178 research outputs found
Optimality and duality of the turbo decoder
Proceedings of the IEEE, 95(6): pp. 1362-1377.The near-optimal performance of the turbo
decoder has been a source of intrigue among communications
engineers and information theorists, given its ad hoc origins
that were seemingly disconnected from optimization theory.
Naturally one would inquire whether the favorable performance
might be explained by characterizing the turbo decoder
via some optimization criterion or performance index. Recently,
two such characterizations have surfaced. One draws from
statistical mechanics and aims to minimize the Bethe approximation
to a free energy measure. The other characterization
involves constrained likelihood estimation, a setting perhaps
more familiar to communications engineers. The intent of
this paper is to assemble a tutorial overview of these recent
developments, and more importantly to identify the formal
mathematical duality between the two viewpoints. The paper
includes tutorial background material on the information
geometry tools used in analyzing the turbo decoder, and the
analysis accommodates both the parallel concatenation and
serial concatenation schemes in a common framework
Code designs for MIMO broadcast channels
Recent information-theoretic results show the optimality of dirty-paper coding (DPC) in achieving the full capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). This paper presents a DPC based code design for BCs. We consider the case in which there is an individual rate/signal-to-interference-plus-noise ratio (SINR) constraint for each user. For a fixed transmitter power, we choose the linear transmit precoding matrix such that the SINRs at users are uniformly maximized, thus ensuring the best bit-error rate performance. We start with Cover's simplest two-user Gaussian BC and present a coding scheme that operates 1.44 dB from the boundary of the capacity region at the rate of one bit per real sample (b/s) for each user. We then extend the coding strategy to a two-user MIMO Gaussian BC with two transmit antennas at the base-station and develop the first limit-approaching code design using nested turbo codes for DPC. At the rate of 1 b/s for each user, our design operates 1.48 dB from the capacity region boundary. We also consider the performance of our scheme over a slow fading BC. For two transmit antennas, simulation results indicate a performance loss of only 1.4 dB, 1.64 dB and 1.99 dB from the theoretical limit in terms of the total transmission power for the two, three and four user case, respectively
Robust Sum MSE Optimization for Downlink Multiuser MIMO Systems with Arbitrary Power Constraint: Generalized Duality Approach
This paper considers linear minimum meansquare- error (MMSE) transceiver
design problems for downlink multiuser multiple-input multiple-output (MIMO)
systems where imperfect channel state information is available at the base
station (BS) and mobile stations (MSs). We examine robust sum mean-square-error
(MSE) minimization problems. The problems are examined for the generalized
scenario where the power constraint is per BS, per BS antenna, per user or per
symbol, and the noise vector of each MS is a zero-mean circularly symmetric
complex Gaussian random variable with arbitrary covariance matrix. For each of
these problems, we propose a novel duality based iterative solution. Each of
these problems is solved as follows. First, we establish a novel sum average
meansquare- error (AMSE) duality. Second, we formulate the power allocation
part of the problem in the downlink channel as a Geometric Program (GP). Third,
using the duality result and the solution of GP, we utilize alternating
optimization technique to solve the original downlink problem. To solve robust
sum MSE minimization constrained with per BS antenna and per BS power problems,
we have established novel downlink-uplink duality. On the other hand, to solve
robust sum MSE minimization constrained with per user and per symbol power
problems, we have established novel downlink-interference duality. For the
total BS power constrained robust sum MSE minimization problem, the current
duality is established by modifying the constraint function of the dual uplink
channel problem. And, for the robust sum MSE minimization with per BS antenna
and per user (symbol) power constraint problems, our duality are established by
formulating the noise covariance matrices of the uplink and interference
channels as fixed point functions, respectively.Comment: IEEE TSP Journa
On the BICM Capacity
Optimal binary labelings, input distributions, and input alphabets are
analyzed for the so-called bit-interleaved coded modulation (BICM) capacity,
paying special attention to the low signal-to-noise ratio (SNR) regime. For
8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded
binary code results in a higher capacity than the binary reflected gray code
(BRGC) and the natural binary code (NBC). The 1 dB gap between the additive
white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be
almost completely removed if the input symbol distribution is properly
selected. First-order asymptotics of the BICM capacity for arbitrary input
alphabets and distributions, dimensions, mean, variance, and binary labeling
are developed. These asymptotics are used to define first-order optimal (FOO)
constellations for BICM, i.e. constellations that make BICM achieve the Shannon
limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable
transmission at asymptotically low rates in BICM can be as high as infinity,
that for uniform input distributions and 8-PAM there are only 72 classes of
binary labelings with a different first-order asymptotic behavior, and that
this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general
answer to the question of FOO constellations for BICM is also given: using the
Hadamard transform, it is found that for uniform input distributions, a
constellation for BICM is FOO if and only if it is a linear projection of a
hypercube. A constellation based on PAM or quadrature amplitude modulation
input alphabets is FOO if and only if they are labeled by the NBC; if the
constellation is based on PSK input alphabets instead, it can never be FOO if
the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor
Introduction to Mathematical Programming-Based Error-Correction Decoding
Decoding error-correctiong codes by methods of mathematical optimization,
most importantly linear programming, has become an important alternative
approach to both algebraic and iterative decoding methods since its
introduction by Feldman et al. At first celebrated mainly for its analytical
powers, real-world applications of LP decoding are now within reach thanks to
most recent research. This document gives an elaborate introduction into both
mathematical optimization and coding theory as well as a review of the
contributions by which these two areas have found common ground.Comment: LaTeX sources maintained here: https://github.com/supermihi/lpdintr
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