Asynchronous Orthogonal Differential Decoding for Multiple Access Channels

We propose several differential decoding schemes for asynchronous multi-user MIMO systems based on orthogonal space-time block codes (OSTBCs) where neither the transmitters nor the receiver has knowledge of the channel. First, we derive novel low complexity differential decoders by performing interference cancelation in time and employing different decoding methods. The decoding complexity of these schemes grows linearly with the number of users. We then present additional differential decoding schemes that perform significantly better than our low complexity decoders and outperform the existing synchronous differential schemes but require higher decoding complexity compared to our low complexity decoders. The proposed schemes work for any square OSTBC, any constant amplitude constellation, any number of users, and any number of receive antennas. Furthermore, we analyze the diversity of the proposed schemes and derive conditions under which our schemes provide full diversity. For the cases of two and four transmit antennas, we provide examples of PSK constellations to achieve full diversity. Simulation results show that our differential schemes provide good performance. To the best of our knowledge, the proposed differential detection schemes are the first differential schemes for asynchronous multi-user systems.Comment: To appear in IEEE Transactions on Wireless Communication

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

Sequential Decoding for Multiple Access Channels

The use of sequential decoding in multiple access channels is considered. The Fano metric, which achieves all achievable rates in the one-user case, fails to do so in the multiuser case. A new metric is introduced and an inner bound is given to its achievable rate region. This inner bound region is large enough to encourage the use of sequential decoding in practice. The new metric is optimal, in the sense of achieving all achievable rates, in the case of one-user and pairwise-reversible channels. Whether the metric is optimal for all multiple access channels remains an open problem. It is worth noting that even in the one-user case, the new metric differs from the Fano metric in a nontrivial way, showing that the Fano metric is not uniquely optimal for such channels. A new and stricter criterion of achievability in sequential decoding is also introduced and examined. © 1988 IEE

Polar codes for the two-user multiple-access channel

Arikan's polar coding method is extended to two-user multiple-access channels. It is shown that if the two users of the channel use the Arikan construction, the resulting channels will polarize to one of five possible extremals, on each of which uncoded transmission is optimal. The sum rate achieved by this coding technique is the one that correponds to uniform input distributions. The encoding and decoding complexities and the error performance of these codes are as in the single-user case: $O(n\log n)$ for encoding and decoding, and $o(\exp(-n^{1/2-\epsilon}))$ for block error probability, where $n$ is the block length.Comment: 12 pages. Submitted to the IEEE Transactions on Information Theor

Fundamental Limits of Low-Density Spreading NOMA with Fading

Spectral efficiency of low-density spreading non-orthogonal multiple access channels in the presence of fading is derived for linear detection with independent decoding as well as optimum decoding. The large system limit, where both the number of users and number of signal dimensions grow with fixed ratio, called load, is considered. In the case of optimum decoding, it is found that low-density spreading underperforms dense spreading for all loads. Conversely, linear detection is characterized by different behaviors in the underloaded vs. overloaded regimes. In particular, it is shown that spectral efficiency changes smoothly as load increases. However, in the overloaded regime, the spectral efficiency of low- density spreading is higher than that of dense spreading

Polar Codes for Arbitrary DMCs and Arbitrary MACs

Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is $o(2^{-N^{1/2-\epsilon}})$, where $N$ is the block length. Encoding and decoding for these codes can be implemented with a complexity of $O(N\log N)$. It is shown that the same technique can be used to construct polar codes for arbitrary multiple access channels (MAC) by using an appropriate Abelian group structure. Although the symmetric sum capacity is achieved by this coding scheme, some points in the symmetric capacity region may not be achieved. In the case where the channel is a combination of linear channels, we provide a necessary and sufficient condition characterizing the channels whose symmetric capacity region is preserved by the polarization process. We also provide a sufficient condition for having a maximal loss in the dominant face.Comment: 32 pages, 1 figure. arXiv admin note: text overlap with arXiv:1112.177