Energy-Efficient LDPC Decoder using DVFS for binary sources

ACEEE Int. J. on Information Technology, Vol. 01, No. 01, Mar 2011

Energy-Efficient LDPC Decoder using DVFS for
binary sources
S.karthikeyan1, S.Jayashri2
1
Sathyabama university/Dept of Electronics and communication Engineering, Chennai, India
Email: urkarthikeyan@rediffmail.com
2
Adhiparasakthi Engineering college/Principal, Melmaruvathur,TN,India
Email: jayaravi2010@gmail.com

Abstract- This paper deals with reduction of the transmission a codeword has been found). Also, LDPC codes of almost
power usage in the wireless sensor networks. A system with any rate and block length can be created simply by specifying
FEC can provide an objective reliability using less power the shape of the parity check matrix, while the rate of turbo
than a system without FEC. We propose to study LDPC codes is governed largely by a puncturing schedule, so
codes to provide reliable communication while saving power flexibility in rate is obtained only through considerable
in the sensor networks. As shown later, LDPC codes are more
design effort. Also, since the validity of a codeword is
energy efficient than those that use BCH codes. Another
method to reduce the transmission cost is to compress the validated if its parity checks, even if errors occur, they are
correlated data among a number of sensor nodes before almost always detected errors (especially for long codes).
transmission. A suitable source encoder that removes the As an additional boon on the commercial side, LDPC codes
redundant information bits can save the transmission power. are not patent protected. On the negative side, LDPC codes
Such a system requires distributed source coding. We propose have a significantly higher encode complexity than turbo
to apply LDPC codes for both distributed source coding and codes, being generically quadratic in the code dimension,
source-channel coding to obtain a two-fold energy savings. although this can be reduced to some extent. Also, decoding
Source and channel coding with LDPC for two correlated nodes may require many more iterations than turbo decoding, which
under AWGN channel is implemented in this paper. In this
has implications for latency.
iterative decoding algorithm is used for decoding the data, and
it’s efficiency is compared with the new decoding algorithm B. Constructing LDPC Codes:
called layered decoding algorithm which based on offset min
sum algorithm. The usage of layered decoding algorithm and Several different algorithms exists to construct suitable
Adaptive LDPC decoding for AWGN channel reduces the LDPC codes. Only binary LDPC codes are considered here.
decoding complexity and its number of iterations. So the power We use N to denote the length of the code and K to denote
will be saved, and it can be implemented in hardware. its dimension and M = N-K. Since the parity check matrices
we consider are generally not in systemic form, we usually
Index Terms- LDPC codes, Distributed Source coding, Source use the symbol A to represent parity check matrices, reserving
Channel coding, iterative decoding algorithm, layered decoding
the symbol H for parity check matrices in systematic form.
algorithm.
Following the general vector m is a K x 1 vector; a codeword
is a N x 1 vector. The generator matrix G is N x K and the
I. INTRODUCTION
parity check matrix A is ( N-K) x N , such that HG=0.
We denote the rows of a parity check matrix as
A. Low-Density-Parity Check-LDPC Codes:
Low-density parity-check (LDPC) codes are a class
of linear block LDPC codes. The name comes from the
characteristic of their parity-check matrix which contains
only a few 1’s in comparison to the amount of 0’s. Their
main advantage is that they provide a performance which is The equation aiTc= 0 is said to be a linear parity-
very close to the capacity for a lot of different channels and check constraint on the codeword c. We use the notation zm
linear time complex algorithms for decoding. LDPC codes = amTc and call zm a parity check or, more simply, a check.
have performance exceeding, in some cases, that of turbo For a code specified by a parity check matrix A, it is expedi-
codes, with iterative decoding algorithms which are easy to ent for encoding purposes to determine the corresponding
implement (with the per-iteration complexity much lower generator matrix G. A systematic generator matrix may be
than the per-iteration complexity of turbo decoders), and are found as follows. Using Gaussian elimination with column
also parallelizable in hardware. There are other potential pivoting as necessary (with binary arithmetic) determine an
advantages to LDPC codes as well. In a very natural way,
the decoder declares a decoding failure when it is unable to
correctly decode, whereas turbo decoders must perform extra If such a matrix A , does not exist, then A is rank
computations for a stopping criterion (and even then, the deficient, r = rank(A) < M . In this case, form H by truncat-
stopping criterion depends upon a threshold that must be ing the linearly dependent rows from Ap-1A . The correspond-
established, and the stopping criterion does not establish that ing code has R = K / N > (N - M) / N , so it is a higher rate

