# Turbo Decoder for Low-Power Ultrawideband Communication Systems

Authors: Esam A. Obiedat; Lei Cao
Journal: International Journal of Digital Multimedia Broadcasting
 (2008)

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## Abstract

A new method to reduce the computational complexity
of the turbo decoding in ultrawideband (UWB) orthogonal
frequency division multiplexing (OFDM) system is proposed.
Existing stopping techniques for turbo decoding process using
constrained decoding assume fixed signal-to-noise ratio (SNR)
for all the OFDM symbol bits so they fail to yield an acceptable
bit-error rate (BER) performance in multicarrier systems. In
this paper, we propose a bit-level stopping technique for turbo
decoding process based on the constrained decoding method. In
this technique, we combine the cyclic redundancy check (CRC)
with an adaptive threshold on the log likelihood ratio (LLR)
on each subcarrier to detect for convergence. The threshold is
adaptive in the sense that the threshold on the LLR of a bit is
determined by the average SNR of the OFDM symbol and the
channel gain of the transmission subcarrier. Results show that
when the channel state information (CSI) is used to determine
the threshold on LLR, the stopping technique can reduce the
computational complexity by about 0.5–2.5 equivalent iterations
compared to GENIE turbo without degradation in the BER
performance.


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## Body

## 1. Introduction

A leading
candidate for fast data  transfer is the ultrawideband (UWP), a wireless technology designed for
short-range Personal area networks (PANs). High data throughput and low power
consumption for distances of less than 10 meters are among the main features of
UWB orthogonal frequency division multiplexing (OFDM)
systems, which are very applicable to digital home requirements. Due
to the Shannon limit approaching performance, turbo codes are expected to play
a key role in UWB systems. Turbo codes make it possible to increase data rate
without increasing the power of transmission, or they can be used to decrease
the amount of power used to transmit  at a certain data rate. However, the
increase in computational complexity, power consumption, and latency due to the
additional computations is big considerations
before implementation in UWB systems.The main challenge in implementing turbo codes in the
UWB systems is the consequent complexity consideration in spite of the high bit-error rate (BER)
performance and savings in transmission power consumption as pointed out above.
The complexity of Log-MAP is approximately four times that of Viterbis algorithm for a
single iteration, which means that to complete 10 full iterations in turbo
code, the computational complexity will be around 40 times the computational
complexity of the convolutional decoder in addition to increased power
consumption and latency due to additional computations. The attractive
enhancement in performance and reduction in transmission power for the system
with turbo codes makes it important to study the implementation issue in UWB
systems in order to reduce the complexity to a reasonable level while
maintaining the same performance.Approaches for reducing the complexity of turbo
decoder have appeared and are referred to as early detection or stopping
techniques [1–8]. These approaches are based on stopping the iterative
process of turbo decoder at a certain point instead of continuing a fixed
number of iterations. A criterion is used to determine when the iterative
process can be stopped with minimum loss in BER performance. All previously
proposed stopping techniques were based on single-carrier systems, where the signal-to-noise
ratio is assumed to be constant for all frame bits. These approaches may not be
directly implemented for turbo decoder in multicarrier systems like UWB OFDM,
since each bit (or group of bits) undergoes different
signal-to-noise ratios (SNRs) due to the different fading parameters of
different subcarriers. The resultant different SNRs for each subcarrier after
channel equalizations imply different
reliabilities, this necessitates different stopping strategies at each
subcarrier in turbo decoding.In this paper, we introduce a new criterion for
bit-level stopping for turbo decoders on UWB systems that assign different
stopping strategies to each subcarrier based on the average SNR and the
instantaneous SNR of that subcarrier. The proposed technique uses constrained
decoding method [1, 5] by clamping the bits satisfying the log likelihood ratio (LLR) threshold
condition, and stops the decoding process when the cyclic redundancy check (CRC) detects that the whole
frame is correctly decoded. The threshold is adaptively determined using channel state information (CSI)
values of the UWB channel. The results are compared to the ideal case of the
stopping techniques, which is called the GENIE case. In GENIE stopping
technique, the decoder is assumed to know all the transmitted bits and stops
the decoding process when all the bits are correctly decoded, unless the number
of iterations reaches the maximum allowed iterations. Therefore, GENIE case is assumed
to have the best BER performance and the least number of iterations that can be
achieved by any frame-based stopping criterion for a given BER
performance.The remainder of the paper is organized as follows.
The quasistatic UWB channel model and general assumptions made for the system
model used in the simulations are given in Section2. In Section
3, we
briefly review the current stopping techniques and present simulation results
for existing packet-level stopping techniques in UWB channels. The propose
stopping technique for turbo decoder is presented in Section 4.


