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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