Yu-Chih Huang

Lattices over Eisenstein integers for compute-and-forward

We consider the use of lattice codes over Eisenstein integers for implementing a compute-and-forward protocol in wireless networks when channel state information is not available at the transmitter. We prove the existence of a sequence of infinite-dimensional nested lattices over Eisenstein integers where the coarse lattice is simultaneously good for quantization and additive white Gaussian noise (AWGN) channel coding and the fine lattice is good for AWGN channel coding. Using this, we show that the information rates achievable with nested lattice codebooks over Eisenstein integers can be higher than those achievable with nested lattices over integers considered by Nazer and Gastpar in [1] for some set of channel realizations. We also propose a practical coding scheme based on the concatenation of a non-binary low density parity check code with a modulation scheme derived from the ring of Eisenstein integers.

Lattices Over Eisenstein Integers for Compute-and-Forward

In this paper, we consider the use of lattice codes over Eisenstein integers for implementing a compute-and-forward protocol in wireless networks when channel state information is not available at the transmitter. We extend the compute-and-forward paradigm of Nazer and Gastpar to decoding Eisenstein integer combinations of transmitted messages at relays by proving the existence of a sequence of pairs of nested lattices over Eisenstein integers in which the coarse lattice is good for covering and the fine lattice can achieve the Poltyrev limit. Using this result, we show that both the outage performance and error-correcting performance of the nested lattice codebooks over Eisenstein integers surpass those of lattice codebooks over integers considered by Nazer and Gastpar with no additional computational complexity.

Multistage Compute-and-Forward with Multilevel Lattice Codes Based on Product Constructions

Product construction with two levels proposed in [1] is a lattice construction which can be thought of as Construction A with codes that can be represented as the Cartesian product of two linear codes. This paper first generalizes the product construction to arbitrary number of levels. More importantly, the existence of a sequence of such lattices that are good for quantization and Poltyrev-good under multistage decoding is proved. This family of lattices is then used to generate a sequence of nested lattice codes based on the recent construction of Ordentlich and Erez. This allows one to achieve the same computation rate of Nazer and Gastpar for compute-and-forward with multistage decoding, which is termed multistage compute-and-forward.

Joint source-channel coding with correlated interference

We study the joint source-channel coding problem of transmitting a discrete-time analog source over an additive white Gaussian noise (AWGN) channel with interference known at transmitter. We consider the case when the source and the interference are correlated. We first derive an outer bound on the achievable distortion and then, we propose two joint source-channel coding schemes. The first scheme is the superposition of the uncoded signal and a digital part which is the concatenation of a Wyner-Ziv encoder and a dirty paper encoder. In the second scheme, the digital part is replaced by the hybrid digital and analog scheme proposed by Wilson et al. When the channel signal-to-noise ratio (SNR) is perfectly known at the transmitter, both proposed schemes are shown to provide identical performance which is substantially better than that of existing schemes. In the presence of an SNR mismatch, both proposed schemes are shown to be capable of graceful enhancement and graceful degradation. Interestingly, unlike the case when the source and interference are independent, neither of the two schemes outperforms the other universally. As an application of the proposed schemes, we provide both inner and outer bounds on the distortion region for the generalized cognitive radio channel.

Adaptive compute-and-forward with lattice codes over algebraic integers

We consider the compute-and-forward relay network with limited feedback. A novel scheme called adaptive compute-and-forward is proposed to exploit the channel knowledge by working with the best ring of imaginary quadratic integers. This is enabled by generalizing Construction A lattices to other rings of imaginary quadratic integers which may not form principal ideal domains and by showing such construction can produce good lattices for coding in the sense of Poltyrev and for MSE quantization. Since there are channel coefficients (complex numbers) which are closer to elements of rings of imaginary quadratic integers other than Gaussian and Eisenstein integers, by always working with the best ring among them, we can obtain better performance than that provided by working over Gaussian or Eisenstein integers.

