Finite-Length Linear Schemes for Joint Source-Channel Coding over Gaussian Broadcast Channels with Feedback

Abstract

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.

On the Energy-Distortion Tradeoff of Gaussian Broadcast Channels with Feedback

“…We note that linear and uncoded transmission, as implemented in the OL and in the LQG schemes, has important advantages, including low computational complexity, short coding delays and small storage requirements, which make this type of coding very desirable. We further note that although the LQG channel coding scheme of [32] for the two-user GBCF (with two messages) achieves the largest rate region out of all known channel coding schemes, in [36], it was shown that when the time horizon is finite, JSCC based on the OL scheme can achieve MSE distortion pairs lower than the JSCC based on the LQG scheme. In the present work, we analyze lossy source coding over GBCFs using SSCC and JSCC schemes based on a different performance metric: the EDT.…”

“…JSCC for the transmission of correlated Gaussian sources over GBCFs when the number of transmitted symbols is finite (referred to as the finite horizon regime) was previously considered in [36], which studied the minimal number of channel uses required to achieve a target MSE distortion pair. Three linear encoding schemes based on uncoded transmission were considered: the first scheme was a JSCC scheme based on the coding scheme of [28], to which we shall refer as the OL scheme; the second scheme was a JSCC scheme based on the scheme of [32], to which we shall refer as the LQG scheme; and the third scheme was a JSCC scheme whose parameters are obtained using dynamic programming (DP) (in the present work we discuss only the former OL and LQG schemes since the scheme based on DP becomes analytically and computationally infeasible as the number of channel uses goes to infinity).…”

“…As both SSCC schemes apply coding over multiple samples of the source pairs, they require high computational complexity, long delays and large storage space. We then consider the uncoded JSCC OL scheme presented in [36]. For this scheme, we first consider the case of fixed SNR and derive an upper bound on the number of channel uses required to achieve a target distortion pair.…”

Energy-distortion tradeoff for the gaussian broadcast channel with feedback

“…4] we adapted the LQG scheme for [11] to the transmission of correlated Gaussian sources over GBCFs. We have observed in [12] that obtaining a closed-form expression for E LQG (D) seems intractable. Yet, using the results and analysis of [12] one can find good approximations for E LQG (D).…”

“…Previous works on GBCFs mainly studied the channel coding aspects which applies to independent and uniformly distributed messages [9]- [11]. JSCC of correlated Gaussian sources over GBCFs was also studied in [12], in which the minimal number of channel uses required to achieve a target MSE distortion pair was characterized for three linear encoding schemes, using uncoded transmission: The first scheme is a JSCC scheme based on the coding scheme of Ozarow and Leung [9], to which we shall refer as the OL scheme; the second scheme iss a JSCC scheme based on the linear quadratic Gaussian (LQG) coding scheme of [11], to which we shall refer as the LQG scheme; and the third scheme iss a JSCC scheme whose parameters are obtained using dynamic programming (DP). 1 We note that the advantages of linear and uncoded transmission, as implemented in the OL and LQG schemes, include a low computational complexity, low coding delays, and low storage requirements.…”