Performance improvement of turbo codes by error range ... - IEEE Xplore

Chang et al.: Pcrkmnance lmprovemcnt of Turbo Codes by Error Range Search Method in Rayleigh Fading Channel

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PERFORMANCE IMPROVEMENT OF TURBO CODES BY ERROR RANGE SEARCH METHOD IN RAYLEIGH FADING CHANNEL Jinsu Chang’, Jiung Jeon’, Moon Ho Lee’, and Daechul Park* Dept. of Info. & Comm., Chonbuk National Univ., Chonju, Korea 2 Dept. of Info. & Comm. Eng., Hannam National Univ., Daejeon, Korea 1

Currently, some of the communication systems (CDMA,

ABSTRACT Turbo codes has better performance as the number

TCM, Equalizer etc.) are beginning to apply principles of

of iteration and interleaver’s size increases. This

Turbo Codes and iterative decoding [3].

requires the delay and computational complexity for

Recently, Turbo code is proposed to ITU as a candidate

decoding an input data. In this paper, we propose an

channel coding for higher rate transmission in IMT-2000

efficient method of decoding Turbo codes that can

(International Mobile Telecommunication-2000). But in

greatly reduce the iteration number with very low-

spite of the high performance and some applications, there

complexity. The MAP algorithm depends on the

are still remained problems such as increment of

adjacent bits or received symbols. Therefore, to

complexity by decoding computation, latency by inter-

improve performance of MAP algorithm, the reliability

leaver and iterative decoding. The decoders in a turbo decoder mainly use the MAP

of adjacent received symbols has to be guaranteed Thus, we propose a simple ERS (Error Range Search)

(Maximum a Posteriori) or SOVA (Sofi Output Viterbi

method for reliability of received symbols in MAP

Algorithm). The MAP algorithm has been most commonly

algorithm. Using the proposed ERS method, we

used in turbo codes because of high performance. At low

analyze the performance of ERS/MAP algorithm and

Eb/No and high BERs, MAP algorithm can outperform

ERS/Turbo decoder in Rayleigh fading channel.

SOVA by 0.5 d 5 or more. In contrast, the SOVA is offer slightly worse bit error performance but with reduced

1. INTRODUCTION

complexity when compared to the MAP algorithm [3]-[lo].

Turbo codes were introduced in 1993 by Berrou, Glavieux

Convolutional encoding process and its reverse process

and Thitimajshima [l]. Turbo Code is that the encoder is

(MAP decoding) depend on the common adjacent bits or

made up of two component codes, separated by an

received symbols. Thus, we propose a simple ERS method

interleaver. These encoders have generally been RSC

for MAP algorithm and analyze the performance of MAP

(Recursive Systematic Convolutional) codes, due to some

algorithm and Turbo codes in Rayleigh fading channel.

suitable characteristics. Due to the interleaver, the two encoders are excited by two different input sequences, and

2. ITERATIVE DECODING OF MAP ALGORITHM

thus need two separate decoders, these also being

AND TURBO CODES

separated by interleavers. In original paper, they exhibited The MAP algorithm performs decoding process to

remarkable BER performance of at an E,R\T, of 0.7dB using only a 112 rate code, large interleaver size and

estimate the APP (a posteriori probabilities) of the states

sufficient number of decoding iteration [ l ] . Turbo codes

and transitions of a Markov source observed through a

have been a very active area of research for over five years.

discrete inemoryless channel, was first presented by Bahl

Manuscript receivcd June 28, 1999

0099 3063/99 $10.00

‘1999 IEEE

IEEE Transactions on Consumci Electronics, Vol. 45, No. 1,AUGUST 1999

668

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..

...*

T

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DECODER2

Figure 1 . Structure of Iterative Decoder (for Turbo Codes)

et. al. in [2]. This yields the APP for each decoded bit and it is an optimal decoding method for linear codes which minimizes the bit error probability. The MAP algorithm was as applied to be used with Turbo codes in [l], but its structure was still complex. In [7], S. Pietrobon described the algorithm which made possible its hardware implementation. For a single code, the MAP algorithm minimizes the

is based only on the received The term L?yr/c/,,u,lc systematic symbol at time k and the term L,,,,,,,,, is based on the a priori information on the input bit

d k . For

the decoding of a single convolutional encoder, the usual assumption is that of equiprobable input values which gives

Loprrr,,? = 0. The final term, which has been referred

symbol error probability. Therefore, after receiving Y , it is the job of the decoder to determine the most likely input bits, d 's, based on the received symbols. The log-

to as extrinsic information [l], is the new information

likelihood ratio for the input symbol indexed at time k is

systematic information except the systematic value at time

defined as

k , It is this decomposition of the log-likelihood ratio that

L ( d k )=log

P(d, = 1 I Y ) P(dk = 0 I Y )

pertaining to the input bit d . It is based on all parity and k

will motivate the iterative turbo decoder and makes the MAP algorithm a very compatible decoding algorithm for turbo codes. Figure 1. shows the iterative decoding process

In this expression, p ( d , = i 1 y ) is the a posteriori probability of d - i given knowledge of the received

of Turbo codes. As mentioned above, to improve performance of MAP

data y . The decoder produces estimates, d k 's, of the

algorithm, the reliability of adjacent received symbols has

to a

to be guaranteed. However, MAP algorithm itself can't

threshold. For equiprobable input values over an AWGN

give it for any operation. Thus, we propose a simple ERS

channel, the estimator is given as

method for reliability of received symbols in MAP

k -

information bits based on the comparison o f L ( d

algorithm.

I 0

if if

L(d,)>O L(d,)