USC - Communication Sciences Institue

CSI Advances

This page contains a few topics in which CSI faculty, students, and alumni have made notable contributions. This content will change each time the page is loaded or you may view all summaries.

The Welch Bound: the limits of pseduo-orthogonality

Constructing orthogonal functions on a finite interval of the real line is a well-known technique in electrical engineering. If the real coordinate is time, these functions have to be synchronous (occupy the same time interval) to demonstrate orthogonality when used as inputs on the arms of a correlator. Functions that are not synchronous and retain nearly orthogonal properties are the modulation building blocks for spread-spectrum multiple-access systems. Prof. Lloyd Welch in his classic paper "Lower Bounds on the Maximum Correlation of Signals" produced a lower bound on asynchronous correlation that is only a function of the dimension of the signal space and the number of signals desired in the signal set. The bound often is nearly achievable by good signal-set design, and has become "The Welch Bound" standard by which spread-spectrum signal-set designs are judged. For more on this, see his original paper in the IEEE Trans. On Information Theory, pp. 397-399, May 1974. For more on the Welch bound and its use in spread spectrum signal design, see Prof. Scholtz's Chapter 5 in The Spread Spectrum Communications Handbook by M. K. Simon et al.

The Viterbi Algorithm

The Viterbi algorithm was developed by Dr. Andrew Viterbi in 1968 while he was a faculty member at UCLA, just a few years after receiving his Ph.D. in EE at USC. The Viterbi algorithm (VA) is the optimal decoder for a convolutional code and also solves several related problems in communications (e.g., data detection in intersymbol interference channels). The discovery and popularization of the VA coincided with the realization of large scale integrated circuitry. This was fortuitous because the VA maps nicely onto digital hardware architectures. Dr. Viterbi and his associates recognized these capabilities and founded Linkabit, and later Qualcomm, essentially launching the "telecom valley" in North County San Diego.

Scrambling Codes for 3G Cellular Communication Systems

Code-Division Multiple-Access or CDMA is the preferred method of allowing multiple users to share the same cellular communication channel in third-generation (3G) cellular communication systems. In a CDMA system, the signals of different users are kept separate by assigning to each user, a distinct scrambling code. A family of efficient scrambling codes, introduced in a 1996 paper authored by P. V. Kumar, T. Helleseth, A. R. Calderbank and A. R. Hammons, Jr., is under use as the short scrambling code of the 3G W-CDMA standard. While traditional scrambling codes employ a binary alphabet, the scrambling codes of Kumar et. al. have a quaternary alphabet that is well-suited to the quaternary nature of the signal modulation employed in third-generation cellular communication. This family of scrambling codes also has large cardinality, enabling scrambling codes to be assigned to a large number of potential users.

CSI Advances
		This page contains a few topics in which CSI faculty, students, and alumni have made notable contributions. This content will change each time the page is loaded or you may view all summaries. The Welch Bound: the limits of pseduo-orthogonality Constructing orthogonal functions on a finite interval of the real line is a well-known technique in electrical engineering. If the real coordinate is time, these functions have to be synchronous (occupy the same time interval) to demonstrate orthogonality when used as inputs on the arms of a correlator. Functions that are not synchronous and retain nearly orthogonal properties are the modulation building blocks for spread-spectrum multiple-access systems. Prof. Lloyd Welch in his classic paper "Lower Bounds on the Maximum Correlation of Signals" produced a lower bound on asynchronous correlation that is only a function of the dimension of the signal space and the number of signals desired in the signal set. The bound often is nearly achievable by good signal-set design, and has become "The Welch Bound" standard by which spread-spectrum signal-set designs are judged. For more on this, see his original paper in the IEEE Trans. On Information Theory, pp. 397-399, May 1974. For more on the Welch bound and its use in spread spectrum signal design, see Prof. Scholtz's Chapter 5 in The Spread Spectrum Communications Handbook by M. K. Simon et al. The Viterbi Algorithm The Viterbi algorithm was developed by Dr. Andrew Viterbi in 1968 while he was a faculty member at UCLA, just a few years after receiving his Ph.D. in EE at USC. The Viterbi algorithm (VA) is the optimal decoder for a convolutional code and also solves several related problems in communications (e.g., data detection in intersymbol interference channels). The discovery and popularization of the VA coincided with the realization of large scale integrated circuitry. This was fortuitous because the VA maps nicely onto digital hardware architectures. Dr. Viterbi and his associates recognized these capabilities and founded Linkabit, and later Qualcomm, essentially launching the "telecom valley" in North County San Diego. Scrambling Codes for 3G Cellular Communication Systems Code-Division Multiple-Access or CDMA is the preferred method of allowing multiple users to share the same cellular communication channel in third-generation (3G) cellular communication systems. In a CDMA system, the signals of different users are kept separate by assigning to each user, a distinct scrambling code. A family of efficient scrambling codes, introduced in a 1996 paper authored by P. V. Kumar, T. Helleseth, A. R. Calderbank and A. R. Hammons, Jr., is under use as the short scrambling code of the 3G W-CDMA standard. While traditional scrambling codes employ a binary alphabet, the scrambling codes of Kumar et. al. have a quaternary alphabet that is well-suited to the quaternary nature of the signal modulation employed in third-generation cellular communication. This family of scrambling codes also has large cardinality, enabling scrambling codes to be assigned to a large number of potential users.