© 2011 ACEEE 1
DOI: 01.IJIT.01.01.37


code than the dimensions of A would suggest) Having found
H, from

We study the asymmetric distributed source cod-
Then HG=0, so ApHG = AG = 0, so G is a generator ing scenario in which it is assumed the signal X1 is com-
matrix for A. While A may be sparse neither the systematic pressed conventionally and sent at full rate RX1 e” H(X1),
generator G nor H is necessarily sparse. Fewer than half of and is recovered perfectly at the decoder. We want to com-
the elements are nonzero. Since the A matrix is sparse, it can press the X2 as close as possible to the Slepian-Wolf bound
be represented efficiently using lists of its nonzero locations. of H(X2|X1). As we can see the chosen rates for RX1 and
In this notation, bits are typically indexed by n or n’ and the RX2 satisfy the inequalities of above equations.
checks are typically indexed by m or m’. The set of bits that The corresponding sensor communication is shown in
participate in check zm (i.e., the nonzero elements on the mth figure 1.
row of A is denoted

Fig.1. System for compression of X2 with the side information of X1 at
Thus we can write the mth check as
the Decoder

B. Encoding and decoding with LDPC codes:
A low-density parity-check (LDPC) code is determined
by its parity-check matrix (H) or, equivalently by its bipartite
graph. An ensemble of LDPC codes is described by the
The set of bits that participate in Zm except for
degree distribution polynomials ë(x), and ñ(x). The bipartite
bit n is denoted graph is used in the message-passing decoding algorithm.
Encoding- Given, H to encode, i.e., compress, an
arbitrary binary input sequence, we multiply X with H and
The notation INmI indicates the number of elements find the corresponding syndrome. Z1 [length (n-k)]
in the set Nm.These sets should be considered ordered lists, equivalently, in the bipartite graph, this can be viewed as
with the ith element of Nm being indicated by Nm (i). The set binary addition of all the variable node values that are
of checks in which bit cn participates (i.e., the nonzero ele- connected to the same check node.
ments of the nth column of A ) is denoted Decoding algorithm- The decoder must estimate the
n-length sequence X from its (n — k) long syndrome Z1
and the corresponding n-length sequence Y
We use the following notation:
II. EXISTING METHODOLOGY • xi, yi £ {0, 1}, i = 1, 2, ..., n, are the current
values of Xi and Yi. respectively, corresponding to
A. Distributed Source Coding Between Two Correlated the i th variable node vi:
Sources: • Li£ {2, 3, ...},i< = 1,2, ..., n, is the degree of V i
Consider a communication system of two statistically • ,qouti,m (qini,m )£ R, i= 1, 2, ..., n, m = 1, 2,....li.is
dependent signals, X1 and X2. The dependency between X1 the log-likelihood ratio
and X2 can be fully described by the conditional probability (LLR) sent along the mth edge
mass function P[X1|X2]. A suitable source encoder that from (to) V i,
removes the redundant information bits, reduces both the • Sj £ {0, 1} j = 1, 2, ..., n — k, is the value of
length of the transmitting information and the power Z1,j corresponding to the
consumption. The correlation between signals X1 and X2 Jth check node Cj, i.e., the j th syndrome
can be modelled as the input and output of a binary symmetric component;
channel with the crossover probability of P[X1 ‘“ X2|X1] = • r j £ {2, 3, ...}, j = 1, 2, ..., n — k, is the degree
p. According to Slepian-Wolf theorem. The output of two of c j ;
correlated sources that do not communicate can be • toutjm (tinj,m )£ e R, j = 1, 2, ..., n-k, m = 1, 2, ...rj,
compressed with the same rate as if they were is the LLR sent along the mth edge from (to) c j .
communicating. This is true when the decoder has access to Step 1: Setting
the both compressed outputs. Such a system requires
distributed source coding. The Slepian-Wolf rate region can
be expressed as following:

