Joint Wyner–Ziv/Dirty-Paper Coding by Modulo-Lattice Modulation

Abstract

The combination of source coding with decoder side information (the Wyner-Ziv problem) and channel coding with encoder side information (the Gel'fand-Pinsker problem) can be optimally solved using the separation principle. In this work, we show an alternative scheme for the quadratic-Gaussian case, which merges source and channel coding. This scheme achieves the optimal performance by applying a modulo-lattice modulation to the analog source. Thus, it saves the complexity of quantization and channel decoding, and remains with the task of "shaping" only. Furthermore, for high signal-to-noise ratio (SNR), the scheme approaches the optimal performance using an SNR-independent encoder, thus it proves for this special case the feasibility of universal joint source-channel coding.Index Terms-Analog transmission, broadcast channel, joint source/channel coding, minimum mean-squared error (MMSE) estimation, modulo lattice modulation, unknown signal-to-noise ratio (SNR), writing on dirty paper, Wyner-Ziv (WZ) problem. I. INTRODUCTIONC ONSIDER the quadratic-Gaussian joint source/channel coding problem for the Wyner-Ziv (WZ) source [1] and Gel'fand-Pinsker channel [2], as depicted in Fig. 1. In the Wyner-Ziv setup, the source is jointly distributed with some side information (SI) known at the decoder. In the Gaussian case, the WZ-source sequence is given by(1)where the unknown source part, , is Gaussian independent and identically distributed (i.i.d.) with variance , while is an arbitrary SI sequence known at the decoder. In the Gel'fand-Pinsker setup, the channel transition distribution depends on a state that serves as encoder SI. In the Gaussian case, known as the dirty-paper channel (DPC) [3], the DPC output, , is given by (2)

An Achievable Rate Region for the Three-User Interference Channel Based on Coset Codes

“…Philosof and Zamir [10] employ coset codes for efficient communication over doubly dirty MACs and Gaussian version of this problem was studied using lattice codes in [11]. [12] and [13] propose lattice-based schemes for communicating over Gaussian multi-terminal networks. An achievable rate region based on Abelian group codes was provided for the general DSC problem in [14].…”

“…In other words, we provide an example where codes built over groups outperform unstructured codes as well as codes built over finite fields. 13 Example 9: Consider a quaternary 3−to−1 IC with input and output alphabets X j = Y j = Z 4 = {0, 1, 2, 3} being the Abelian group of cardinality 4. Let ⊕ 4 denote the group operation, i.e., addition mod−4 in Z 4 .…”

Lattice-Based Source-Channel Coding in Wireless Sensor Networks

“…The gap to the Wyner-Ziv bound is 6-7 dB, however, it is worth to stress that this bound assumes infinite dimensions in both the source and channel coding. In [16] it is in fact shown that MLM can reach the Wyner-Ziv bound as the lattice dimension goes to infinity.…”

“…The idea of MLM originates from nested lattice codes in digital systems [17], [18] and was mentioned in [15] as a means of performing analog communication with side information. The idea is analyzed in [16] in a pointto-point scenario, where it is shown that MLM asymptotically reaches the Wyner-Ziv bound as the lattice dimension goes to infinity. Another motivation for MLM in situations where side information is available at the decoder can be found in [19].…”

Lattices are everywhere

“…For example, for side-information problems known as the "Wyner-Ziv" source and the "dirty-paper" channel, a nested pair of lattices is needed where one component lattice forms a good channel code while the other component lattice forms a good source code. For joint source-channel coding problems, lattices with a good NSM-VNR product are desired [34].…”