Jan Sykora

Layered Design of Hierarchical Exclusive Codebook and Its Capacity Regions for HDF Strategy in Parametric Wireless 2-WRC

This paper addresses a hierarchical decode-and-forward (HDF) strategy in the wireless two-way relay channel (2-WRC). This strategy uses a Hierarchical eXclusive Code (HXC) that allows full decoding of the hierarchical symbols at the relay. The HXC represents two data sources only through the exclusive law and requires side information on the complementary data at the destination (which naturally holds for the 2-WRC). The HDF strategy has the advantage over classical medium-access control (MAC) stage relaying with joint decoding in that its rate region extends beyond the classical MAC region. We present a layered design of the HXC codebook, which uses an arbitrary outer state-of-the-art capacity-approaching code [e.g., low density parity check (LDPC)] and an inner layer with an exclusive symbol alphabet. We provide basic theorems, showing that this scheme forms an HXC, and we also evaluate its alphabet-constrained rate regions. The rate regions depend on the relative channel phase parameters. Some channel rotation leads to catastrophic violation of the exclusive law. However, these values appear only in a limited range of phases and have only a mild impact on the mean capacity for some component symbol constellations.

Hierarchical Alphabet and Parametric Channel Constrained Capacity Regions for HDF Strategy in Parametric Wireless 2-WRC

The paper addresses wireless the 2-Way Relay Channel (2-WRC) system with a Hierarchical Decode and Forward strategy. This strategy uses a Hierarchical eXclusive Code (HXC) that allows full decoding of the hierarchical symbols at the relay. The HXC represents two data sources only through the exclusive law and requires side information on the complementary data at the destination (which naturally holds for the 2-WRC). The HDF strategy has the advantage over classical MAC stage relaying with joint decoding that its rate region extends beyond the classical MAC region. We evaluate the hierarchical MAC capacity regions for various alphabets, constellation point indexing and various channel parametrization and compare that to the alphabet limited and unconstrained cut-set bounds.

Network Coded Modulation with partial side-information and hierarchical decode and forward relay sharing in multi-source wireless network

We present a strategy for the relay sharing in the 2-source relay wireless network with the hierarchical decode and forward relaying. It processes both incoming coded symbols through the minimal hierarchical symbol mapping of the same cardinality as the two individual symbol streams and requires a full (perfect) Complementary Side-Information (C-SI) on the other stream available at the destination. This scheme is known to have an advantage in a rectangular shape capacity region which provides higher sum-capacity than the classical MAC. We investigate the capacity region of the case where the destination has only partial C-SI available through a wireless link. We conclude that the overall finite alphabet constrained capacity region including both MAC and BC phase remains rectangular. The BC phase region is limited by the C-SI link capacity and we conjecture that it obeys (in some cases with some small margin) the capacity product law of the individual relay to destination and C-SI links.

Constant envelope space-time modulation trellis code design for Rayleigh flat fading channel

A constant envelope space-time modulation seems to be an attractive option especially for very high frequency and mobile applications because of its resistance to nonlinear distortion. The paper first analyzes the mean squared distance of the constant envelope space-time modulated signal in a Rayleigh slowly flat fading spatial diversity channel with independent coefficients. It is shown that the distance evaluation depends on both the modulator trellis and the distance evaluation trellis. The latter has special properties regarding its free paths. These properties, a critical path and the distance increments behavior, are the basis for the space-time trellis code design. The paper identifies the trellis code design rules minimizing the mean squared distance. The critical path is shown to be the determining factor.

Non-Uniform 2-Slot Constellations for Bidirectional Relaying in Fading Channels

In this paper we introduce the constellation alphabets suitable for bidirectional relaying in parametric wireless channels. Based on the analysis of hierarchical minimum distance, we present a simple design algorithm for the non-uniform 2-slot constellation alphabets. These novel constellation alphabets outperform traditional linear modulation schemes in Hierarchical-Decode-and-Forward and Denoise-and-Forward relaying strategies in fading channels without sacrificing the overall system throughput.