Asynchronous Physical-Layer Network Coding With Quasi-Cyclic Codes

Communication in the presence of bounded timing asynchronism, which is known to the receiver but cannot be easily compensated, is studied. Examples of such situations include point-to-point communication over intersymbol interference (ISI) channels and asynchronous wireless networks. In these scenarios, although the receiver may know all the delays, it is often not an easy task for the receiver to compensate the delays as the signals are mixed together. A novel framework, which is called interleave/deinterleave transform (IDT), is proposed to deal with this problem. It is shown that the IDT allows one to design the delays so that quasi-cyclic (QC) codes with a proper shifting constraint can be used accordingly. When used in conjunction with QC codes, IDT provides significantly better performance than existing schemes relying solely on cyclic codes. Two instances of asynchronous physical-layer network coding, namely, the integer-forcing equalization for ISI channels and asynchronous compute-and-forward, are then studied. For integer-forcing equalization, the proposed scheme provides improved performance over using cyclic codes. For asynchronous compute-and-forward, the proposed scheme shows that there is no loss in the achievable information rates due to delays that are integer multiples of the symbol duration. Furthermore, the proposed approach shows that delays introduced by the channel can sometimes be exploited to obtain higher information rates than those obtainable in the synchronous case. The proposed IDT can be thought of as a generalization of the interleaving/deinterleaving idea proposed by Wang et al., which allows the use of QC codes, thereby substantially increasing the design space.

Coding for parallel Gaussian bi-directional relay channels: A deterministic approach

We study the design of good coding schemes and the achievable exchange rates for the parallel Gaussian bidirectional relay channel. We first consider the corresponding linear deterministic model and propose two different schemes that can achieve the exchange capacity for this linear deterministic model. The insights obtained from this are used to design coding schemes for the original parallel Gaussian bi-directional relay channel. The first coding scheme uses superposition-based coding at both nodes and reorders codewords that cannot be transmitted within their own sub-channels to the sub-channels that can support the transmission at the relay. The second coding scheme employs lattice partition chains proposed by Nam et al. in the multiple access phase and then performs coding across sub-channels in the broadcast phase. While both schemes are optimal for the linear deterministic model, the performance of their Gaussian counterparts are different in general and which one performs better depends on the operating SNR and channel coefficients. Numerical results show that both schemes substantially outperform the decode-and-forward scheme and also provide non-trivial gains over the scheme proposed by Huang et al. Moreover, it is shown that the performance of both schemes is close to that of the cut-set bound and that the second scheme is asymptotically optimal.

Interleaved Concatenations of Polar Codes With BCH and Convolutional Codes

We analyze interleaved concatenation schemes of polar codes with outer binary BCH codes and convolutional codes. We show that both BCH-polar and Conv-polar codes can have a frame error rate that decays exponentially with the code length for all rates up to capacity, which is a substantial improvement in the error exponent over stand-alone polar codes. Interleaved concatenation with long constraint length convolutional codes is an effective way to leverage the fact that polarization increases the cutoff rate of the channel. Simulation results show that Conv-polar codes when decoded with the proposed soft-output multistage iterative decoding algorithm can outperform stand-alone polar codes decoded with successive cancellation or belief propagation decoding. It may be comparable to stand-alone polar codes with list decoding in the high SNR regime. In addition to this, we show that the proposed concatenation scheme requires lower memory and decoding complexity in comparison to belief propagation and list decoding of polar codes. Practically, the scheme enables rate compatible outer codes which ease hardware implementation. Our results suggest that the proposed method may strike a better balance between performance and complexity compared to existing methods in the finite-length regime.

Lattices from codes for harnessing interference: An overview and generalizations

In this paper, using compute-and-forward as an example, we provide an overview of constructions of lattices from codes that possess the right algebraic structures for harnessing interference. This includes Construction A, Construction D, and Construction πA (previously called product construction) recently proposed by the authors. While most of the results in this paper have been available in the literature, we discuss two generalizations where the first one is a general construction of lattices named Construction πD subsuming the above three constructions as special cases and the second one is to go beyond principal ideal domains and build lattices over algebraic integers.

Energy-efficient communication in the presence of synchronization errors

Communication systems are traditionally designed to have tight transmitter-receiver synchronization. This requirement has negligible overhead in the high-SNR regime. However, in many applications, such as wireless sensor networks, communication needs to happen primarily in the energy-efficient regime of low SNR, where requiring tight synchronization can be highly suboptimal. In this paper, we model the noisy channel with synchronization errors as an insertion/deletion/substitution channel. For this channel, we propose a new communication scheme that requires only loose transmitter-receiver synchronization. We show that the proposed scheme is asymptotically optimal for the Gaussian channel with synchronization errors in terms of energy efficiency as measured by the rate per unit energy. In the process, we also establish that the lack of synchronization causes negligible loss in energy efficiency. We further show that, for a general discrete memoryless channel with synchronization errors and a general cost function (with a zero-cost symbol) on the input, the rate per unit cost achieved by the proposed scheme is within a factor two of the information-theoretic optimum.