Properties of the MMSE of “bad” codes

Author

Bustin, Ronit ; Shamai, Shlomo

Author_Institution

Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel

fYear

2011

fDate

28-30 Sept. 2011

Firstpage

1779

Lastpage

1784

Abstract

We examine non-optimal codes (alternatively referred to as "bad" codes), over the additive Gaussian noise channel. These codes are required to attain a minimum rate at a specific signal-to-noise ratio (snr). For these codes, we provide a tight lower bound on the minimum mean square error (MMSE), valid for any snr, attainable by superposition codebooks, optimal for a specific degraded Gaussian broadcast channel (BC). Moreover, the MMSE function of codes, attaining a minimum required rate at some snr, and the lower bound on the MMSE at some other snr, is completely defined for all snr, and is the one obtained by the corresponding superposition codebooks.

Keywords

AWGN channels; broadcast channels; codes; least mean squares methods; Gaussian broadcast channel; MMSE function; SNR; additive Gaussian noise channel; bad codes; minimum mean square error; nonoptimal codes; signal-to-noise ratio; superposition codebooks; Decoding; Error probability; Interference channels; Mutual information; Relays; Reliability; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on

Conference_Location

Monticello, IL

Print_ISBN

978-1-4577-1817-5

Type

conf

DOI

10.1109/Allerton.2011.6120384

Filename

6120384