Xiujie Huang

Channel Modeling and Capacity Bounds for Two-Dimensional Magnetic Recording

Two-dimensional magnetic recording (TDMR) differs from traditional track recording in that the bit-size-to-grain-size ratio is drastically reduced so that the channel bits are roughly of the same sizes as those of the magnetic media grains. This is envisioned to be achieved by shingled writing, a write-process in which the corner-writer partially overwrites the previously written adjacent track, effectively writing very closely spaced narrow tracks with no guard bands. Since the tracks are very narrow, they can be read by an array of read-elements whose spacing is equal to the narrow track pitch, creating a two-dimensional (2-D) array of readback signals (the two dimensions being the cross-track and the down-track dimensions). In the absence of an array of read elements, the same 2-D readback can be obtained by progressive scans of a single read element that reads one narrow track at a time and stores the readback signal in a 2-D array. In this paper, we present simple magnetic grain media models and shingled-write process models that capture the essence of TDMR. We assume that the granular recording medium consists of randomly shaped tiles (each tile represents a grain), randomly covering the medium plane. We then derive a suitable 2-D read/write process model. Using proper information-theoretic inequalities and bounding techniques, we derive methods to bound the capacities of TDMR channels. The results reveal that information capacities in excess of 0.6 user bits per grain are possible to attain over TDMR channels.

Optimal Detector for Multilevel NAND Flash Memory Channels with Intercell Interference

In this paper we derive the optimal detector for multilevel cell (MLC) flash memory channels with intercell interference (ICI). We start with the MLC channel model proposed by Dong et al. and just slightly alter the model to guarantee mathematical tractability of the optimal detectors (maximum likelihood and maximum a-posteriori sequence and symbol detectors). The optimal detector is obtained by computing branch metrics using Fourier transforms of analytically computable characteristic functions (corresponding to likelihood functions). We derive the detectors for both simple one-dimensional (1D) channel models and more realistic page-orientated two-dimensional (2D) channel models. Simulation results show that the hard-output bit error rate (BER) performance matches some previously known detectors, but that the soft-output detector outperforms previously known detectors by 0.35 dB.

Accessible Capacity of Secondary Users

A new problem formulation is presented for the Gaussian interference channels with two pairs of users, which are distinguished as primary users and secondary users, respectively. The primary users employ a pair of encoder and decoder that were originally designed to satisfy a given error performance requirement under the assumption that no interference exists from other users. In the scenario when the secondary users attempt to access the same medium, we are interested in the maximum transmission rate (defined as accessible capacity) at which secondary users can communicate reliably without affecting the error performance requirement by the primary users under the constraint that the primary encoder (not the decoder) is kept unchanged. By modeling the primary encoder as a generalized trellis code (GTC), we are then able to treat the secondary link and the cross link from the secondary transmitter to the primary receiver as finite state channels. Based on this, upper and lower bounds on the accessible capacity are derived. The impact of the error performance requirement by the primary users on the accessible capacity is analyzed by using the concept of interference margin. In the case of nontrivial interference margin, the secondary message is split into common and private parts and then encoded by superposition coding, which delivers a lower bound on the accessible capacity. For some special cases, these bounds can be computed numerically by using the BCJR algorithm. Numerical results are also provided to gain insight into the impacts of the GTC and the error performance requirement on the accessible capacity.

Accessible capacity of secondary users over the Gaussian interference channel

A new problem formulation is presented for the Gaussian interference channels (GIFC) with two pairs of users, which are distinguished as primary users and secondary users, respectively. The primary users employ a pair of encoder and decoder that were originally designed to satisfy a given error performance requirement (EPR) under the assumption that no interference exists. In the case when the secondary users attempt to access the same medium, we are interested in the maximum transmission rate (defined as accessible capacity) at which secondary users can communicate reliably without affecting the EPR under the constraint that the primary encoder (not the decoder) is kept unchanged. The relation of the accessible capacity to the capacity region of the GIFC is revealed. By modeling the primary encoder as a generalized trellis code (GTC), we are able to treat the secondary links as finite state channels. Then upper and lower bounds on the accessible capacity are derived and computed by using the BCJR algorithm. The numerical results show us either expected or interesting facts.

An Information-Spectrum Approach to the Capacity Region of the Interference Channel

In this paper, a general formula for the capacity region of a general interference channel with two pairs of users is derived, which reveals that the capacity region is the union of a family of rectangles. In the region, each rectangle is determined by a pair of spectral inf-mutual information rates. The presented formula provides us with useful insights into the interference channels in spite of the difficulty of computing it. Specially, when the inputs are discrete, ergodic Markov processes and the channel is stationary memoryless, the formula can be evaluated by the BCJR (Bahl-Cocke-Jelinek-Raviv) algorithm. Also the formula suggests that considering the structure of the interference processes contributes to obtaining tighter inner bounds than the simplest one (obtained by treating the interference as noise). This is verified numerically by calculating the mutual information rates for Gaussian interference channels with embedded convolutional codes. Moreover, we present a coding scheme to approach the theoretical achievable rate pairs. Numerical results show that the decoding gains can be achieved by considering the structure of the interference.

