Rate and diversity impose a fundamental trade-off in communications. This trade-off was investigated for flat-fading channels in as well as for Inter-symbol Interference (ISI) channels in . A different point of view was explored in where high-rate codes were designed so that they have a high-diversity code embedded within them. These diversity embedded codes were investigated for flat fading channels both from an information-theoretic viewpoint and from a coding theory viewpoint in . In this paper, we explore the use of diversity embedded codes for inter-symbol interference channels. In particular the main result of this paper is that the diversity multiplexing trade-off for fading MISO/SIMO/SISO ISI channels is indeed successively refinable. This implies that for fading ISI channels with a single degree of freedom one can embed a high diversity code within a high rate code without any performance loss (asymptotically). This is related to a deterministic structural observation about the asymptotic behavior of frequency response of channel with respect to fading strength of time domain taps as well as a coding scheme to take advantage of this observation.

Multiplexing rate and diversity impose a fundamental trade-off in wireless communications. This tradeoff was investigated for inter-symbol interference (ISI) channels in (Grokop, 2004). A different point of view was explored in (Diggavi et al., 2008) where high-rate codes were designed so that they have a high-diversity code embedded within them. It was shown in (Diggavi, 2005) that the diversity-multiplexing (D-M) tradeoff for channels with one degree of freedom (SIMO/MISO) is successively refinable i.e., one can perfectly embed a high diversity code within a high rate code. The performance of such diversity embedded codes were investigated for ISI channels in (Dusad, 2006) where it was shown that for SISO/SIMO ISI fading channels the D-M tradeoff is still successively refinable, in contrast to parallel flat fading channels (Diggavi, 2006). The main result of this paper is that the diversity multiplexing tradeoff for fading MISO ISI channels is indeed successively refinable. This is related to a deterministic structural observation about the asymptotic behavior of frequency response of channel with respect to fading strength of time domain taps as well as a coding scheme to take advantage of this observation.

Rate and diversity impose a fundamental tradeoff in wireless communication. High-rate space-time codes come at a cost of lower reliability (diversity), and high reliability (diversity) implies a lower rate. However, wireless networks need to support applications with very different quality-of-service (QoS) requirements, and it is natural to ask what characteristics should be built into the physical layer link in order to accommodate them. In this paper, we design high-rate space-time codes that have a high-diversity code embedded within them. This allows a form of communication where the high-rate code opportunistically takes advantage of good channel realizations while the embedded high-diversity code provides guarantees that at least part of the information is received reliably. We provide constructions of linear and nonlinear codes for a fixed transmit alphabet constraint. The nonlinear constructions are a natural generalization to wireless channels of multilevel codes developed for the additive white Gaussian noise (AWGN) channel that are matched to binary partitions of quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations. The importance of set-partitioning to code design for the wireless channel is that it provides a mechanism for translating constraints in the binary domain into lower bounds on diversity protection in the complex domain. We investigate the systems implications of embedded diversity codes by examining value to unequal error protection, rate opportunism, and packet delay optimization. These applications demonstrate that diversity-embedded codes have the potential to outperform traditional single-layer codes in moderate signal-to-noise (SNR) regimes.

Designs for transmit alphabet constrained space-time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multilevel space-time codes for flat-fading channels have been designed from sets of binary matrices with rank distance guarantees over the binary field by mapping them onto quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations. In this paper, we demonstrate that diversity embedded space-time codes for fading intersymbol interference (ISI) channels can be designed with provable rank distance guarantees. As a corollary, we obtain an asymptotic characterization of the fixed transmit alphabet rate-diversity tradeoff for multiple antenna fading ISI channels. The key idea is to construct and analyze properties of binary matrices with a particular structure (Toeplitz structure) induced by ISI channels.

Designs for transmit alphabet constrained space-time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multi-level space-time codes for flat fading channels have been designed by using sets of binary matrices with rank distance guarantees over the binary field and mapping them onto QAM and PSK constellations. In this paper we give the design of diversity embedded space-time codes for fading Inter-Symbol Interference (ISI) channels with provable rank distance guarantees. In the process of doing so we also get a (asymptotic) characterization of the rate-diversity trade-off for multiple antenna fading ISI channels when there is a fixed transmit alphabet constraint. The key idea is to construct and analyze properties of binary matrices with the particular structure induced by ISI channels.

In this correspondence, we present an efficient protocol for the delay-limited fading ARQ single relay half-duplex channel. The source is using an Automatic Retransmission reQuest (ARQ) retransmission protocol to send data to the relay and the destination. When the relay is able to decode, both the relay and the source send the same data to the destination providing additional gains. The proposed protocol exploits two kinds of diversity: 1) space diversity available through the cooperative (relay) terminal, which retransmits the source's signals and 2) ARQ diversity obtained by leveraging the retransmission delay to enhance the reliability. The performance characterization is in terms of the achievable diversity, multiplexing gain and delay tradeoff for a high signal-to-noise ratio (SNR) regime. Finally, we show the benefits of power control on the diversity by controlling the source's power level over the retransmission rounds.

Inspired by the combinatorial denoising method DUDE, we present efficient algorithms for implementing this idea for arbitrary contexts or for using it within subsequences. We also propose effective, efficient denoising error estimators so we can find the best denoising of an input sequence over different context lengths. Our methods are simple, drawing from string matching methods and radix sorting. We also present experimental results of our proposed algorithms.

In this paper, we present an efficient protocol for the delay-limited fading automatic retransmission request single relay channel. The source is using an ARQ retransmission protocol to send data to the relay and the destination. When the relay is able to decode, both the relay and the source send the same data to the destination providing additional gains. The proposed protocol exploits two kinds of diversity: (i) space diversity available through the cooperative (relay) terminal, which retransmits the source's signals, (ii) ARQ diversity obtained by leveraging the retransmission delay to enhance the reliability. The performance characterization is in terms of the achievable diversity, multiplexing gain and delay tradeoff for a high signal-to-noise ratio (snr) regime