Abstract — It has been shown that signature (multi-) sets that meet Welch’s lower bound on the total squared correlation (TSC), maximize the sum capacity of the synchronous code division multiple access (CDMA) channel with equal average input energy constraints. However, a signature set that is TSC-optimum (i.e. achieves the lower bound on TSC), doesn’t necessarily have a low cross-correlation spectrum. Hence, for various system loads there may be users that experience high probability of error due to high cross-correlation of their assigned signature to others in the set. In this paper we present a search method to obtain new optimum TSC binary signature sets with low cross-correlation spectrum. We also show, based on our search method, that if we relax the TSC optimality constraint, codes with better crosscorrelation spectrum may be found. In addition, a catastrophic binary code (i.e. a code having complementary codewords) can be TSC-optimal. Therefore, practically speaking, it is important that the TSC-optimality be sought along with the minimization of the cross-correlation spectrum. Finally our codes are tested on fully-loaded and overloaded synchronous CDMA systems, and simulation results show that they are a promising alternative to the Hadamard-Walsh codes, since they offer higher capacity. I.

In this letter, we report results on the relative performance of scalable video transmission via a singlerate or a multirate direct sequence code-division multiple-access (DS-CDMA) channel using minimum total squared correlation (TSC) spreading codes. Our findings demonstrate the superiority of the multirate system on a wide range of chip rates of practical interest.

In this paper, we derive closed-form expressions for the maximum squared correlation (MSC), total asymptotic efficiency (TAE), and sum capacity (Csum) of minimum total squared correlation (TSC) quaternary signature sets. While TSC, MSC, TAE, and Csum are equivalent optimization metrics over the real/complex field, our developments show that such equivalence does not hold, in general, over the quaternary field. We establish conditions on the number of signatures and signature length under which simultaneous optimization can or cannot be possible. 1.

Code Design Based on Metric-Spectrum and Applications. (December 2004) Panayiotis D. Papadimitriou, B.S., University of Patras, Greece; M.S., University of Patras, Greece Chair of Advisory Committee: Dr. Costas N. Georghiades We introduced nested search methods to design (n, k) block codes for arbitrary channels by optimizing an appropriate metric spectrum in each iteration. For a given k, the methods start with a good high rate code, say k/(k + 1), and successively design lower rate codes up to rate k/2 corresponding to a Hadamard code. Using a full search for small binary codes we found that optimal or near-optimal codes of increasing length can be obtained in a nested manner by utilizing Hadamard matrix columns. The codes can be linear if the Hadamard matrix is linear and non-linear otherwise. The design methodology was extended to the generic complex codes by utilizing columns of newly derived or existing unitary codes. The inherent nested nature of the codes make them ideal for progressive transmission.