For the first time Boolean functions on 9 variables having nonlinearity$241$are discovered, that remained as an open question in literature for almost three decades. Such functions are found by heuristic search in the space of rotation symmetric Boolean functions (RSBFs). This shows that there exist Boolean functions on$n$(odd) variables having nonlinearity$> 2^{n-1} - 2^{{ n-1}\over { 2}}$if and only if$n > 7$. Using similar search technique, balanced Boolean functions on 9, 10, and 11 variables are attained having autocorrelation spectra with maximum absolute value$< 2^{\lceil {{ n}\over { 2}}\rceil }$. On odd number of variables, earlier such functions were known for 15, 21 variables; there was no evidence of such functions at all on even number of variables. In certain cases, our functions can be affinely transformed to obtain first-order resiliency or first-order propagation characteristics. Moreover, 10 variable functions having first-order resiliency and nonlinearity$492$are presented that had been posed as an open question at Crypto 2000. The functions reported in this paper are discovered using a suitably modified steepest descent based iterative heuristic search in the RSBF class along with proper affine transformations. It seems elusive to get a construction technique to match such functions.

In this paper, we analyze the total ergodic spectral efficiency and sum-rates error-exponents of randomly-spread CDMA systems with diversity-combining linear multiuser receivers over time-varying frequency-selective multipath Rayleigh/Ricean fading channels. The basis of our analysis mainly being the joint/average eigenvalue density of the random cross-correlation matrices, our focus is on equal-rate/equal-energy identical users with statistically i.i.d. channels. The upper-bound ergodic spectral efficiency and the corresponding sum-rates error-exponent expressions are derived in closed-form in terms of the key system parameters for linear multiuser receivers with single-user ML decoding. The analysis sheds light onto asymptotic behaviour of channel-coded wideband CDMA systems over multipath fading channels.

We address in this paper the derivation and analysis of the outage spectral efficiencies achievable with linear multiuser receivers over randomly-spread multipath fading time-varying coded-CDMA channels. The basis of the derivations is the use of non-asymptotic average eigenvalue densities of random crosscorrelation matrices. The analyses give important clues on the achievable capacity with linear multiuser receivers under non-ergodic transmission situations.

The algorithm given by Rouanne and Costello (1989) for the computation of the distance spectrum is improved for trellis-coded modulation schemes having uncoded bits, i.e., for trellis diagrams having parallel paths. It is shown that, when through a trellis corresponding to such kind of codes, all parallel transitions (labeled by signal selectors) between states are considered as a single branch labeled by a subset, then defining subset selector distance polynomials makes the computational complexity of the distance spectrum dependent on the number of states as compared to the complexity of Rouanne and Costello algorithm which depends on the number of paths to be extended.

Two decoding algorithms for double-byte error correcting-triple-byte error detecting (DBEC-TBED) Reed-Solomon (RS) codes are implemented using Turbo-Pascal. The first one is the noniterative decoding algorithm developed by R.H. Deng and D.J. Costello (ibid., vol.C-36, p.1359-63, Nov. 1987). The second one is a frequency-domain RS decoding method given by R.E. Blahut (Theory and Practice of Error Control Codes, Reading, MA, Addison-Wesley, 1983), which implements a standard Berlekamp-Massey algorithm; it is used as reference. Several executions of the software show that the algorithm of Deng-Costello fails in the detection of some triple-byte errors, whereas the standard reference algorithm succeeds in detection always. An example is presented in which the algorithm of Deng-Costello cannot detect a triple-error pattern. The authors also propose a modification to the algorithm of Deng-Costello for its proper operation and make a comparison between the two algorithms.>

The noniterative method of adaptive channel equalization proposed by Butler and Cantoni [1] is investigated. Its start-up time is improved remarkably by choosing the period of the training sequence judiciously and performing the estimation of channel parameters exactly over one period. The resulting version of the algorithm is as fast as the fastest known iterative algorithms, such as Godard's Kaiman algorithm [2].