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