Design criteria for hierarchical exclusive code with parameter-invariant decision regions for wireless 2-way relay channel

The unavoidable parametrization of the wireless link represents a major problem of the network-coded modulation synthesis in a 2-way relay channel. Composite (hierarchical) codeword received at the relay is generally parametrized by the channel gain, forcing any processing on the relay to be dependent on channel parameters. In this paper, we introduce the codebook design criteria, which ensure that all permissible hierarchical codewords have decision regions invariant to the channel parameters (as seen by the relay). We utilize the criterion for parameter-invariant constellation space boundary to obtain the codebooks with channel parameter-invariant decision regions at the relay. Since the requirements on such codebooks are relatively strict, the construction of higher-order codebooks will require a slightly simplified design criteria. We will show that the construction algorithm based on these relaxed criteria provides a feasible way to the design of codebooks with arbitrary cardinality. The promising performance benefits of the example codebooks (compared to a classical linear modulation alphabets) will be exemplified on the minimum distance analysis.

Symmetric capacity of nonlinearly modulated finite alphabet signals in MIMO random channel with waveform and memory constraints

The paper shows a procedure for evaluating the symmetric ergodic capacity of nonlinearly modulated finite alphabet signals in the MIMO random channel. We first investigate informationally an equivalent signal space representation for finite alphabet signals. The signals are allowed to be multidimensional per one antenna to reflect the modulation nonlinearity. The informationally equivalent signal space representation allows a factorization per one eigenmode (depending purely on one marginal eigenvalue) in the capacity evaluation in the MIMO channel. The evaluation complexity does not depend on the MIMO dimensions. We consider two types of channel signal constraints. (1) A constraint on the waveform only. (2) A constraint on the waveform and memory (modeled as a Markov chain). The mean symmetric capacity for the former one is derived. For the latter one, we derive lower and upper bounds based on the entropy rate approximation.

Superposition coding for wireless Butterfly Network with partial Network Side-Information

Although the 2-source wireless Butterfly Network (BN) represents a natural extension of the well-known 2-Way Relay Channel (2-WRC) scenario, a direct implementation of conventional Wireless Network Coding (WNC)/Physical Layer Network Coding (PLNC) principles in this network is not straightforward. While the information necessary for decoding of the desired data from WNC-coded data at each destination is naturally available in 2-WRC, in the BN the destinations can obtain such information only by overhearing the wireless transmission from the unintended source. Since the amount of such received “Network” Side-Information (N-SI) would be limited by the quality of the corresponding source-destination link, the assumption of perfect side-information is no longer valid in BN, rising many novel research challenges for the design of WNC-based BN. In this paper we propose the Superposition Coding (SC) based scheme as a feasible strategy for relaying in BN. We will show that by a proper optimization of its parameters (rates & power allocation of underlying SC messages), SC is able to achieve the upper bound of two-way rate in BN for both the zero and perfect N-SI case and moreover, it represents a viable solution even for the case where only partial N-SI is available at both destinations.

Information waveform manifold based preprocessing for nonlinear multichannel modulation in MIMO channel

The nonlinear multichannel modulation (particularly the CPM class) can better respect technological constraints on the transmitter (e.g. nonlinearity) due to its multidimensional waveform space which allows to decouple the second order properties of the constellation and the actual waveform shape (e.g. constant envelope). However the receiver processing complexity, especially in MIMO channel, is very high due to this waveform multidimensionality. We present an information waveform manifold (IWM) based preprocessing reducing the dimensionality of the problem. It is based on nonlinear projector, optional processing on IWM and decoding isomorphism with channel symbols expansion space. We show that the nonlinear projector is generally suboptimal, however the information loss comparing with optimal processing is negligible. The decoding isomorphism also directly separates the individual components of the received signal in MIMO channel

On Indexing of Lattice-Constellations for Wireless Network Coding with Modulo-Sum Decoding

We consider wireless (physical-layer) network coding 2-way relaying where both terminals use constellations curved from a common lattice structure and the relay node decodes modulo-sum operation of transmitted data symbols at the multiple-access stage. Performance of such a system with additive white Gaussian noise is strongly determined by used constellation indexing. For some indexing, the minimal distance of modulo-sum decoding is 0 (some points of superimposed- constellation are equal despite corresponding to unequal modulo-sum of data symbols) which causes considerable loss in alphabet-constrained capacity. In this paper, we show that if indices form a modulo-arithmetic progression along each lattice (real) dimension (denoted Affine Indexing (AI)), the minimal distance of modulo-sum decoding equals to minimal distance of primary terminal constellation. Some canonical constellation shapes prevent existence of AI, therefore we propose a greedy-sphere packing algorithm for constellation shape design which jointly maximises minimal distance and keeps existence of AI.