Capacity Theorems for the AWGN Multi-Way Relay Channel

The L-user additive white Gaussian noise multi-way relay channel is considered, where multiple users exchange information through a single relay at a common rate. Existing coding strategies, i.e., complete-decode-forward and compress-forward are shown to be bounded away from the cut-set upper bound at high signal-to-noise ratios (SNR). It is known that the gap between the compress-forward rate and the capacity upper bound is a constant at high SNR, and that between the complete-decode-forward rate and the upper bound increases with SNR at high SNR. In this paper, a functional-decode-forward coding strategy is proposed. It is shown that for L >= 3, complete-decode-forward achieves the capacity when SNR <= 0 dB, and functional-decode-forward achieves the capacity when SNR >= 0 dB. For L=$, functional-decode-forward achieves the capacity asymptotically as SNR increases.Comment: accepted and to be presented at ISIT 201

The Multi-way Relay Channel

The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multi-way relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, where the users within the same cluster wish to exchange messages among themselves. It is assumed that the users cannot receive each other's signals directly, and hence the relay terminal in this model is the enabler of communication. In particular, restricted encoders, which ignore the received channel output and use only the corresponding messages for generating the channel input, are considered. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of exchange rates in a symmetric Gaussian network scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the exchange capacity independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward (AF) protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding based achievable schemes, a nested lattice coding based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity.Comment: Revised version of our submission to the Transactions on Information Theor

Full Diversity Space-Time Block Codes with Low-Complexity Partial Interference Cancellation Group Decoding

Partial interference cancellation (PIC) group decoding proposed by Guo and Xia is an attractive low-complexity alternative to the optimal processing for multiple-input multiple-output (MIMO) wireless communications. It can well deal with the tradeoff among rate, diversity and complexity of space-time block codes (STBC). In this paper, a systematic design of full-diversity STBC with low-complexity PIC group decoding is proposed. The proposed code design is featured as a group-orthogonal STBC by replacing every element of an Alamouti code matrix with an elementary matrix composed of multiple diagonal layers of coded symbols. With the PIC group decoding and a particular grouping scheme, the proposed STBC can achieve full diversity, a rate of $(2M)/(M+2)$ and a low-complexity decoding for $M$ transmit antennas. Simulation results show that the proposed codes can achieve the full diversity with PIC group decoding while requiring half decoding complexity of the existing codes.Comment: 10 pages, 3 figures

On Universal Properties of Capacity-Approaching LDPC Ensembles

This paper is focused on the derivation of some universal properties of capacity-approaching low-density parity-check (LDPC) code ensembles whose transmission takes place over memoryless binary-input output-symmetric (MBIOS) channels. Properties of the degree distributions, graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information-theoretic bounds. These bounds are expressed in terms of the target block/ bit error probability and the gap (in rate) to capacity. Most of the bounds are general for any decoding algorithm, and some others are proved under belief propagation (BP) decoding. Proving these bounds under a certain decoding algorithm, validates them automatically also under any sub-optimal decoding algorithm. A proper modification of these bounds makes them universal for the set of all MBIOS channels which exhibit a given capacity. Bounds on the degree distributions and graphical complexity apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. The bounds are compared with capacity-approaching LDPC code ensembles under BP decoding, and they are shown to be informative and are easy to calculate. Finally, some interesting open problems are considered.Comment: Published in the IEEE Trans. on Information Theory, vol. 55, no. 7, pp. 2956 - 2990, July 200

Minimum mean-squared error iterative successive parallel arbitrated decision feedback detectors for DS-CDMA systems

In this paper we propose minimum mean squared error (MMSE) iterative successive parallel arbitrated decision feedback (DF) receivers for direct sequence code division multiple access (DS-CDMA) systems. We describe the MMSE design criterion for DF multiuser detectors along with successive, parallel and iterative interference cancellation structures. A novel efficient DF structure that employs successive cancellation with parallel arbitrated branches and a near-optimal low complexity user ordering algorithm are presented. The proposed DF receiver structure and the ordering algorithm are then combined with iterative cascaded DF stages for mitigating the deleterious effects of error propagation for convolutionally encoded systems with both Viterbi and turbo decoding as well as for uncoded schemes. We mathematically study the relations between the MMSE achieved by the analyzed DF structures, including the novel scheme, with imperfect and perfect feedback. Simulation results for an uplink scenario assess the new iterative DF detectors against linear receivers and evaluate the effects of error propagation of the new cancellation methods against existing ones

How to Achieve the Capacity of Asymmetric Channels

We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances in coding for symmetric channels help provide more efficient solutions for the asymmetric case. We consider, in more detail, three basic coding paradigms. The first one is Gallager's scheme that consists of concatenating a linear code with a non-linear mapping so that the input distribution can be appropriately shaped. We explicitly show that both polar codes and spatially coupled codes can be employed in this scenario. Furthermore, we derive a scaling law between the gap to capacity, the cardinality of the input and output alphabets, and the required size of the mapper. The second one is an integrated scheme in which the code is used both for source coding, in order to create codewords distributed according to the capacity-achieving input distribution, and for channel coding, in order to provide error protection. Such a technique has been recently introduced by Honda and Yamamoto in the context of polar codes, and we show how to apply it also to the design of sparse graph codes. The third paradigm is based on an idea of B\"ocherer and Mathar, and separates the two tasks of source coding and channel coding by a chaining construction that binds together several codewords. We present conditions for the source code and the channel code, and we describe how to combine any source code with any channel code that fulfill those conditions, in order to provide capacity-achieving schemes for asymmetric channels. In particular, we show that polar codes, spatially coupled codes, and homophonic codes are suitable as basic building blocks of the proposed coding strategy.Comment: 32 pages, 4 figures, presented in part at Allerton'14 and published in IEEE Trans. Inform. Theor