Matched Metrics and Channels

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel. In this work we study channels and metrics for which those two criteria do and do not coincide for general codes

Gaussian Broadcast Channels with an Orthogonal and Bidirectional Cooperation Link

This paper considers a system where one transmitter broadcasts a single common message to two receivers linked by a bidirectional cooperation channel, which is assumed to be orthogonal to the downlink channel. Assuming a simplified setup where, in particular, scalar relaying protocols are used and channel coding is not exploited, we want to provide elements of response to several questions of practical interest. Here are the main underlying issues: 1. The way of recombining the signals at the receivers; 2. The optimal number of cooperation rounds; 3. The way of cooperating (symmetrically or asymmetrically; which receiver should start cooperating in the latter case); 4. The influence of spectral resources. These issues are considered by studying the performance of the assumed system through analytical results when they are derivable and through simulation results. For the particular choices we made, the results sometimes do not coincide with those available for the discrete counterpart of the studied channel

Construction of Capacity-Achieving Lattice Codes: Polar Lattices

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity \frac{1}{2}\log(1+\SNR) of the additive white Gaussian-noise (AWGN) channel. Our construction follows the multilevel approach of Forney \textit{et al.}, where we construct a capacity-achieving polar code on each level. The component polar codes are shown to be naturally nested, thereby fulfilling the requirement of the multilevel lattice construction. We prove that polar lattices are \emph{AWGN-good}. Furthermore, using the technique of source polarization, we propose discrete Gaussian shaping over the polar lattice to satisfy the power constraint. Both the construction and shaping are explicit, and the overall complexity of encoding and decoding is $O(N\log N)$ for any fixed target error probability.Comment: full version of the paper to appear in IEEE Trans. Communication

Accessible Capacity of Secondary Users

A new problem formulation is presented for the Gaussian interference channels (GIFC) with two pairs of users, which are distinguished as primary users and secondary users, respectively. The primary users employ a pair of encoder and decoder that were originally designed to satisfy a given error performance requirement under the assumption that no interference exists from other users. In the scenario when the secondary users attempt to access the same medium, we are interested in the maximum transmission rate (defined as {\em accessible capacity}) at which secondary users can communicate reliably without affecting the error performance requirement by the primary users under the constraint that the primary encoder (not the decoder) is kept unchanged. By modeling the primary encoder as a generalized trellis code (GTC), we are then able to treat the secondary link and the cross link from the secondary transmitter to the primary receiver as finite state channels (FSCs). Based on this, upper and lower bounds on the accessible capacity are derived. The impact of the error performance requirement by the primary users on the accessible capacity is analyzed by using the concept of interference margin. In the case of non-trivial interference margin, the secondary message is split into common and private parts and then encoded by superposition coding, which delivers a lower bound on the accessible capacity. For some special cases, these bounds can be computed numerically by using the BCJR algorithm. Numerical results are also provided to gain insight into the impacts of the GTC and the error performance requirement on the accessible capacity.Comment: 42 pages, 12 figures, 2 tables; Submitted to IEEE Transactions on Information Theory on December, 2010, Revised on November, 201