Reduced Complexity Maximum Likelihood Decoding Algorithm for LDPC Code Correction Technique

Asian Journal of Applied Science and Technology (AJAST)
Volume 1, Issue 1, Pages 126-130, February 2017
© 2017 AJAST All rights reserved. www.ajast.net
Page | 126
Reduced Complexity Maximum Likelihood Decoding Algorithm for LDPC Code
Correction Technique
A.V.Manjupriya1
and G.Yuvaraj2
1
PG Student, Department of ECE, Vivekanandha College of Engineering for Women, Tiruchengode, Tamilnadu, India.
2
Assistant Professor, Department of ECE, Vivekanandha College of Engineering for Women, Tiruchengode, Tamilnadu, India.
Article Received: 13 February 2017 Article Accepted: 22 February 2017 Article Published: 27 February 2017
1. INTRODUCTION
NONBINARY low-density parity-check (NB-LDPC) codes
are a real kind of linear block codes defined over Galois fields
(GFs) GF (q = 2p) with p >1. NB-LDPC codes have lot of
advantages over its binary counterparts, including better error
correction performance for short/medium code word length,
higher burst error correction capability, and improved
performance in the error-floor region. The main disadvantage
of NB-LDPC codes is the high complexity of the decoding
algorithms and the derived hardware architectures, which
limit their application in real scenarios where high throughput
and reduced silicon area are important requirements. The
main drawbacks of T-EMS, T-MM, and OMO-TMM are: 1)
the high number of exchanged messages between the CN and
the VN (q × dc reliabilities), which impacts in the wiring
congestion, limiting the maximum throughput achievable and
2) the high amount of storage elements required in the
hardware implementations of these algorithms, which
supposes the major part of the decoder’s area. This reduction
in messages introduces a performance loss in the coding gain
that can be controlled by means of the parameter L.
NB-LDPC codes are decoded applying iterative algorithms
where messages that represent reliability values are passed
from VN to CN and vice versa.
Extended min-sum (EMS) and min–max algorithms were
proposed with the aim of reducing the complexity offered by
the solutions based on QPSA. In these algorithms, the CN
equations are simplified by making approximations to involve
only additions and comparisons in their parity-check
equations. Since both the algorithms make use of
forward–backward (FB) metrics in the CN processor, the
maximum throughput is bounded due to serial computations.
The number of exchanged messages between CN and variable
node (VN) for both the algorithms is nm × dc, where nm is a
fraction of q total reliabilities, nm _ q, and dc the CN degree.
Therefore, the number of messages between the nodes is
lower than the previous solutions from the literature.
Improvements based on QSPA, such as Fast Fourier
Transform-SPA, log-SPA, and max-log-SPA, reduce the
computational load of the parity-check equations without
introducing any performance loss. The recently proposed
trellis max-log-QPSA algorithm improves considerably both
the area and the decoding throughput compared with the
previous solutions based on QPSA, making use of a path
construction scheme to generate the output message in the
check-node (CN) processor. These solutions offer the highest
coding gain for high-rate NB-LDPC codes, but at the same
time, they include costly processing that limits their
application in real communication and storage systems.
2. EXISTING SYSTEM
2.1 Introduction
The analysis of the algorithm then views on the work required
for the merging process, because it is the merge work needed
for a given subdivision scheme that ultimately determines the
growth of complexity. In this we introduce a recursive
approach to the construction of codes which generalizes the
product code construction and suggests that the design of
algorithms for encoding and decoding is amenable to the first
techniques of complexity theory. Long codes are built from a
bipartite graph and one or more sub codes; a new code is
defined explicitly by its decomposition into shorter sub codes.
These sub codes are then used by the decoder as centres of
local partial computations that, when performed iteratively,
correct the errors. The decoding algorithms we propose
generalize and unify the decoding schemes originally
presented the product codes and those of low-density
parity-check code. Furthermore, the proper choice of the
transmission order for the bits can guarantee better
performance against burst errors or a mixture of burst and
random errors.
ABSTRACT
In this paper, low linear architectures for analyzing the first two maximum or minimum values are of paramount importance in several uses, including
iterative decoders. The min-sum giving out step is to that it produces only two diverse output magnitude values irrespective of the number of
incoming bit-to check communication. These new micro-architecture structures would utilize the minimum number of comparators by exploiting the
concept of survivors in the search. These would result in reduced number of comparisons and consequently reduced energy use. Multipliers are
complex units and play an important role in finding the overall area, speed and power consumption of digital designs. By using the multiplier we
can minimize the parameters like latency, complexity and power consumption. The decoding algorithms we propose generalize and unify the
decoding schemes originally presented the product codes and those of low-density parity-check codes.
Keywords: Check–node (CN) processing, high-rate, high-speed, layered schedule, message compression, NB-LDPC, trellis min-max (T-MM) and
VLSI design.

