Real-Time Turbo Decoder

Nasir Ahmed

Mani Vaya

Elec 434Rice University

Outline

Description of Turbo Encoding

Description of Turbo Decoding

DSP Implementation issues

Performance Analysis

Conclusions

Turbo Codes

First introduced in 1993

Parallel Concatenation of two Convolutional Coders with interleaving

Original results showed a BER of 10E-5 at 0.7dB using block size 65,536 bits

For rate R=1/2 code, 0.7dB off channel capacity

Turbo Encoder

Parallel concatenation of at least two RSC encoders, with second encoder seeing interleaved version of data

Utilize only one of the systematic streams

RSC1

RSC2 I

xs

xp1

xp2

u

Turbo Encoder

The output stream of data consists of the systematic data, parity bits from encoder1, and parity bits from encoder2

Through the use of the interleaver, the decoder will have two independent looks at the same data, and can use both streams to decode the information sequence

Convolutional Coder

Utilize recursive systematic (RSC) encoders Unlike feed forward coders, a single 1 in the input

will lead to large weight codeword Performance of turbo codes dependent on low

weight codewords

D D u

xp

xs

State transition Diagram

Interleaver

Interleaving is used to reorder the input bits

Random interleaver used for large block sizes

For small block sizes (<1000), random/block interleavers show similar performance

Block interleavers have simple interleaving/de-interleaving mechanism

Importance of Interleaver

At a given SNR, tradeoff between latency due to interleaver and QOS

Small block sizes (~300 bits) can be used for real time voice

Mid range block sizes (~4000 bits) used for video play back

Large block sizes (~16000 bits) large latency, very low BER, useful for file transfer

Turbo Decoding

Two decoders used in serial fashion, with output of one decoder used as prior information to next decoder

Feedback in decoding circuit allows for multiple iterations, and improves bit error performance

D1 D2 I

Inv(I)

Parity2

Parity1 Le12 Le21

Systematic

Decoder

Constituent decoders need bit probability estimates to be used as priors to the next decoder: standard Viterbi cannot be used for this reason

Soft Output Viterbi Algorithm used (SOVA)

The output of decoder1 contains information that can be used as a prior probabilities for decoder2, and vice versa

Steps in Viterbi Algorithm

Calculation of branch metric (distance from received data)

Calculation of path metric (Add compare select)

On reaching the end of trellis, start from the best state

Trace back (knowing the Path metrics)

Decide the data bits while tracing back

Hard Decision Viterbi Basics

Steps in Turbo Decoding

Evaluate the path metrics Trace back to obtain the decisions (x) Trace back using alternate paths to obtain the metric

differences Compute the minimum of all possible metric

differences for that stage Obtain the reliability of decision Pass this reliability of decision to next decoder Iterate the above steps

Path Metric Calculation for SOVA

kpcksc

ikk

ik

ik

uyLuyL

uuLsMsM

***5.0***5.0

*)(*5.0)()(

1

)()('1

)(

s(i) : state of ith path at time k

uk(i): information bit

Ys: received systematic bit, Yp: received parity bit

Mk(s(i)): path metric of ith path at time k

Lc : Channel value = 4*Ec/N0

L(uk): output from previous decoder

Soft Value (L(u)) Computation

Reliability of decisions

Δlk= Mk+l(s(i

l)) – Mk+l

(s(i’l))

Δlk : Metric difference

l: index of all non surviving paths

L(uk) = uk * Min( Δlk)

Min(Δlk ) : Reliability of the decision

Our Implementation

Rate 1/3 coding

Constraint length = 3

Frame length = 400

SOVA algorithm used

Number of iterations are flexible

Algorithmic Issues

Two iterations of Turbo decoding used Traceback depth set at 5 times the constraint length

(optimal for Viterbi decoding)

BPSK modulation used (+/-1)

Extrinsic Information (Le(u)) scaled after every decoder

Fixed point Issues

Used Q-15 format

Received signal (from AWGN channel) clipped to lie in a range of +/-1

Received signal scaled by a constant factor (32) to avoid overflow

Performance in AWGN channel

Data Rates

•Clock cycles / decoder = 654659

•Execution time / decoder = 4.36 ms

•Data rate /decoder = 91.6 Kbps

•Data rate/ iteration = 45.8 Kbps

Conclusions

Fixed point SOVA based Turbo decoder implemented

Performance of DSP matches MATLAB at high SNRs

Real time voice processing possible using our implementation (~22 Kbps for 2 iterations)