© 2011 ACEEE 2
DOI: 01.IJIT.01.01.37


Step 2: i=1,2…..n, p<=0.5 the LLR sent from the i th iterations is insufficient. This paper describes a more
variable node vi along the mth edge is comprehensive design that accommodates both fading
channels and the more difficult case of AWGN channels.
This paper presents the LDPC decoding algorithm based on
offset min-sum and layered decoding.
Assume binary phase shift keying (BPSK) modulation (
M=1,2,.....li,i=1,2,....n where initially qini,j=0
1 is mapped to “1 and 0 is mapped to 1) over an additive
Step 3: The values qouti,m are assigned to the corresponding
white Gaussian noise (AWGN) channel. The received values
tinj,ð (i,m,j) according to the connections in the bipartite yn are Gaussian with mean xn = 1 and variance ä^(2). The
graph and are then used to do the processing at the check Iterative two-phase message-passing (TPMP) algorithm, also
nodes. From the “tanh rule” and the syndrome information, known as belief-propagation (BP) algorithm is computed in
the LLR sent from the jth check node cj along the mth two phases. One is a check node processing and the other is
edge is variable node processing. In the check node processing, each
row of the parity matrix is checked to verify that parity check
constraints are satisfied. In the variable node processing the
probability will be updated by summing up the other
j= 1, 2, ..., n-k, m = 1, 2, ...rj, The
probabilities from the rest of the rows and the a prior
inclusion of the (1 — 2sj) factor accounts for the probabilities from the channel output. The message passing
syndrome information. algorithm can be simplified to the belief-propagation based
step 4: Now qini,m = toutj,ð (i,m,j) for all edges in the bipartite
algorithm (also called Min-Sum algorithm). While greatly
graph, which can be used to start a new iteration and estimate
reducing the decoding complexity in implementation, the
xi from
Min-Sum degrades the coding performance. The improved
BP based algorithm, Normalized-Min-Sum and Offset-Min-
Sum eliminates this performance degradation. Following the
same notation in [8], the check node processing can be
expressed as:
R(i)mn = ä(i)mn max (ê (i)mn “ â, 0)
III. PROPOSED METHODOLOGY
ê (i)mn =%R(i)mn % = min % Q (i”1)n’m %
A. LDPC Layered Decoding Based on Offset MIN-SUM
Algorithm: n”N(m)n
In practice, the LDPC decoder is typically set to
(i)
run for data convergence until a prescribed maximum num- Where Q nm
is the message from variable node n to
ber of iterations (e.g. 20) depending on the code rate. How- check node m,
ever, the actual number of decoding iterations varies from R(i)mn is the message from check node m to
frame to frame. In the case that channel data comes in con- variable node n, and superscript i denotes the ith iteration.
stant time interval, a conventional decoder has to be config- M(n) is the set of the neighbouring check nodes for
ured to accommodate the worst case scenario. As a result, variable node n, and N(m) is the set of the neighbouring
the decoder often remains idle since for most frames, the variable nodes for check node m, â is a positive constant
decoding process ends far earlier than the maximum num- and depends on the code parameters
ber of iterations. Thus it is not power efficient. In the decod- The sign of check-node message R(i)mn is defined as
ers proposed is based on an on-the-fly computation para-
digm, optimized dataflow graphs are introduced to reduce ä(i)mn = ( Ï sgn (Q(i”1)n’m ))
the logic and internal memory requirements of the LDPC n_”N(m)n
In the variable node processing,
decoder and at the same time the decoder’s parallelization is
tailored to average number of decoding iterations for the
Qn = L(0)n + “ R(i)mn
target frame error rate for the operating SNR region. These
decoders buffer statistically for different parallelization based
m”M(n)/m
on average number of decoding iterations while ensuring
Where the log-likelihood ratio of bit n is L(0)n = yn. For
the performance similar to that of a fixed iteration decoder
final Decoding
configured for maximum number of iterations. These de-
Pn = L(0)n + “ R(i)mn
coders are almost fully utilized and run at the maximum fre-
m”M(n)
quency. The proposed paper improves the system. There have
A hard decision is taken by setting xn = 0 if Pn(xn) e” 0, and
been researches on early termination of frame that cannot
xn = 1 if Pn(xn) d” 0. If xHT = 0, the decoding process is
be decoded even if the maximum iterations are applied. In
finished with ˆxn as the decoder output; otherwise, repeat
both of papers, early termination of the iterative process is
processing of Equation. If the decoding process does not
determined by checking the messages during the decoding.
end within predefined maximum number of iterations, itmax,
Between initial check error and number of decoding
3
© 2011 ACEEE
DOI: 01.IJIT.01.01.37


