Precoded Integer-Forcing Universally Achieves the MIMO Capacity to Within a Constant Gap

An open-loop single-user multiple-input multiple-output communication scheme is considered where a transmitter, equipped with multiple antennas, encodes the data into independent streams all taken from the same linear code. The coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space-time code. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. It is shown that this communication architecture achieves the capacity of any Gaussian multiple-input multiple-output channel up to a gap that depends only on the number of transmit antennas.Comment: to appear in the IEEE Transactions on Information Theor

Distributed Structure: Joint Expurgation for the Multiple-Access Channel

In this work we show how an improved lower bound to the error exponent of the memoryless multiple-access (MAC) channel is attained via the use of linear codes, thus demonstrating that structure can be beneficial even in cases where there is no capacity gain. We show that if the MAC channel is modulo-additive, then any error probability, and hence any error exponent, achievable by a linear code for the corresponding single-user channel, is also achievable for the MAC channel. Specifically, for an alphabet of prime cardinality, where linear codes achieve the best known exponents in the single-user setting and the optimal exponent above the critical rate, this performance carries over to the MAC setting. At least at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used at most for one of the users. Even when the MAC channel is not additive, it may be transformed into such a channel. While the transformation is lossy, we show that the distributed structure gain in some "nearly additive" cases outweighs the loss, and thus the error exponent can improve upon the best known error exponent for these cases as well. Finally we apply a similar approach to the Gaussian MAC channel. We obtain an improvement over the best known achievable exponent, given by Gallager, for certain rate pairs, using lattice codes which satisfy a nesting condition.Comment: Submitted to the IEEE Trans. Info. Theor

Approximate quantum error correction for generalized amplitude damping errors

We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes. The performance of such error-correcting schemes is quantified by means of the entanglement fidelity as a function of the damping probability and the non-zero environmental temperature. The recovery scheme employed throughout our work applies, in principle, to arbitrary quantum codes and is the analogue of the perfect Knill-Laflamme recovery scheme adapted to the approximate quantum error correction framework for the GAD error model. We also analytically recover and/or clarify some previously known numerical results in the limiting case of vanishing temperature of the environment, the well-known traditional amplitude damping channel. In addition, our study suggests that degenerate stabilizer codes and self-complementary nonadditive codes are especially suitable for the error correction of the GAD noise model. Finally, comparing the properly normalized entanglement fidelities of the best performant stabilizer and nonadditive codes characterized by the same length, we show that nonadditive codes outperform stabilizer codes not only in terms of encoded dimension but also in terms of entanglement fidelity.Comment: 44 pages, 8 figures, improved v

Optimum Linear LLR Calculation for Iterative Decoding on Fading Channels

On a fading channel with no channel state information at the receiver, calculating true log-likelihood ratios (LLR) is complicated. Existing work assume that the power of the additive noise is known and use the expected value of the fading gain in a linear function of the channel output to find approximate LLRs. In this work, we first assume that the power of the additive noise is known and we find the optimum linear approximation of LLRs in the sense of maximum achievable transmission rate on the channel. The maximum achievable rate under this linear LLR calculation is almost equal to the maximum achievable rate under true LLR calculation. We also observe that this method appears to be the optimum in the sense of bit error rate performance too. These results are then extended to the case that the noise power is unknown at the receiver and a performance almost identical to the case that the noise power is perfectly known is obtained.Comment: This paper will be presented in IEEE International Symposium on Information Theory (ISIT) 2007 in Nice, Franc

Optimizing GNSS Navigation Data Message Decoding in Urban Environment

Nowadays, the majority of new GNSS applications targets dynamic users in urban environments; therefore the decoder input in GNSS receivers needs to be adapted to the urban propagation channel to avoid mismatched decoding when using soft input channel decoding. The aim of this paper consists thus in showing that the GNSS signals demodulation performance is significantly improved integrating an advanced soft detection function as decoder input in urban areas. This advanced detection function takes into account some a priori information on the available Channel State Information (CSI). If no CSI is available, one has to blindly adapt the detection function in order to operate close to the perfect CSI case. This will lead to avoid mismatched decoding due to, for example, the consideration by default of the Additive White Gaussian Noise (AWGN) channel for the derivation of soft inputs to be fed to soft input decoders. As a consequence the decoding performance will be improved in urban areas. The expressions of the soft decoder input function adapted for an urban environment is highly dependent on the available CSI at the receiver end. Based on different model of urban propagation channels, several CSI contexts will be considered namely perfect CSI, partial statistical CSI and no CSI. Simulation results will be given related to the GPS L1C demodulation performance with these different advanced detection function expressions in an urban environment. The results presented in this paper are valid for any kind of soft input decoders, such as Viterbi decoding for trellis based codes, the MAP/BCJR decoding for turbo-codes and the Belief Propagation decoding for LDPC codes

Using Channel Output Feedback to Increase Throughput in Hybrid-ARQ

Hybrid-ARQ protocols have become common in many packet transmission systems due to their incorporation in various standards. Hybrid-ARQ combines the normal automatic repeat request (ARQ) method with error correction codes to increase reliability and throughput. In this paper, we look at improving upon this performance using feedback information from the receiver, in particular, using a powerful forward error correction (FEC) code in conjunction with a proposed linear feedback code for the Rayleigh block fading channels. The new hybrid-ARQ scheme is initially developed for full received packet feedback in a point-to-point link. It is then extended to various different multiple-antenna scenarios (MISO/MIMO) with varying amounts of packet feedback information. Simulations illustrate gains in throughput.Comment: 30 page