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Near-ML for unreliable symbols
: near-ML decoded symbolsComplexity reduction
• Error-rate performance
-- ML matching error-rate performance
• Getting into details [6]
ZF filter
ZF filter output
where
• Current decoders
-- exhaustive ML-decoding [2]
-- exploiting ISI pattern [3]
-- partial ML + ZF-SIC decoding [4]
Quality of instantaneous channel is not utilized in
[2]-[4]
• Idea
-- can we simplify decoding for at least “good channels”?
-- linear decoders for “good channels” and non-linear
decoders for ”bad channels”
• Golden Code structure
-- : : complex symbols, M-QAM constellation
-- are system constants
--
• Received complex signal
-- : signal to noise ratio
-- (channel coefficients)
-- (noise)
-- received complex signal
-- , : transmission/reception time slot
• Equivalent channel model [5]
-- decoupling real and imaginary components
-- received signal in real domain
-- and : stacking element-wise real and
imaginary comp. of and
-- : equivalent real channel matrix
-- : function of constant
• Complexity comparison
-- 98% complexity savings at 30 dB for 16-QAM
-- decoding complexity reduces with increasing SNR
• Reason for complexity savings (16-QAM)
-- linear decoder usage increases with increasing SNR
Golden Code decoding
Reliability-based channel adaptive decoding
Significant complexity savings
ML-matching error performance
Proposed algorithm exploits:
SNR structure
ISI structure
instantaneous channel quality
information
a brief review/history
• Multiple-Input Multiple-Output (MIMO) -- boosting data-rate (e.g. V-BLAST)
-- enhancing reliability (e.g. STBCs)
-- practical interest : 2 Tx, 1+ Rx
• V-BLASTchannel capacity ∝ min (# Tx, # Rx) [1]
high decoding complexity
poor error performance
• STBCsfull diversity codes (e.g. Alamouti code)
not full-rate for more than 1 Rx antennas
• Golden Code (GC): a celebrated solutionfull-diversity code
full-rate for 2 or more Rx antenna
open loop code (no feed back)
variant of GC incorporated in IEEE 802.11e standard
very high decoding complexity
reduce the high decoding complexity of Golden Code.
maintain state-of-the-art error-rate performance
Introduction
Chronicles of Golden Code
System Model
2005
2009
2013
...0100111 Space-Time Modulation
(GC)
(0,1) (1,1)
(1,0)(0,0)
• Bird’s eye view
-- process received signal using ZF filter
-- examine reliability of each symbol
-- detect and remove reliable symbols
-- near-ML over unreliable symbols
Take-home Message
References
[1] G. J. Foschini Jr. and M. J. Gans, “On limits of wireless
communication in a fading environment when using multiple antennas,”
Wireless Personal Commun., Mar. 1998.
[2] J. C. Belfiore, G. Rekaya, and E. Viterbo, “The golden code: A 2 X 2 full-
rate space-time code with nonvanishing determinants,” IEEE Trans. Inf.
Theory, vol. 51, no. 4, pp. 1432-1436, Apr. 2005.
[3] M. O. Sinnokrot and J. Barry, “Fast maximum-likelihood decoding of the
Golden code,” IEEE Trans. Wireless Commun., vol.9, pp. 26-31, Jan. 2010.
[4] L. P. Natarajan and B. S. Rajan, “An adaptive conditional zero-forcing
decoder with full-diversity, least complexity and essentially-ml
performance for STBCs,” IEEE Trans. Signal Process., vol. 61, pp. 253-263,
Jan. 2013.
[5] S. Kundu, D. A. Pados, W. Su, and R. Grover, “Towards a preferred 4 X 4
space-time block code: A performance-versus-complexity sweet spot with
linear-filter decoding,“ IEEE Trans. Commun., vol. 61, pp. 1847-1855, May
2013.
[6] S. Kundu, S. Chamadia, D. A. Pados, and S. N. Batalama, ”Fastest-known
near-ML decoding of Golden code,’’ Signal Process. Adv. Wireless
Commun. (SPAWC), submitted Mar. 2014.
Proposed Decoder
• System setup
-- # Tx = 2, # Rx = 2, T = 2 time slots
-- perfect channel state information (CSI) at receiver
-- no CSI at transmitter
Can we reduce the decoding
– complexity while maintain
ML error-rate performance
Linear
ML
Decoding Complexity
Erro
r p
erfo
rman
ce
Linear-SIC
Fastest-Known Near-ML Decoding of Golden Code Shubham Chamadia, Sandipan Kundu, Dimitris A. Pados, and Stella N. Batalama
Department of Electrical Engineering
The State University of New York at Buffalo, NY 14260
E-mail: {shubhamc, skundu, pados, batalama}@buffalo.edu
HelloUB
HelloUB
1110010...
Reliability computation
Reliability condition
where
and are two closest neighbor of
is a function of , and noise variance
Detect and remove reliable symbols
: detected reliable symbols by ZF
Final decoded symbols
Performance Comparison
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