TURBO CODE DISTANCE SPECTRUM CALCULATOR Version 1.2
Created by Seokhyun Yoon, May, 2001
Center for Comm. & Signal Processing Research
New Jersey Institute of Technology, Newark, NJ
The software computes the distance spectrum of parallel or
serially concatenated convolutional code ( overall rate of
1/3 for PCCC and 1/4 for SCCC ) where the same 1/2 rate
systematic convolutional code is used for both the
constituent codes. You can test with various parity
equations and interleaver size. It creates a text file
containing the BER performance, as well as the distance
spectrum, of the user-specified turbo code.
1. Using the Software
1) Set the Code Parameters
-. Concatenation Type: PCCC or SCCC
-. Parity Equation of the Constiturnt Systematic
Convolutional Code: The parity equation have
both the numerator and denominator. Setting the
numerator to 1 corresponse to a non-recursive
systematic convolutional code. The followings are
examples of the parity equation of constituent 1/2
rate convolutional code
Ex1) Recursive Systematic Convolutional encoder
1+D+D^2+D^3 17
( 1, ----------- ) = (1, -- ) in octal format
1+D^3 11
Ex2) Non-Recursive Systematic Convolutional encoder
1+D^2
( 1, ----- ) = ( 1, 7 ) in octal format
1
-. Input Frame Size: Larger than 1024 may requires
the OS to allocate the needed meory to Hard disk
causing an exccessive computation time. If that case
you will need to expand your CPU memory (RAM).
2) Set "Options" for BER bounds: See below
3) Press "Get it" button to obtain a text file, which
contains all the information of the concatenated codes,
including Trellis information, Distance Spectra and
BER bounds.
2. Output Text File divided into 3 parts
1) Trellis Information of the constituent codes
2) Distance Spectrum and Weighted Distance Spectrum
Distance Spectrum is equal to the number of codewords
that has certain Hamming weight, averaged over all
possible permutations (Uniform Interleaver Assumption).
It is for computaion of Codeword Error probability bound.
While, the weighted Distance Spectrum is for computation
of Bit Error Probability Bound.
For more details, refer to the papers
S. Benedetto and G. Montorsi,
"Unveiling turbo codes: Some results on parallel
concatenated coding scheme", IEEE Trans. on
Information Theory, Vol.42 pp.409-428, March. 1996
and
D. Divsalar and F. Pollara,
"Weight Distributions for turbo codes using random and
nonrandom permutations",
JPL TDA Progress Report 42-122, pp.56-65, Aug. 1995
3) BER Bounds
Three type of BER bound provided: Union bound with Q-
function, Union bound with exponention-function and An
Improved union bound (termed as Viterbi bound).
For the Viterbi bound, refer to the paper
A.M. Viterbi & A.J. Viterbi,
"Improved Union Bound on Linear Codes for Input-Binary
AWGN Channel with Application to Turbo Codes",
Proc. ISIT?998 pp.29, Cambridge, MA, Aug.16-21, 1998
The distance spectrum of punctured turbo code will be available
shortly (It requires more advanced setup including puncturing
period, rate and patterns).
So, please visit ECCpage or "web.njit.edu/~sxy3211/"
from time to time, to check if it's available or not.
If you have any question or suggestions, please feel free to
contact me by emailing to "seokhyun.yoon@njit.edu"
June 1, 2002