Title :
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
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;
Conference_Titel :
Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on
Conference_Location :
Monticello, IL
Print_ISBN :
978-1-4577-1817-5
DOI :
10.1109/Allerton.2011.6120384
