THE PERSPECTIVES OF MULTITHRESHOLD

DECODERS APPLICATION IN HIGH SPEED

COMMUNICATION SYSTEMS

Zolotarev V.V., Ovechkin G.V.Space Research Institute RAS, Russia

The Ryazan state radio engineering academy Conference «Networks and communication system - 2005»

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A using of error-correction codes is one of major methods for decreasing of bit error probability in the communication systems

A coding is consist in the introducing of redundancy into a transmitted message

k – information bits

+

r – parity bits

R = k / n – code rate (the part of information bits in transmitted message)

n = k + r – code length

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THE MAIN ADVANTEGES OF USING ERROR-CORRECTING CODESThe using of error-correcting codes allows to get a

coding gain, each decibel of which is estimated in millions dollars. The coding gain is used for:

• decreasing transmitter power;• increasing speed of data transfer;• decreasing size of antennas;• increasing range of communication;• decreasing used bandwidth;• work over more noisy channels.

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WHAT KIND OF CODES IS NEED TO BE USED?

Codes is need be • long;• accepted to low cost and effective decoding.

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THE BIT ERROR RATE FOR OPTIMAL DECODING BLOCK CODES VERSUS CHANNEL BIT ERROR RATE OVER A BINARY SYMMETRIC CHANNEL

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THE MOST EFFECTIVE CODES AND THE MOST EFFECTIVE CODES AND DECODING METHODS ISDECODING METHODS IS

• Viterby decoder;• Reed-Solomon code and short convolutional code

decoding with the Viterby decoder;• turbo convolutional codes;• turbo product codes;• low-density parity-check codes;• repeat-accumulate codes;• product-accumulate codes;• multithreshold decoders.

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THRESHOLD DECODER

Diagram of threshold decoder for convolutional code with R=1/2 and d=5.

Threshold decoder is very simple scheme for error correction, but it’s efficiency is too low.

Diagram of encoder for convolutional code with R=1/2 and d=5.

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THRESHOLD DECODER

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MULTITHRESHOLD DECODER

Multithreshold decoder (MTD) is the development of an ordinary threshold decoder.

In MTD for the first time effective iterative decoding method is used, which later applied for turbo codes decoding.

MTD during decoding can many times change of received information bits and so can attain an optimal decoder decision with linear complexity.

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MULTITHRESHOLD DECODERDiagram of multithreshold decoder with two decoding iterations for convolutional code with R=1/2 and d=5

The main property of MTD – with each change of an information bit the decision of MTD is approach to an optimal decoder decision

0 1 2 3 4 5 6

0 1 2 3 4 5 6

6 5 4 3 2 1

TE

0

0 1 2 3 4 5 6

0 1 2 3 4 5 6

6 5 4 3 2 1

TE

0

Syndrome register

Information register

Difference register

u

v

0

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MULTITHRESHOLD DECODER PERFORMANCE OVER AN AWGN CHANNEL

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PERFORMANCE OF CONCATENATED SCHEME BASED ON MULTITHRESHOLD DECODER OVER AN

AWGN CHANNEL

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1. The complexity of software implementation: NMTD=(I+1)(d+2) additive equivalent operations on an information bit, where I is iterations number and d is code distance.

2. MTD is applicable for codes with d<20 and needs about 10-20 decoding iterations.

3. It’s possible to low operations number to about NМПД=4d+3I operations. It is much less than turbo codes decoder complexity!

SOFTWARE IMPLEMENTATION OF MULTITHRESHOLD DECODER

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SOFTWARE COPMLEXITY COMPARISON

1E+1

1E+2

1E+3

1E+4

1E+5

1 2 3 4 5 6E b /N 0

oper

atio

ns p

er

info

rmat

ion

bit

Viterby

MTD

MTD+PCC

Turbo

Fast MTD

MTD is in 10 or more times less complex than other methods for error correcting with comparable efficiency

Number of operations on an information bit are needed for achieving bit error rate of 10-5

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HARDWARE IMPLEMENTATION OF MULTITHRESHOLD DECODER

1. MTD consists of memory elements or shift registers. They are the fastest elements in PLIS or BIS. The part of other elements in MTD is less than 1%.

2. MTD consists of 3 - 40 work in parallel shift registers and single-cycle threshold elements. That’s why the complexity of MTD implemented on PLIS is in 100 and more times faster than, for example, turbo codes decoder.

3. Characteristics of MTD codec implemented on PLIS: - information speed is about 160 - 480 Mbps and more, - coding gain is about 6,5 - 8,5 dB.

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PHOTO OF MULTITHRESHOLD DECODER IMPLEMENTED ON PLIS XILINX

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PERFORMANCE OF MULTITHRESHOLD DECODER IMPLEMENTED ON PLIS XILINX

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CONTACT INFORMATION

Zolotarev Valery Vla18dimirovich Phone: (095) 333-23-56, (095) 261-54-44 Mobile: +7-916-518-86-28 e-mail: zolotasd@yandex.ruOvechkin Gennady Vladimirovich Phone: (0912) 92-00-56 Mobile: +7-910-644-51-46 e-mail: g_ovechkin@mail.ru

web-site: www.mtdbest.iki.rssi.ru