67 research outputs found
Why winning a soccer game is worth 5 points
Ranking is used in sport leagues to determine a champion and/or to decide on
promotion/relegation of teams. Arguably, the best known ranking method relies
on scores obtained by cumulating the points associated with the wins and the
draws of all teams, which are then ranked by sorting the score obtained. There
are two main problems with this ranking method. First, the meaning of the
ranking is undefined, and, second, it depends on the relative value of the wins
that is arbitrarily set. We remedy these issues by introducing a probabilistic
model of the game results and by showing an interpretation of the ranking that
is consistent with the model. We also propose a methodology to estimate the
parameter of the model which allows us to objectively determine the value of
the win. In particular, using data from the association football (soccer), we
show that the value of the win is close to five (5) points
On BICM receivers for TCM transmission
Recent results have shown that the performance of bit-interleaved coded
modulation (BICM) using convolutional codes in nonfading channels can be
significantly improved when the interleaver takes a trivial form (BICM-T),
i.e., when it does not interleave the bits at all. In this paper, we give a
formal explanation for these results and show that BICM-T is in fact the
combination of a TCM transmitter and a BICM receiver. To predict the
performance of BICM-T, a new type of distance spectrum for convolutional codes
is introduced, analytical bounds based on this spectrum are developed, and
asymptotic approximations are also presented. It is shown that the minimum
distance of the code is not the relevant optimization criterion for BICM-T.
Optimal convolutional codes for different constrain lengths are tabulated and
asymptotic gains of about 2 dB are obtained. These gains are found to be the
same as those obtained by Ungerboeck's one-dimensional trellis coded modulation
(1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be
asymptotically as good as 1D-TCM.Comment: Submitted to the IEEE Transactions on Communication
Towards Fully Optimized BICM Transceivers
Bit-interleaved coded modulation (BICM) transceivers often use equally spaced
constellations and a random interleaver. In this paper, we propose a new BICM
design, which considers hierarchical (nonequally spaced) constellations, a
bit-level multiplexer, and multiple interleavers. It is shown that this new
scheme increases the degrees of freedom that can be exploited in order to
improve its performance. Analytical bounds on the bit error rate (BER) of the
system in terms of the constellation parameters and the multiplexing rules are
developed for the additive white Gaussian Noise (AWGN) and Nakagami- fading
channels. These bounds are then used to design the BICM transceiver. Numerical
results show that, compared to conventional BICM designs, and for a target BER
of , gains up to 3 dB in the AWGN channel are obtained. For fading
channels, the gains depend on the fading parameter, and reach 2 dB for a target
BER of and .Comment: Submitted to the IEEE Transactions on Communication
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