates under these simplified and pragmatic conditions. The second part of the thesis is dedicated to study the problem of designing several classes of capacity-achieving LDPC codes in relay channels. First, a new ensemble of LDPC codes, termed multi-edge-type bilayer-expurgated LDPC (MET-BE-LDPC) codes, is introduced to closely approach the theoretical limit of the DF scheme in the relay channel. We propose two design strategies for optimizing MET-BE-LDPC codes; the bilayer approach and the bilayer approach with intermediate rates. Second, we address the issue of constructing capacity-achieving distributed LDPC codes in the multiple-access and two-way relay channels, with broadcast transmissions and time-division multiple accesses. We propose a new methodology to asymptotically optimize the code’s degree distribution when different segments within the distributed codeword have been transmitted through separate channels and experienced distinct signal-to-noise ratio in the relay system. Third, we investigate the use of LDPC codes under the soft-decode-and forward (SDF) scheme in the half-duplex relay channel. We introduce the concept of a K-layer doping matrix that enables one to design the rate-compatible (RC) LDPC code with a lower triangular parity-check matrix, subsequently allowing the additional parity bits to be linearly and systematically encoded at the relay. We then present the soft-decoding and soft-re-encoding algorithms for the designed RC-LDPC code so that the relay can forward soft messages to the destination when the relay fails to decode the source’s messages. Special attention is given to the detection problem of the SDF scheme. We propose a novel method, which we refer to as soft fading, to compute the log-likelihood ratio of the received signal at the destination for the SDF scheme

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