Abstract-We consider a degraded broadcast channel with maximum likelihood decoders and derive lower bounds on the error exponent of each user. Unlike earlier results, our exponents pertain to optimal decoding and include both rates.
We consider zero-delay single-user and multi-user source coding with average distortion constraint and decoder side information. The zerodelay constraint translates into causal (sequential) encoder and decoder pairs as well as the use of instantaneous codes. For the single-user setting, we show that optimal performance is attained by time sharing at most two scalar encoder-decoder pairs, that use zero-error side information codes.Side information lookahead is shown to useless in this setting. We show that the restriction to causal encoding functions is the one that causes the performance degradation, compared to unrestricted systems, and not the sequential decoders or instantaneous codes. Furthermore, we show that even without delay constraints, if either the encoder or decoder are restricted a-priori to be scalar, the performance loss cannot be compensated by the other component, which can be scalar as well without further loss. Finally, we show that the multi-terminal source coding problem can be solved in the zero-delay regime and the rate-distortion region is given.
Abstract-We study linear encoding for a pair of correlated Gaussian sources transmitted over a two-user Gaussian broadcast channel in the presence of unit-delay noiseless feedback, abbreviated as the GBCF. Each pair of source samples is transmitted using a linear transmission scheme in a finite number of channel uses. We investigate three linear transmission schemes: A scheme based on the Ozarow-Leung (OL) code, a scheme based on the linear quadratic Gaussian (LQG) code of Ardestanizadeh et al., and a novel scheme derived in this work using a dynamic programming (DP) approach. For the OL and LQG schemes we present lower and upper bounds on the minimal number of channel uses needed to achieve a target mean-square error (MSE) pair. For the LQG scheme in the symmetric setting, we identify the optimal scaling of the sources, which results in a significant improvement of its finite horizon performance, and, in addition, characterize the (exact) minimal number of channel uses required to achieve a target MSE. Finally, for the symmetric setting, we show that for any fixed and finite number of channel uses, the DP scheme achieves an MSE lower than the MSE achieved by either the LQG or the OL schemes.
Motivated by the practical requirement for delay and complexity constrained broadcasting, we study uncoded transmission of a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel with unit-delay noiseless feedback links (GBCF). Differently from previous works, in the present work we focus on the finite horizon regime. We present two joint source-channel coding schemes, one is based on the Ozarow-Leung (OL) coding scheme for the GBCF and the other is based on the linear quadratic Gaussian (LQG) code by Ardestanizadeh et al. Our LQG-oriented code uses an improved decoder which outperforms the original decoder of Ardestanizadeh et al. in the finite horizon regime. We further derive lower and upper bounds on the minimal number of channel uses needed to achieve a specified pair of distortion levels for each scheme, and using these bounds, we explicitly characterize a range of transmit powers in which the OL code outperforms the LQG-oriented code.
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