17,050 research outputs found
Orthogonal Codes for Robust Low-Cost Communication
Orthogonal coding schemes, known to asymptotically achieve the capacity per
unit cost (CPUC) for single-user ergodic memoryless channels with a zero-cost
input symbol, are investigated for single-user compound memoryless channels,
which exhibit uncertainties in their input-output statistical relationships. A
minimax formulation is adopted to attain robustness. First, a class of
achievable rates per unit cost (ARPUC) is derived, and its utility is
demonstrated through several representative case studies. Second, when the
uncertainty set of channel transition statistics satisfies a convexity
property, optimization is performed over the class of ARPUC through utilizing
results of minimax robustness. The resulting CPUC lower bound indicates the
ultimate performance of the orthogonal coding scheme, and coincides with the
CPUC under certain restrictive conditions. Finally, still under the convexity
property, it is shown that the CPUC can generally be achieved, through
utilizing a so-called mixed strategy in which an orthogonal code contains an
appropriate composition of different nonzero-cost input symbols.Comment: 2nd revision, accepted for publicatio
Source Broadcasting to the Masses: Separation has a Bounded Loss
This work discusses the source broadcasting problem, i.e. transmitting a
source to many receivers via a broadcast channel. The optimal rate-distortion
region for this problem is unknown. The separation approach divides the problem
into two complementary problems: source successive refinement and broadcast
channel transmission. We provide bounds on the loss incorporated by applying
time-sharing and separation in source broadcasting. If the broadcast channel is
degraded, it turns out that separation-based time-sharing achieves at least a
factor of the joint source-channel optimal rate, and this factor has a positive
limit even if the number of receivers increases to infinity. For the AWGN
broadcast channel a better bound is introduced, implying that all achievable
joint source-channel schemes have a rate within one bit of the separation-based
achievable rate region for two receivers, or within bits for
receivers
Competitive minimax universal decoding for several ensembles of random codes
Universally achievable error exponents pertaining to certain families of
channels (most notably, discrete memoryless channels (DMC's)), and various
ensembles of random codes, are studied by combining the competitive minimax
approach, proposed by Feder and Merhav, with Chernoff bound and Gallager's
techniques for the analysis of error exponents. In particular, we derive a
single--letter expression for the largest, universally achievable fraction
of the optimum error exponent pertaining to the optimum ML decoding.
Moreover, a simpler single--letter expression for a lower bound to is
presented. To demonstrate the tightness of this lower bound, we use it to show
that , for the binary symmetric channel (BSC), when the random coding
distribution is uniform over: (i) all codes (of a given rate), and (ii) all
linear codes, in agreement with well--known results. We also show that
for the uniform ensemble of systematic linear codes, and for that of
time--varying convolutional codes in the bit-error--rate sense. For the latter
case, we also show how the corresponding universal decoder can be efficiently
implemented using a slightly modified version of the Viterbi algorithm which em
employs two trellises.Comment: 41 pages; submitted to IEEE Transactions on Information Theor
Space-time autocoding
Prior treatments of space-time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval-in which case there is a nonzero “outage capacity”-or multiple fading intervals-in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In short, space-time signals are their own channel codes. We call this phenomenon space-time autocoding, and the accompanying capacity the space-time autocapacity. Let an M-transmitter antenna, N-receiver antenna Rayleigh flat fading channel be characterized by an M×N matrix of independent propagation coefficients, distributed as zero-mean, unit-variance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a T-symbol coherence interval, and there is a fixed total transmit power. Let the coherence interval and number of transmitter antennas be related as T=βM for some constant β. A T×M matrix-valued signal, associated with R·T bits of information for some rate R is transmitted during the T-symbol coherence interval. Then there is a positive space-time autocapacity Ca such that for all R<Ca, the block probability of error goes to zero as the pair (T, M)→∞ such that T/M=β. The autocoding effect occurs whether or not the propagation matrix is known to the receiver, and Ca=Nlog(1+ρ) in either case, independently of β, where ρ is the expected signal-to-noise ratio (SNR) at each receiver antenna. Lower bounds on the cutoff rate derived from random unitary space-time signals suggest that the autocoding effect manifests itself for relatively small values of T and M. For example, within a single coherence interval of duration T=16, for M=7 transmitter antennas and N=4 receiver antennas, and an 18-dB expected SNR, a total of 80 bits (corresponding to rate R=5) can theoretically be transmitted with a block probability of error less than 10^-9, all without any training or knowledge of the propagation matrix
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