## 2. Simulation Environment

The UWB
channel is classified as multipath quasistatic fading channel, meaning that the
channel impulse response remains almost constant for a number of transmitted
frames and the channel estimation gives almost perfect estimates for the CSI.
The channel modeling subgroup of the IEEE 802.15.3 committee proposed a channel
model for UWB systems [9] based on the S-V model [10] for arriving multipath components, which are
considered to arrive in clusters of rays (paths). The rays have independent
uniform phases, and independent Rayleigh amplitudes with variances that decay
exponentially with cluster and ray delays. The clusters and the rays within the
cluster form Poisson arrival processes with different, but fixed, rates. The
clusters are formed by the building superstructure, while the individual rays
are formed by objects in the vicinity of both the transmitter and the receiver.
According to [9], the
channel impulse response for the mth transmitted multiband OFDM symbol is given
by(1)hm(t)=∑c=0C−1∑r=0Rc−1ρm(c,r)αm(c,r)δ(t−Tcm−τc,rm),where αm(c,r) and ρm(c,r) are the multipath gain and reflection
coefficient, respectively, of the rth ray in the cth cluster, and the reflection coefficient has
equal probability on “+1” or “−1.” The total number of clusters is C,
each contains Rc rays. Tcm and τc,rm are the excess
delay of the cth cluster and the excess delay of the rth ray in the cth cluster, respectively. The values of    αm(c,r),ρm(c,r),Rc,Tcm,
and τc,rm are assumed to be constant for each OFDM
symbol transmission (quasistatic channel). The corresponding channel frequency
response for this realization at the kth subcarrier is given by(2)Hk=∑c=0C−1∑r=0Rc−1ρm(c,r)αm(c,r)e−j2π(f0+kΔf)(Tc+τc,r),where f0 is the first subcarrier (lowest frequency) of
the OFDM symbol, and Δf is the bandwidth of each subcarrier.The CRC turbo-encoded sequence is first interleaved
and converted to modulation symbols and then the latter is OFDM modulated.
Frequency hopping is applied to the OFDM symbols before transmitting them
through the UWB channel. At the receiver, the channel output is converted back
to the frequency domain by fast Fourier transform (FFT) after removing the
cyclic prefix. In the frequency domain, if we letX=[X1,X2,…,XN]T be the binary phase shift keying (BPSK)
modulated baseband symbols transmitted in a single OFDM symbol, then the
received symbols Y=[Y1,Y2,…,YN]T after the FFT stage are(3)Y=HX+Z,where Z=[Z1,Z2,…,ZN]T is the Additive white Gaussian noise (AWGN)
vector. H=Diag(Hk),k=1,…,N, where Hk is defined in (2) and N is the number of subcarriers.The matrixH components “channel gains” are used to
equalize the received signal Y.
The resultant soft channel output BPSK demodulated vector after equalization X^=[X^1,X^2,…,X^N],
where X^i=4R(Eb/N0)Re{YiHi*},i=1,…,N,
is deinterleaved before sending it to the turbo decoder.For all the simulations in this paper, the channel is
assumed to be perfectly estimated and there is no intercarrier interference
(ICI) (i.e., the delay spread is less than the cyclic prefix). All interleavers
used in the simulation model, the turbo encoder interleaver, and the channel
interleaver which proceeds the OFDM modulation, are random interleavers. After
adding the CRC sequence for the frame, the 1024 bit frame is turbo encoded with
1/2(7,5)oct recursive systematic convolutional (RSC)
encoder. For each UWB channel model, CM1 line of sight (LOS) (0–4 m), CM2
nonline of sight (NLOS) (0–4 m), CM3 NLOS (4–10 m), and CM4 extreme NLOS, the
channel impulse response is obtained randomly according to the channel model
characteristics in [11].


