improved low complexity.pptx

7/29/2019 Improved Low Complexity.pptx

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Submitted By

ANKIT SANCHETI

2011PEC5324


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TURBO Convolutional Codes (TCC) are also known as Parallel

Concatenated Convolutional Codes.

TCC have shown near Shannon capacity performance.

At BER of 105, in a 16-state rate-1/2 TCC with interleaver

length of 65536, /is 0.5 dB away from Shannons limitin

AWGN channel.

TCC decoder algorithm is computationally complex


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Concatenated coding schemes, using relatively simple constituent

Convolutional and Block codes, can achieve performance close to the

theoretical limits.

Concatenated Zigzag codes are low complexity parallel concatenated

block codes.

These codes perform better for large interleaver length. However, an

interleaver with large length has more time latency as each decoder

requires longer delay in interleaving and deinterleaving the received bits.


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BER performance of ILCHTC is better than that of LCHTC as error

convergence of ILCHTC is better than that of LCHTC.

ILCHTC decoder requires less number of iterations than LCHTC

decoder.

Decoding complexity of ILCHTC is considerably lower than that of

TCC.

For the interleaver length of N, trellis length for TCC decoder is N

times the number of constituent codes. For ILCHTC, maximum trellis

length is N


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A. Constituent Encoder

A sequence of information bits is arranged in a

rectangular array of size . Alternatively, an (+((1))) information bit is

denoted by (, ).

d = {(, )}, 1 1 The Zigzag parity vector z(m)of constituent

encoder is,

z(m)= { ()()}, 1


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Zigzag parity bits are computed progressively as follows:

()(0) = 0

()( ) =[ (, ) + ()( 1)]2,

where 1

First, L rows of the array of information bits are encoded

using a rate-1/2 RSC code. Parity vector of RSC for row

of information array in first constituent encoder is,

J

j 1


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Interleaver for ILCHTC is designed in 2-stages.

1. Random interleaver is used to interleave N information bits.

2. N information bits are arranged in array.

-condition is realized in each of the J rows of array.

-condition ensures that the short distance between two errors is

mapped to the long distance by keeping at least distance

between the columns of() and() of array. If < Then,() () > , 0 <


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Parallel concatenation ofconstituent encoders forms the

overall ILCHTC encoder.

Let represent the interleaverfor th constituent encoder.

Overall ILCHTC encoder with =

The transmitted code word, c is represented by,

c = {d, r(1), z(1), z(2), . . ., z(M)}

Code rate, of ILCHTC is given by

=/( + +)


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Soft In Soft Out A Posteriori Probability (APP)is used for decoding Zigzag-Convolutional

codes of first constituent decoder. A priori values of Log Likelihood Ratio (LLR) of

received information bits are computed.

LLRs are arranged in an array of size .


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i. Decode each row of the array using a priori LLRs as input to

Convolutional decoder. Output produced is a posteriori LLR of each

row of the information bits.

ii. A damping factor, D, is applied to a posteriori LLR found in step

(i). This ensures that LLRs are successfully updated in a gradual

way.

iii. Decode each column of the array using, output of (ii) as a priori

LLRs for Zigzag decoder.

iv. For overall decoder, global iterative decoding is implemented.


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Computational complexity of ILCHTC decoder depends upon the number

of multiplications and additions required to decode information bits.

The total trellis length is forTCC.

Let

be the number of states in Convolutional encoder,

be the number of Multiplications/Information Bit/Iteration (M/IB/I)

be the number of Additions/Information Bit/Iteration (A/IB/I)

required by a decoder.


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For Turbo Convolutional decoder,

= 8

= [(16+ 2) ] 2 For ILCHTC decoder,

= [ (8 4)]/

= [(16 1)/] +(5 + 4/) 1

For LCHTC decoder,

= [ (8 4)]/

= [(16 1)/] +(5 + 4/) 1


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ILCHTC are simulated to investigate the BER performance at

various/with N = 1452.

An 8-state RSC code with generator polynomial,= [1,

(15/13)]8 is used in Convolutional encoders of TCC, LCHTC

and ILCHTC.

It is observed that ILCHTC achieves BER of 105 at/of

1.9 dB, which is 0.4 dB more than that for TCC.


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TCC requires less number of iterations than ILCHTC

and LCHTC.

In one iteration, the number of computations required

by TCC decoder is almost two times the number of

computations for ILCHTC and LCHTC decoders.

Therefore, overall decoder complexity of ILCHTC is

less than that of TCC.


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Complexity analysis shows that ILCHTC decoder requires less number of

computations than TCC decoder.

Rate-1/3 ILCHTC code requires 50% multiplication and 60% addition

equivalent operations per information bit per iteration as compared to

TCC.

For the interleaver length ofN = 1452, BER of 105 is achieved at /=

1.9 dB for ILCHTC which is 0.4 dB more than that for TCC.

Since TCC requires 10% less number of iterations and 50% more

computations/per iteration than ILCHTC the computational complexity

of overall ILCHTC decoder is 45% less than that of TCC decoder.


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Improved Low Complexity Hybrid Turbo Codes and their

Performance Analysis, by Archana Bhise and Prakash D.

Vyavahare, Member, IEEE

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 58, NO.

6, JUNE 2010

improved low complexity.pptx

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