Parity Assisted Decision Making for QAM Modulation Page: 1
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Parity Assisted Decision Making for QAM Modulation
Amer H. Alhabsi, Hussain M. Al-Rizzo and Robert Akl *
A simple technique which involves the trans-
mission of a Quadrature Amplitude Modulation
(QAM) symbol and two parity bits in separate
channels to improve the performance of commu-
nication systems is devised. When a symbol is
received, a decision is made not solely by its
Euclidean distances to the constellation points.
Rather, the two parity bits are used to assist in
making the decision. Unlike standard error cor-
recting codes (ECC), the proposed method op-
erates on the received symbols at the detector
level and before the ECC. The parity bits and
the information symbols can be sent in differ-
ent channels (frequency division) or at different
times on the same channel (time division). The
available energy for transmission can be distrib-
uted unevenly among the information bits and
the parity bits to improve the performance. Sim-
ulation results show large gains in required signal
to noise ratios over uncoded system to achieve
the same performance. The scheme is simple and
is well suited for systems with low computational
In traditional QAM, each k information bits are
associated with a point in a M-point constel-
lation diagram where M = 2k. A waveform
corresponding to the coordinates of the constel-
lation point is transmitted to convey the in-
formation. In Additive White Gaussian Noise
(AWGN) channels and when the symbols occur
with equal probabilities, the receiver makes a de-
cision as which symbol was transmitted accord-
*A. Alhabsi is with Sultan Qaboos University. H. M.
Al-Rizzo is a professor at UALR. R. Akl is an asst. prof.
at the university of Texas at Denton.
ing to the Euclidean distances of the received
symbol to all constellation points.
In hard-decision decoding, the output of the
demodulator is quantized into a small num-
ber, usually M, of discrete levels. This kind
of decision-making highly simplifies the receiver
structure. This simplification comes at a cost
in terms of performance. Soft-decision decoding,
on the other hand, does not quantize the output
of the demodulator. The demodulator output
is sent to the decoder as is for further process-
ing. It is also possible to quantize the output
of the demodulator to a large number of levels,
much larger than M, and still achieve perfor-
mance close to that of pure un-quantized output.
In BPSK where M = 2, for example, the perfor-
mance when 3-bit quantization, i.e., 8 levels, is
used is similar to that of no quantization.
When hard decision is used instead of soft de-
cision, there is a loss of about 2-3 dB per bit to
achieve the same level of performance in terms of
bit error rate. To compensate for the loss associ-
ated with hard decision, the authors investigated
the use of parity-assisted decoding (PAD). This
technique involves sending two parity bits in ad-
dition to the QAM symbol. The parity bits are
sent using QPSK in a different channel. The par-
ity bits can also be sent at alternating times with
the information symbols on the same channel.
The two parity bits are simply logical functions
of the bits of the word corresponding to the sym-
bol to be transmitted. This simple coding tech-
nique is particularly attractive for systems where
high computational power is not available.
Standard error correcting codes (ECC) correct
errors after the received symbols have been de-
tected. The received word is compared, through
certain algorithms, to all codewords. The code-
word closest to the received one, in Hamming dis-
tances for hard decisions and Euclidean distances
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Alhabsi, Amer H.; Al-Rizzo, Hussain Mudhaffar Younis, 1957- & Akl, Robert G. Parity Assisted Decision Making for QAM Modulation, paper, September 2006; [New York, New York]. (digital.library.unt.edu/ark:/67531/metadc30829/m1/1/: accessed February 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Engineering.