## 3. Review of the Current Stopping Techniques Based on CRC Detection

It is noted from simulations of turbo codes that after
a certain number of iterations, the improvement in BER performance for any
additional iteration is so small that the decoding process can be stopped with
minimum degradation in performance. Considering this, many researchers have
sought the best method to detect the stopping point considering three main
targets: (1) to maintain the performance degradation (if the stopping method
results in a degradation) within certain limits from the performance of turbo decoder
with fixed number of iterations; (2) to minimize the number of iterations while
keeping in mind the first objective; (3) to assure
that the added computation complexity for detecting
the early stopping point should not exceed the computation complexity reduced
by stopping the iterations.Generally, stopping techniques can be categorized into
three different classes according to the clamping level of bits: frame level,
packet level, and bit level. The frame-level stopping technique terminates the
iterative process for the entire frame only when the condition for termination
has been satisfied. On the other hand, packet and bit-level stopping techniques
use constrained decoding by only clamping the bits that are satisfying the
criterion condition and continuing on decoding process for remaining bits.
There are many examples in the literature of stopping techniques based on frame
level, but few methods use the bit- and packet-level terminations. An example
of the bit-level stopping technique is the method [2] which implements a trellis
slicing algorithm to detect information and codeword symbols as well as state
variables during the decoding. However, since the slicing in [2] is based on LLR values, a
very large error floor may result.A generic packet-level method for early detection in
iterative decoding processes is introduced in [1], which suggests dividing the
full frame into smaller packets and adding a small CRC sequence to each
individual packet. The CRC sequences are used at the receiver as an inner code
to detect any decoding error in the turbo-decoded packet after each half
iteration. If a certain packet is error-free, the decoder stops decoding
“constrain” its bits. The bits found by CRC detection stage to be correct are
constrained on the trellis in the following decoding stages so that the number
of possible paths are reduced.The method suggested in [1] is an efficient method when
implemented for single-carrier systems. It reduces the average computational
complexity by reducing the number of paths in trellis as the termination
process starts to clamp the correctly decoded packets. However, the constrained
decoding methods can lead to error propagation if the clamped bits were not
correct. By observing the performance of CRC detection techniques, it was noted
that there is a chance of erroneously determining that a CRC protected packet
to be correct while it is not (the misdetection in CRC decoder). If a CRC
misdetection occurs, some bits will be erroneously clamped; consequently, the
number of search paths for the decoding process will be limited and potentially
lead to decoding errors for the neighboring bits.Simulations show that error propagation problem is
more serious in multicarrier channels than single-carrier channels. This might
be due to the fact that every bit (or group of bits) is transmitted over a
different channel with different SNRs, and since the bits with low SNR are more
likely to be erroneously clamped than bits with high SNR, the effect of low SNR
bits on the performance will dominate over the effect of bits with high SNR,
especially for the hard to decode frames. Thus, a good termination method for
multicarrier systems (such as UWB OFDM) should take into account the different
SNRs for different bits if constrained decoding is implemented.The error  propagation in CRC early stopping techniques
can be alleviated by setting the minimum number of CRC detected correct packets(ρmin) required before starting to clamp their bits.
Figure 1 shows the BER performance of a turbo decoding in the UWB CM1 channel
with CRC-stopping criterion that starts searching for correct packets
immediately after the first stage of decoding and starts clamping bits when ρmin=1,4, and 8, respectively, packets are found
to be correct.Figure 1
BER Performance
of CRC-turbo with CM1 channel, 128 bit packet (12 bit CRC), start termination after 0.5 iteration,ρmin=1,4,8.