Page | 127
2.2 Project Description
NON-BINARY low-density parity-check (NB-LDPC) codes
are a promising kind of linear block codes defined over Galois
fields (GFs) GF(q = 2p) with p >1. NB-LDPC codes have
numerous advantages over its binary counterparts, including
better error correction performance for short/medium code
word length, higher burst error correction capability, and
improved performance in the error-floor region.
2.3 T-MM Decoding Algorithm with Compressed Messages
A sparse parity-check matrix H defines an NB-LDPC code,
where each nonzero element h m ,n belongs to a GFs GF(q =
2p). Another common way to characterize the NB-LDPC
codes is by means of a Tanner graph, where two kinds of
nodes are differentiated representing all N columns (VNs) and
M rows (CNs) of H. N(m) denotes the set of VNs connected to
a CN m and M(n) denotes the set of CNs connected to a VN n;
therefore, the cardinality of the sets corresponds to dc and dv.
2.4 T-MM Algorithm with Reduced Set of Messages
In this section, we introduce a novel method to reduce the
number of messages exchanged between the CN and the VN
compared with the proposal from [11]. First, we define the
reduced set of compressed messages that are sent from CN to
VN and an approximation to obtain the rest of values in the
VN. Second, the performance of the method is analyzed.
Third, a technique to generate the most reliable values of the
set I (a) without building a complete trellis structure is
presented
2.5 Reduction of the CN-to-VN Message
The sets I (a) and P(a) are required to generate the messages
Rm,n(a) at the VN processor, as shown in (3). Reducing the
cardinality of I (a), the one of P(a) is also reduced. Our
proposal is to keep the L most reliable values of I (a) and the
corresponding ones of P(a) and E(a), where L < (q
−1).Defining the complementary set a__ ∈a a_, we propose
to set E∗(a__) = m1(a__). Therefore, the cardinality of the set
E∗(a) is kept in q −1. Table I includes the number of bits of
each one of the sets exchanged from CN-to-VN processors
compared with the proposal from [11], where w is the number
of bits used to quantize the reliabilities.
Fig.1. Mean value of each reliability
2.6 Conclusion
The main drawbacks of T-EMS, T-MM, and OMO-TMM are:
1) the high number of exchanged messages between the CN
and the VN (q × dc reliabilities), which impacts in the wiring
congestion, limiting the maximum throughput achievable and
2) the high amount of storage elements required in the
hardware implementations of these algorithms, which
supposes the major part of the decoder’s area. To overcome
the drawbacks of T-EMS and T-MM, the proposal in [11]
introduces a technique of message compression that reduces
the wiring congestion between the CN and the VN and the
storage elements used in the derived architectures. The
messages at the output of the CN are reduced to four
elementary sets that include the intrinsic and extrinsic
information, the path coordinates, and the hard-decision
symbols.
3. PROPOSED SYSTEM
The block diagram for the proposed CN is detailed in Fig. 2a.
The CN input messages are Q m, n, which come from the VN
processor and the tentative hard-decision symbols z. Both the
input messages are used to compute the normal to-
delta-domain transformation (N →_ block in Fig. 2b). DC
transformation networks are needed in the CN, each one
requires q×log(q) w-bit MUX following the approach
proposed in [19], where w is the number of bits for the data
path. Z is also used to obtain the syndrome β adding all dc
tentative hard-decision symbols. This operation requires w ×
(dc − 1) XOR gates.
Fig.2a. Proposed check node Block Diagram
β is used to generate the new hard decision symbols z∗, which
are sent to the VN to generate the R∗m,n messages using (4).
Z ∗ symbols are generated using GF(q) adders that require dc
× w XOR gates to implement them.
3.1 Decoding
As with other codes, optimally decoding an LDPC code on
the binary symmetric channel is the NP-complete problem,
although techniques based on iterative belief propagation
used in practice lead to good approximations. In contrast,
belief propagation on the binary erasure channel is usually
simple where it consists of iterative constraint satisfaction.

