Reduced Energy Min-Max Decoding Algorithm for Ldpc Code with Adder Correction Technique

ISSN (e): 2250 – 3005 || Volume, 06 || Issue, 11|| November – 2016 ||
International Journal of Computational Engineering Research (IJCER)
www.ijceronline.com Open Access Journal Page 1
Reduced Energy Min-Max Decoding Algorithm for Ldpc Code
with Adder Correction Technique
A.V.Manjupriya1
, G.Yuvaraj2
1
PG student,Department of ECE, Vivekanandha College of engineering for women, Tiruchengode.
2
AP/ECE, Department of ECE, Vivekanandha College of engineering for women, Tiruchengode.
I. INTRODUCTION
A. General 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.
ABSTRACT
In this paper, high linear architectures for analysing the first two maximum or minimum values are of
paramount importance in several uses, including iterative decoders. We proposed the adder and
LDPC. The min-sum processing step that it gives only two different output magnitude values
irrespective of the number of incoming bit-to check messages. These new micro-architecture layouts
would employ 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.
Keywords: Processing, highrate, high-speed, layered schedule, message compression, NB-LDPC,
trellis min-max (T-MM), VLSI design.

Reduced Energy Min-Max Decoding Algorithm For Ldpc Code With Adder Correction Technique
II. EXISTING SYSTEM
A. 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.
B. 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.
C. 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.
D. 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.
1. 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.
Figure 1: Mean value of each reliability

E. 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.
III. PROPOSED SYSTEM
The block diagram for the proposed CN is detailed in Figure 2 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 4.1). 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.
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.
Figure 2: proposed check node Block Diagram
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. 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.

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.
A. 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.
B. Code construction
For large block sizes, LDPC codes are commonly constructed by first studied the behavior 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 optimized 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.
IV. CMOS TECHNOLOGY
A. 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.
B. 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)
C. Metallization mask
 Aluminium is deposit over the wafer and selectively etched
 The step coverage in this process is most critical (nonlinearity of the wafer surface)
D. 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.
 Mobile application.
E. APPLICATIONS
 Transmission gates may be used as analog multipliers.
 CMOS Technology may also widely used as RF circuits

V. SIMULATION RESULT
 DC signal and Inverter is given as a input to the NAND gate .Clock frequency given as NAND gate for
simulation output.
 Q BAR, QBAR1 is the output signal.
Figure 5.1: Digital schematic for circuit to extracts the jth
minimum value
Figure 5.2: Design Layout for the output waveform
Figure 5.3: Simulation result for voltage vs time
Figure 5.4: Simulation result for voltage and current

Figure 5.5: Simulation Result for voltage vs voltage
Figure 5.6: Simulation result for frequency vs time
Figure 5.7: Simulation result for eye diagram
VI. CONCLUSION AND FUTURE ENHANCEMENT
T-MM algorithm to reduce the complexity of the CN architecture, which was the bottleneck in the previous
solutions from the literature. This reduction allow us to offer post layout results for high-rate NB-LDPC codes
over GF(64) without prohibitive areas and higher throughput than the existing proposals, at the expense of some
performance loss. 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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Reduced Energy Min-Max Decoding Algorithm for Ldpc Code with Adder Correction Technique

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