Thomas Ericson

Spherical codes generated by binary partitions of symmetric pointsets

Several constructions are presented by which spherical codes are generated from groups of binary codes. In the main family of constructions the codes are generated from equally spaced symmetric pointsets on the real line. The main ideas are code concatenation and set partitioning. Extensive tables are presented for spherical codes in dimension n/spl les/24. >

A Gaussian channel with slow fading (Corresp.)

An interleaved fading channel whose state is known to the receiver is analyzed. The reliability function E(R) is obtained for rates R in the range R_c \leq R \leq C . The capacity is shown to be C = E_A \{ \frac{1}{2} \ln (1 + A^2 n)\} where A is a factor describing the fading mechanism and u is the signal-to-noise ratio per dimension.

Structure of optimum receiving filters in data transmission systems (Corresp.)

It has been observed by several authors that a number of different optimum receiving filters (corresponding to different criteria of goodness) for sampled-data transmission systems can be factored as a product of a matched filter and a periodic filter with the period equal to the sampling frequency. By a simple argument it is shown in this correspondence that any reasonable criterion of goodness will lead to an optimum filter that has this form.

Superimposed codes in R/sup n/

The authors introduce the concept of superimposed codes in Euclidean n-space R/sup n/. An asymptotic existence bound is derived for such codes; the proof uses the idea of random coding. In particular, the asymptotic properties of long codes are studied. It is shown that the derived existence bound differs only by a factor of four from a nonexistence bound obtained by a simple sphere-packing argument. >

The noncooperative binary adder channel

Jamming is studied as a game in the binary adder channel. The legal user controls simultaneously the encoder and the decoder by the choice of a key; the jammer controls the channel by the choice of an interference signal. For any given pair of encoder and decoder, this leads to a two-person zero-sum game. It is shown that this game can be solved in many cases of interest. In particular, an exact measure of performance is derived for the class of so-called direct sequence systems.

Superimposed Codes in Rn

A superimposed code in Rn is a finite set C of unit norm vectors x in Euclidean n-space, Rn, with the proporty that any two sums of at most m vectors from C are separated by at least unity distance. The code C has dimension n, order m, and size \( T\mathop{ = }\limits^{\Delta } \left| C \right|. \). The concept has application in various multiple-access communication problems. We derive upper and lower bounds for the maximum size T(n,m) of a superimposed code given the dimension n and order m, and in particular we investigate the asymptotic properties of these bounds.

Optimum PAM filters are always band limited (Corresp.)

Joint optimization of transmitting and receiving filters in pulse-amplitude-modulated stationary Gaussian channels has been considered by a large number of authors under a variety of different circumstances. In most cases it has been found that the optimum filters are strictly band limited. In the present correspondence we give a direct argument why this must be so for a broad class of joint optimization problems.

An improvement of the Gilbert bound for constant weight codes (Corresp.)

Using the Goppa codes as outer codes in a construction devised by Kautz and Singleton, an improvement of the Gilbert bound for constant weight codes is obtained.

Fourier-invariant pairs of partitions of finite abelian groups and association schemes

We consider partitions of finite abelian groups. We introduce the concept of Fourier-invariant pairs and demonstrate that this concept is equivalent to the concept of an association scheme in an abelian group. It follows that Fourier-invariant pairs of partitions might be viewed as a very natural approach to abelian association schemes.

A min-max theorem for antijamming group codes

Slepians idea of group codes for analog channels is adapted to the case of antijamming codes. The main result is a codeword error probability characterized by a min-max theorem. The result is illustrated by the special cases of frequency hopping (FH) and direct sequence (DS).