stop and output an error message flag and proceed to the The results showed how LDPC codes can be used in
decoding of the next data frame. Mansour, introduces the providing reliable data transmission and developing
concept of turbo decoding message passing (also called as aggregation techniques for correlated data in wireless sensor
layered decoding) for their AA-LDPC codes using BCJR networks.. It was shown that while some FEC coding
which is able to reduce the number of iterations without V.
schemes can improve the energy efficiency of a
performance degradation when compared to the standard communication link, it proves that FEC using LDPC codes
message passing algorithm. Contrast to two phase message can reduce the transmission power. The simulation results
passing algorithm, where all check-nodes are updated si- showed that using LDPC codes for FEC is significantly more
multaneously in each iteration, layered decoding view the H efficient than using BCH codes.
matrix as a concatenation of j = dv sub-codes, The H matrix
is divided into different block-rows and block CONCLUSION
columns. After the check-node processing of one layer, the
The ‘Source and channel coding’ and ‘distributed Source
updated messages are immediately used to calculate the vari-
coding‘ of two correlated nodes are done. The performances
able node message, whose results are then applied to next
of Both are compared. And Source and channel coding with
layer of sub-code. Each iteration in the layered decoding
LDPC for two correlated nodes under AWGN channel is
algorithm is composed of j sub-iterations. The processing of
implemented in this paper. In this iterative decoding
one block row is called a sub-iteration and each iteration is
algorithm is used for decoding the data, and it’s efficiency is
composed of j = dv sub-iterations.
compared with the new decoding algorithm called layered
Mathematically, the layered decoding algorithm can be
decoding algorithm which based on offset min sum
described as in
algorithm. From this we can conclude that by using layered
Algorithm:
decoding algorithm the decoding complexity is much
step1: R(0)l,n = 0, “ l” [1, dv],
reduced and its performance is improved when compared
n “ [1, dc]
with iterative decoding algorithm.
step2: Pn = L(0)n , “ n “ [1, dc]
step3: for each i = 1, 2, · · · , itmax
REFERENCE
do
step4: for each l = 1, 2, · · · , dv do [1] A. D. Liveris, Z. Xiong, and C. N. Georghiades, “Compression
step5: for each n = 1, 2, · · · , dc do of binary sources with side information at the decoder using LDPC
Q(i)l,n=PnR(i”1)l,n codes,” IEEE Comm. Letters, vol. 6, pp. 440–442, Oct. 2002.
R(i)l,n = f [Q(i )] “n_ “ [1, dc] [2] T. J. Richardson and R. L. Urbanke, “The capacity of low-
Pn=Q(i)l,n + _R(i)l,n. density paritycheck codes under message passing alorithm,”
IEEE Trans. Inform,Theory, vol. 47, pp. 599–618, Feb. 2001.
IV. RESULT [3] S. S. Pradhan and K. Ramchandran, “Distributed source
coding usingsyndromes (DISCUS): design and construction,”
A. Source Coding for LDPC with Two correlated nodes by Proc. IEEE Data Compression Conference, pp. 158–167, March
using SUM Product and Layered Decoding Algorithm 1999.
[4] S. S. Pradhan and K. Ramchandran, “Distributed source
coding: symmetric rates and applications to sensor networks,”
Proc. IEEE Data Compression Conference, pp. 363–372, March
2001.
[5] Weihuang Wang, Gwan Choi and Kiran K. Gunnam “Low-
Power VLSI Design of LDPC Decoder Using DVFS for AWGN
Channels” 22nd International Conference on VLSI Design. 2009
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Fig.4. The performance of LDPC decoder by using sum product and dM5DMlQSU06zxCQ&cd=1#v=one page&q=&f=false
layered decoding algorithms [8]http://books.google.com/
books?id=z8nmMkUFqdwC&pg=PA
534&dq=offset+minsum+decoding+algorithm%2Bldpc&ei=GvW
XS__dM5DMlQSU06zxCQ&cd=2#v=onepage&q=&f=false

© 2011 ACEEE 4
DOI: 01.IJIT.01.01.37

Energy-Efficient LDPC Decoder using DVFS for binary sources

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