Mr. Ravindra Gaikwad

Mr.Utkarsh KumarM.Tech (ECE)

Dept. of Electronics

Pondicherry University

Turbo codes

Outline

• Introduction

– Forward error correction

– Channel capacity

• Turbo codes

– Encoding

– Decoding

– Application

Error correction

• The key idea of FEC is to transmit enough redundant data to allow receiver to recover from errors all by itself. No sender retransmission required.

• The major categories of FEC codes are

– Block codes,

– Cyclic codes,

– Reed-Solomon codes,

– Convolutional codes,

– Turbo codes.

Channel

encoder

m r

• Input message m contains k symbols.

• Encoded message r contains n symbols.

• n > k where extra bits are redundant bits in the codeword.

• The code rate is k/n

Channel capacity

• The channel capacity C of a continuous channel with

bandwidth B Hertz can be perturbed by additive

Gaussian white noise of power spectral density N0/2,

provided bandwidth B satisfies

Where P is transmitted power

ondbitsBN

PBC sec/1log

0

2

Turbo codes

• Turbo codes were proposed by Berrou and Glavieux in

the 1993 International Conference in Communications.

• Performance close to the Shannon Limit.

• Mix between Convolutional and Block codes.

• The best code among FEC codes.

Key elements

• Concatenated Encoders

• Recursive convolutional encoders

• Pseudo-random interleaving

• Iterative Decoding

Concatenated encoding

• Some times single error correction codes are not good

enough for error protection

• Concatenating two or more codes will results more

powerful codes

• Types of concatenated codes

1. Serial concatenated codes

2. Parallel concatenated codes

Parallel concatenated code

RSC

Encoder 1

RSC

Encoder 2

Interleaver

input Systematic output

Parity 1

Systematic output

Parity 2

One systematic and two parity bits are generated from the message stream

Serial concatenated code

Outer

encoderInterleaver

Inner

encoder

Recursive convolutional encoder

mi

• An RSC encoder can be

constructed from a standard

convolutional encoder by

feeding back one of the

outputs.

• In coded system

performance is dominated

by low weight code words.

• A good code will causes low weight output with low

probability

• RSC will produces low weight and low probability

output

Need of interleaver

• Shannon showed that large block-length random codes

achieve channel capacity

• Only a small number of low-weight input sequences

are mapped to low-weight output sequences

• Make the code appear random, while maintaining

enough structure to permit decoding

• The interleaver ensures that the probability that both

encoders have inputs that causes low weight output is

very low.

Turbo decoding

Conv

Decoder1

Interleaver

Deinterleaver

Conv

Decoder2

Systematic

data

Parity 1

Parity 2

Decoding

• Turbo codes get their name because the decoder uses

feedback, like a turbo engine.

• Each decoder estimates the a posteriori probability

(MAP) of each data bit.

• Decoding continues for a set number of iterations.

• Performance generally improves from iteration to

iteration, but follows a law of diminishing returns

• Information exchanged by the decoders must not be

strongly correlated with systematic info or earlier

exchanges.

APPLICATION

• Wireless multimedia

– Data: use large frame sizes

• Low BER, but long latency

– Voice: use small frame sizes

• Short latency, but higher BER

• Combined equalization and error correction decoding.

• Combined multiuser detection and error correction

decoding.

Pros and cons

• Pros

– Remarkable power

efficiency in AWGN

and flat-fading

channels for

moderately low BER.

– Deign tradeoffs

suitable for delivery

of multimedia

services.

• Cons

– Long latency.

– Poor performance at

very low BER.

– Because turbo codes

operate at very low

SNR, channel

estimation and

tracking is a critical

issue.