Page | 128
For example, consider that the valid code word, 101011, from
the example, is transmitted across a binary erasure channel
and received with first and fourth bit erased to yield. Since the
transmitted message must have full fill the code constraints,
the message can be organized by written the message on the
top of the factor graph. In this example, the first bit cannot yet
be recovered, because all of the constraints connected to it
have more than one unknown bit. In order to proceed with
decoding the message, this procedure is then iterated. The
new value for the fourth bit can now be used in conjunction
with the first constraint to recover the first bit as shown below.
This means that the first bit must be a 1 to satisfy the leftmost
constraint.
Fig.2b. Block Diagram
Thus, the message can be decoded iteratively. For next
channel models, the messages passed inside the variable
nodes and check nodes are real numbers, which express
probabilities and likelihoods of belief. This result can be
validated by multiplying the corrected code word by the
parity-check matrix H:
Because the outcome z (the syndrome) of this operation is the
3 × 1 zero vector, the resulting code word is successfully
validated.
3.2 Lookup table decoding
It is possible to decode LDPC codes on a relatively
low-powered microprocessor by the use of lookup tables.
Whilst codes such as LDPC are generally implemented on
high-powered processors, with long block lengths, there are
also applications which use lower-powered processors and
short block lengths.
3.3 Code construction
For large block sizes, LDPC codes are commonly constructed
by first studied the behaviour of decoders. As the block size
tends to infinity, LDPC decoders can be shown to have a noise
threshold below which decoding is really achieved, and above
which decoding is not achieved.
This threshold can be optimised by finding the best proportion
of arcs from check nodes and arcs from variable nodes. An
approximate graphical approach to visualizing this threshold
is an EXIT chart.
4. CMOS TECHNOLOGY
4.1 Basic concepts
Ideally, a transistor behaves like a switch. For NMOS
transistors, if the input is 1 the switch is on, otherwise it off.
On the other hand, for the PMOS, if the input is 0 the
transistor is on, otherwise the transistor is off.
4.2 N-Well CMOS Technology
 Process starts with a moderately doped (1015 cm-3)
p-type substrate (wafer)
 An initial oxide layer is grown on the entire surface
(barrier oxide)
4.3 Metallization mask
• Aluminum is deposited over the wafer and
selectively etched
• The step coverage in this process is most critical
(nonlinearity of the wafer surface)
4.4 Advantages
High input impedance. The input signal is driven electrodes
with layer of insulation (the metal oxide) between them and
what they are controlling. This gives them a small amount of
capacitance, but virtually infinite resistance.
 The outputs are actively driven both ways
 The outputs are much more rail-to-rail
 CMOS logic takes very little power when held in a
fixed state. The current consumption comes from
switching as both capacitors are charged and
discharged. Even then, it has better speed to power
ratio compared to other logic types.
 CMOS gates are very simple. The basic gate is an
inverter, which is only two transistors. This always
with low power consumption means it lends itself
well to dense integration.
4.5 Applications
 Transmission gates may be used as analog multipliers.
 CMOS Technology may also widely used as RF
circuits.
5. SIMULATION RESULTS
The simulation environment is created in MODELSIM by
using VERILOG language for the training. We consider the
four systems which are in active, sleep, deep sleep and idle
mode correspondingly. The power manager system calculates
the required power to send the data to the subsystems.
Normally we can send heavy or large amount of data to the
system which is in the active mode. (1) DC signal and Inverter
is given as an input to the NAND gate. Clock frequency given

Page | 129
as NAND gate for simulation output. (2) Q BAR, QBAR1 is
the output signal.
Fig.3. Digital schematic for circuit to extract the jth
minimum
value
Fig.4. Design Layout for the output waveform
Fig.5. Simulation result for voltage versus time.
Fig.6. Simulation result for voltage and current
Fig.7. Simulation Result for voltage versus voltage
Fig.8. Simulation result for frequency versus time

Page | 130
Fig.9. Simulation result for eye diagram
6. CONCLUSION AND FUTURE ENHANCEMENT
The low complexity design is prominent requirement of
iterative decoders. We have tried to propose a design that
fulfills the obligation with the completion of the sum min
worker using better architecture. The difficulty is reduced as
the number of register and memory utilization decreases.
NB-LDPC codes are designed using CMOS Technology. It
concludes the T-MM algorithm to reduce the complexity of
CN architecture. Hence the power consumption is reduced. In
future, LDPC codes can be used for reducing the power
consumption. Thus, the post synthesis throughput of the other
works is reduced in the same percentage.
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