## 4. New Stopping Technique

In single-carrier systems, the channel reliability,
which can be obtained by measurement of the channel at the receiver input, is
given byLc=4R(Eb/N0) which is four times the SNR at this single
carrier, where R is the code rate. However, in multicarrier
systems such as MB-OFDM, each subcarrier has a different fading coefficient
(frequency channel response) and thus will have different SNR value from
adjacent subcarriers. Therefore, it is more reasonable to derive the channel
reliability for each subcarrier from the SNR of that subcarrier. In our system,
we use the following relation to calculate channel reliability values that will
be multiplied by the corresponding soft input bits:(4)Lci=4REbN0|Hi|2,where the part (Eb/N0)|Hi|2 represent the instantaneous SNR of the
channel, Eb/N0 is the average SNR
for all carriers, and |Hi| is  magnitude of the channel frequency response
at subcarrier i as shown in (2). As shown in Figure 2, large
improvement in BER performance is gained when this relation is used to
calculate channel reliability from the CSI values obtained from the channel
estimator. In this paper, we show only the results for the turbo decoder using
the channel reliability obtained from (4).Figure 2
BER performance
for turbo decoder with single-carrier channel reliability and multicarrier
channel reliability obtained from (4).In this section, we propose a CRC-based early
detection method combined with a bit-level stopping using threshold on LLR. The
CRC early detection method serves as an accurate method to determine when all
the bits of decoded frame have converged to the correct sequence, and the LLR
threshold method works as bit-level stopping for early stages of the decoding
process. The bit-level stopping threshold on LLR in our the proposed technique
differs from one bit to another and is dynamically updated for each bit from
the CSI, unlike the bit-level stopping technique proposed in [2].For easy-to-decode frames, the LLR output after each
decoding stage keeps growing and the hard decision output converges more to the
correct sequence. While the change in magnitude of LLR output might be large
for easy-to-decode frames, it is small for hard-to-decode frames. The average
signal-to-noise ratio has significant effect on the difference between LLR
values after each iteration. One way to implement an efficient bit-level early
detection is to monitor the magnitudes of the LLR for the decoded bits and
clamp the bits that exceed a certain LLR threshold. However, it was noted from
simulations that, in general, the hard-decoded outputs and the magnitude of LLR
of the bits carried over subcarriers with small SNR are affected by the
magnitude of LLR of the neighboring bits with high SNR. Hence, when designing
an early detection method that is based on thresholding of LLR, it is crucial
to consider two main factors: the average SNR of the OFDM symbol (Eb/N0¯) and the instantaneous SNR at each subcarrier (Eb/N0)i.
This threshold should increase when the average SNR increases and it should be
higher for the bits conveyed on subcarriers with low SNR, so that the bits
carried over low SNR subcarriers will not be misdetected. One simple
implementation satisfying the above two main factors for this threshold is the
following:(5)Ti=Lmax(1−|Hi|2maxj(|Hj|2))+lmin,where Lmax is a multiplicative factor and is used to
adjust the maximum threshold. Hi is channel state information that is given in
(2), and lmin is a constant equal to fixed percent of Lmax and is used to adjust the minimum threshold.
The value of lmin is chosen experimentally to minimize the loss
in BER performance and to maximize the percent of early detected bits. The
normalization to the maximum term in the denominator (maxj(|Hj|2)) can be set to a fixed value to simplify the
implementation.Figure3 displays BER performance for the turbo
decoder with the new stopping technique based on 32 bit CRC detection combined
with thresholding on the values of LLR (code rate is 992/2048  ≈ 0.484). The figure shows the results for three
arbitrarily selected thresholds by setting lmin=0.2Lmax (experimental value) and choosing different
values for the maximum threshold Lmax  asFigure 3
BER performance
for the proposed method on CM1 channel applying different thresholding
strategies:Th1,Th2,Th3  displayed together with BER performance of
GENIE turbo decoder.(1)
Th1:Lmax=1.5*Eb/N0¯+2,(2)
Th2:Lmax=2.5*Eb/N0¯+2,(3)
Th3:Lmax=5*Eb/N0¯+5,where, in this
example, we chose linear equations to relate average SNR value with the maximum
threshold, however, the maximum threshold for each Eb/N0¯ can be selected differently so that the
maximum threshold Lmax increases when the average SNR increases. The
relation between the value of the CSI for a subcarrier and the corresponding
threshold on LLR for the bits carried over this subcarrier, for two values of Eb/N0¯=1.5 dB and 3 dB, is shown in Figure 4, where the
maximum value for CSI is assumed to be 3 dB. The results in Figure 3 show that
the BER performance of the CSI-CRC-turbo decoder will have small degradation
when the threshold has more tolerance (as the maximum threshold Lmax decreases).Figure 4
The thresholdsTh1,Th2,Th3 for Eb/N0¯=1.5 and 3 dB for different subcarriers CSI and
max(Hi) = 3 obtained from (5).At this point, it is important to compare the
reduction in computational complexity resulting from the new stopping technique
for different thresholding strategies after each decoding stage. Figure5 displays
the average number of bits found to be correct after each decoding stage by the
proposed stopping technique applying the three thresholding strategies Th1,Th2, and Th3.
In the case where the threshold Th1 was used, about 47% of the bits on average
will be clamped after the
first decoding  stage (after 0.5 iteration) at Eb/N0¯=3 dB, and about 89% and 98% of bits on average
will be clamped after 1.0 and 1.5 iterations, respectively, which results in a