Structural Analysis of Array-Based Non-Binary LDPC Codes

Structural properties of array-based non-binary low-density parity-check (NBLDPC) codes are studied in this paper. First, we characterize graphical substructures induced by codewords of symbol weight six in array-based NBLDPC codes defined by parity-check matrices with column weight three. We also reveal necessary conditions for these graphical substructures to incur weight-6 codewords. Such conditions can be used to select nonzero elements for avoiding weight-6 codewords or reducing the multiplicity of weight-6 codewords. Second, we show that there exist weight-7 codewords in array-based NBLDPC codes defined by parity-check matrices with column weight three. As a byproduct, we find that the graphical substructure induced by a weight-7 codeword takes the graphical substructure induced by the related weight-6 codewords as a subgraph. Third, we show that there may exist codewords with symbol weight four, six, and seven in array-based NBLDPC codes defined by parity-check matrices with column weight two. These results enrich the structural analysis of array-based LDPC codes. In addition, simulation results show the performance advantage of array-based NBLDPC codes.

All-bit-line MLC flash memories: Optimal detection strategies

We are concerned with the optimal detector design for the all-bit-line MLC flash memory. We provide a channel model of the MLC flash memory, where the channel parameters are mathematically tractable. Then we present an optimal maximum a-posteriori sequence detector. The optimal detector can be executed over a trellis whose branch metrics can be computed by using Fourier transforms of analytically computable characteristic functions (corresponding to likelihood functions). The soft-output detectors for both simple one-dimensional channel models and more realistic page-orientated two-dimensional channel models are derived. Simulation results show not only that the soft-output detector has the same hard-output bit-error-rate performance as some previously known detectors did, but that the soft-output detector outperforms previously known detectors by a gain of 0.23 dB.

Analysis of the Uplink Capacity in the High-Speed Train Wireless Communication with Full-Duplex Mobile Relay

One primary challenge in the high-speed train (HST) communication is that the wireless signal suffers from severe attenuation while it penetrates the sealed carriage of the train. In this letter, we show that such a nuisance can provide an opportunity of improving the uplink capacity when a full-duplex (FD) mobile relay (MR) is furnished on the train. To this end, by introducing the self-interference cancellation (SIC) level, we present an uplink channel model for the HST communication with FD MR. Then the uplink capacity is analyzed under either user equipment power constraint or total power constraint. By comparing with time division scheme, we can derive the required SIC level for the FD scheme to bring capacity improvement, which is confirmed by numerical results. Furthermore, theoretical analysis shows that, for a given SIC level, the uplink channel with severer carriage attenuation has higher capacity, which is also validated by numerical results.

Structural analysis of array-based non-binary LDPC codes

Structural properties of array-based non-binary low-density parity-check (NBLDPC) codes are studied in this paper. First, we characterize graphical substructures induced by codewords of symbol weight six in array-based NBLDPC codes defined by parity-check matrices with column weight three. We also reveal necessary conditions for these graphical substructures to incur weight-6 codewords. Such conditions can be used to select nonzero elements for avoiding weight-6 codewords or reducing the multiplicity of weight-6 codewords. Second, we show that there exist weight-7 codewords in array-based NBLDPC codes defined by parity-check matrices with column weight three. As a byproduct, we find that the graphical substructure induced by a weight-7 codeword takes the graphical substructure induced by the related weight-6 codewords as a subgraph. Third, we show that there may exist codewords with symbol weight four, six, and seven in array-based NBLDPC codes defined by parity-check matrices with column weight two. These results enrich the structural analysis of array-based LDPC codes. In addition, simulation results show the performance advantage of array-based NBLDPC codes.

Achievable rates and forward-backward decoding algorithms for the Gaussian relay channels under the one-code constraint

This paper is concerned with the Gaussian relay channel (GRC) under the one-code constraint, where the source and the relay utilize the same code to send message. An advantage of such one-code constraint is that the error propagation resulting from re-encoding can be mitigated as the relay can forward directly the decoded “codeword” to the destination. The maximal achievable rate of the considered GRC is derived using the technique of superposition block Markov encoding based on the single code. Moreover, the forward-backward (FB) decoding strategies over the sliding window are developed both at the destination and at the relay. When LDPC codes are applied to the GRC system, a practical FB message passing decoding algorithm is presented. Simulation results show that the decoding performance can be improved as the window length increases and a small length (no greater than 4) is good enough for the FB decoding, and that re-encoding at relay may degrade the decoding performance at the destination.