Optimal Reception for Binary Partial Response Channels

Optimal Reception for Binary Partial Response Channels By M. J. F E R G U S O N (Manuscript received September 3, 1971) This paper describes an exceptionally simple scheme for binary partial response signal formats of the form a,: ± (for I ^ 1, and ak = ± / ) . The receiver implements the maximum likelihood detector of the sequence ak assuming additive white Gaussian noise as the channel impairment. It is simpler and more efficient than the scheme recently described by G. D. ForneyIt is, however, not generalizable to multilevel signaling while still retaining its simplicity. I. INTRODUCTION' There 1ms recently been considerable interest in using the inherent redundancy of the partial response signal formal to approach the error rate versus signal-to-noise-ratio performance equivalent to binary antipodal signaling. Forney 1 at the 1970 International Symposium on Information Theory discussed a simple decoding scheme which he shows to be asymptotically optimal for high signal-to-noise ratio for channels with white additive Gaussian noise. This paper describes a receiver for binary partial response signaling which is optimal for white additive Gaussian noise. This demodulator is much simpler than the equivalent two-level scheme of Forney. However, the extension to four or more levels seems to result in a scheme of much greater complexity than Forney's. In the first part of the paper we briefly review binary Class IV partial response signaling. Then we derive the optimal detection scheme for binary signaling which has a particularly simple implementation.