large reduction in computational complexity. Comparing these numbers to the
GENIE turbo, at the same SNR, about 2%, 53%, and 88% of bits on average will be
decoded by the 0.5, 1.0, 1.5 iterations,
respectively. Since there is no bit-level stopping for the case of GENIE turbo
(which is the ideal case when the receiver is assumed to know all the received
bits sequence and so stops the decoding process when all frame bits are found to
be correctly decoded), the curves in Figure 5 for the GENIE case represent the
percentage of the total transmitted frames that were completely decoded after
each decoding stage. When taking the average percentage of completely decoded
frames after a certain decoding stage, this number is equivalent to the average
percentage of frame bits decoded in a bit-level stopping technique after that
decoding stage.Average percent
of early detected bits in turbo decoder with CRC detection and thresholding on
LLR stopping technique applied for the three thresholdsTh1,Th2,Th3,
and GENIE.
(a)(b)(c)(d)Considering this reduction in complexity after each
decoding stage, we can compute the effective number of iterations based on the
total computations required for each method. For ordinary turbo decoder without
stopping techniques applied, the total number of computations required to
complete the fullN iterations (unconstrained decoding) Cud is expressed by (6), where L is the frame length in bits and C is the total number of computations required
to get soft LLR output for single bit in one stage of decoding. For a system applying
bit and packet-level early detection, the total number of computations required
(constrained decoding) Ccd is defined in
(7):(6)Cud=2N×L×C,(7)Ccd=∑i=12NℓiL×C,where 0≤li≤1 is the percent of bits decoded (not yet early
detected) in the ith decoding stage; it is equal to “0”
when all the bits of the frame are considered as correctly decoded, and it is
equal to “1” when none of the frame bits are constrained in the trellis
decoding. Note that in case ℓi=1 for all i,
then (7) reduces to (6).
Equation (7) is used to calculate the average effective
number of iterations required to completely decode the bit sequence by dividing
it by the total number of computations by the number of computations per
decoding stage (L×C) to get the average number of iterations.
Figure 6 shows the equivalent average number of iterations for the three
thresholds examples shown in Figure 5 compared to the ideal case (GENIE turbo).Figure 6
Average
effective number of iterations for turbo decoder with CRC12 detection combined
with thresholding on LLR stopping technique.From the results for the effective number of iteration
in Figure6 we can infer that the computational complexity of the system with
the new stopping technique is reduced by equivalently 2.5 iterations at low SNR
and about 0.5 iteration at high SNR for the system
with Th1 thresholding strategy. The main reason
why the proposed method is more effective at low
SNR, that is, that the stopping technique saves more computations with no
degradation in performance, is that the CRC detection technique takes fewer
decoding stages to decide that the decoded sequence is correct since there are
more errors at low SNR, but the thresholding technique still can detect the
bits sent over high SNR subcarriers and clamp these bits, satisfying the LLR
condition.In the following results, we examine the performance
of the proposed stopping technique in the other four types of UWB channels
presented in [11].
Figure 7 displays the BER performance results for the turbo decoder using CRC
detection combined with thresholding on LLR using Lmax=2*Eb/N0¯+3 and lmin=0.2*Lmax.
The effective number of iterations for these configurations of the stopping
technique is shown in Figure 8. Simulation results show that using the new
stopping technique gives a BER performance that is very close to the GENIE
turbo. While the CRC detection gives an accurate method to terminate the
decoding process, the dynamic thresholding method helps in gaining large
reduction in computational complexity so as to make the turbo codes a good
alternative in UWB OFDM system.Figure 7
The performance
of the new stopping technique in the four different types of UWB channels.Figure 8
The effective
number of iterations for the new stopping technique in the four different types
of UWB channels used.


## 5. Conclusion

In this paper, we show that the existing early
stopping constrained decoding methods for turbo decoder are not appropriate in
multicarrier systems with different fading coefficients for each subcarrier
since they give equal weights for bits with variable SNR. We present a
bit-level stopping technique with adaptive thresholding to reduce the total
number of computations and the power consumed by turbo decoder in UWB OFDM
systems.The proposed stopping technique uses CRC detection
combined with thresholding technique. It reduces the total computational
complexity in the early decoding stages by using a novel technique that compares
the LLR outputs with flexible thresholds that are calculated from the CSI
values of the UWB channel to take into account the low and high values of SNR
for different subcarriers and thus decreasing the average number of iterations.
The CRC detection part of this technique is used to determine the accurate
stopping point when all the bits of the sequence have converged to the correct
sequence.The results show a large
reduction in computational complexity by reducing the average number of
iterations to less than one iteration while keeping the BER performance with
minimum degradation. This means that if turbo decoding technique is to be
implemented  in UWB system, only four times or less the decoding complexity of
Viterbi decoding is needed to obtain a huge improvement in performance.



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*Source: 897069-2009-01-13.xml*