25-10-2012, 03:43 PM
Interleaver Design for Turbo Codes
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Abstract
The performance of a Turbo code with short block
length depends critically on the interleaver design. There are two
major criteria in the design of an interleaver: the distance spectrum
of the code and the correlation between the information input
data and the soft output of each decoder corresponding to its parity
bits. This paper describes a new interleaver design for Turbo codes
with short block length based on these two criteria. A deterministic
interleaver suitable for Turbo codes is also described. Simulation
results compare the new interleaver design to different existing interleavers.
INTRODUCTION
TURBO codes [1] have an impressive near-Shannonlimit
error correcting performance. The superior performance
of Turbo codes over convolutional codes is achieved only when
the length of the interleaver is very large, on the order of several
thousand bits. For large block size interleavers, most random
interleavers perform well. On the other hand, for some applications,
it is preferable to have a deterministic interleaver, to
reduce the hardware requirements for interleaving and deinterleaving
operations. One of the goals of this paper is to propose
a deterministic interleaver design to address this problem. For
short interleavers, the performance of the Turbo code with a
random interleaver degrades substantially up to a point where its
bit error rate (BER) performance is worse than the BER performance
of convolutional codes with similar computational complexity.
For short block length interleavers, selection of the interleaver
has a significant effect on the performance of the Turbo
code. In many applications, such as voice, delay is an important
issue in choosing the block size. For these applications, there is
a need to design short block size interleavers that demonstrate
acceptable BER performance. Several authors have suggested
interleaver designs for Turbo codes suitable for short block sizes
[2]–[5]
TWO-STEP -RANDOM INTERLEAVER DESIGN
A new interleaver design, a two-step -random interleaver,
is presented here. The goal is to increase the minimum effective
free distance, , of the Turbo code while decreasing or
at least not increasing the correlation properties between the information
input data sequence and . Hokfelt et al. [2], [12]
introduced the IDS criterion to evaluate the correlation properties.
The two vectors for the computation of IDS in (5) are very
similar for most interleavers. Thus, it is sufficient to only use
one of them, i.e., . Instead, we can define a new criterion
based on decreasing the correlation coefficients for the third decoding
step, i.e., the correlation coefficients between extrinsic
information from the second decoder and information input data
sequence. In this regard, the new correlation coefficient matrix.
SIMULATION RESULTS AND CONCLUSION
This section provides simulation results for the BER performance
of Turbo codes using the new interleaver design and
comparisons with -random and random interleavers. The constituent
encoders are recursive systematic convolutional codes
with memory and with feedback and feedforward generator
polynomials and , respectively. The trellis
termination is applied only to the first encoder