Aravind R. Iyengar

Windowed Decoding of Protograph-Based LDPC Convolutional Codes Over Erasure Channels

We consider a windowed decoding scheme for LDPC convolutional codes that is based on the belief-propagation (BP) algorithm. We discuss the advantages of this decoding scheme and identify certain characteristics of LDPC convolutional code ensembles that exhibit good performance with the windowed decoder. We will consider the performance of these ensembles and codes over erasure channels with and without memory. We show that the structure of LDPC convolutional code ensembles is suitable to obtain performance close to the theoretical limits over the memoryless erasure channel, both for the BP decoder and windowed decoding. However, the same structure imposes limitations on the performance over erasure channels with memory.

Windowed erasure decoding of LDPC Convolutional Codes

We consider windowed decoding of LDPC Convolutional Codes on the Binary Erasure Channel (BEC) to study the trade-off between the decoding latency and the code performance. We make some key observations about regular LDPC Convolutional code ensembles under windowed decoding and give modified constructions of these codes that allow us to efficiently trade-off performance for gains in latency.

Write Channel Model for Bit-Patterned Media Recording

We propose a new write channel model for bit-patterned media recording that reflects the data dependence of write synchronization errors. It is shown that this model accommodates both substitution-like errors and insertion-deletion errors whose statistics are determined by an underlying channel state process. We study information theoretic properties of the write channel model, including the capacity, symmetric information rate, Markov-1 rate, and the zero-error capacity.

Windowed Decoding of Spatially Coupled Codes

Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach the Shannon limit, as well as for finite lengths, since degree-2 variable nodes that result in high error floors can be completely avoided. However, to realize the promised good performance, one needs large blocklengths. This in turn implies a large latency and decoding complexity. For the memoryless binary erasure channel, we consider the decoding of spatially coupled codes through a windowed decoder that aims to retain many of the attractive features of belief propagation, while trying to reduce complexity further. We characterize the performance of this scheme by defining thresholds on channel erasure rates that guarantee a target erasure rate. We give analytical lower bounds on these thresholds and show that the performance approaches that of belief propagation exponentially fast in the window size. We give numerical results including the thresholds computed using density evolution and the erasure rate curves for finite-length spatially coupled codes.

LDPC codes for the cascaded BSC-BAWGN channel

We study the performance of LDPC codes over the cascaded BSC-BAWGN channel. This channel belongs to a family of binary-input, memoryless, symmetric-output channels, one that we call the {CBMSC(p, σ)} family. We analyze the belief propagation (BP) decoder over this channel by characterizing the decodable region of an ensemble of LDPC codes. We then give inner and outer bounds for this decodable region based on existing universal bounds on the performance of a BP decoder. We numerically evaluate the decodable region using density evolution. We also propose other message-passing schemes of interest and give their decodable regions. The performance of each proposed decoder over the CBMS channel family is evaluated through simulations. Finally, we explore capacity-approaching LDPC code ensembles for the {CBMSC(p, σ)} family.

Lattice-Based WOM Codes for Multilevel Flash Memories

We consider t-write codes for write-once memories with n cells that can store multiple levels. Assuming an underlying lattice-based construction and using the continuous approximation, we derive upper bounds on the worst-case sum-rate optimal and fixed-rate optimal n-cell t-write write-regions for the asymptotic case of continuous levels. These are achieved using hyperbolic shaping regions that have a gain of 1 bit/cell over cubic shaping regions. Motivated by these hyperbolic write-regions, we discuss construction and encoding of codebooks for cells with discrete support. We present a polynomial-time algorithm to assign messages to the codebooks and show that it achieves the optimal sum-rate for any given codebook when n = 2. Using this approach, we construct codes that achieve high sum-rate. We describe an alternative formulation of the message assignment problem for n≥ 3, a problem which remains open.

Protograph-Based LDPC Convolutional Codes for Correlated Erasure Channels

We consider terminated LDPC convolutional codes (LDPC-CC) constructed from protographs and explore the performance of these codes on correlated erasure channels including a single-burst channel (SBC) and Gilbert-Elliott channel (GEC). We consider code performance with a latency- constrained message passing decoder and the belief propagation decoder. We give theoretical bounds on the code efficiency over the SBC and describe a construction that achieves this bound.We show that the designed codes with belief propagation (BP) decoding perform as well as the regular LDPC-CCs presented in the literature on the binary erasure channel (BEC) and the GEC, while achieving significant gains on the SBC. In the case of windowed decoding, our codes perform much better than the best known regular LDPC-CCs over the BEC and the GEC, with very low decoding latencies.

Latency constrained protograph-based LDPC convolutional codes

We propose a windowed decoding scheme for protograph-based LDPC convolutional codes (LDPC-CC) that allows us to efficiently trade-off decoding performance for gains in latency. We study the performance of regular LDPC-CC with the windowed decoding scheme. In particular, we show that the class of LDPC-CC proposed in the literature with good belief propagation performance is ill-suited for windowed decoding. Further, we establish properties of code ensembles with good windowed decoding performance over erasure channels with and without memory.

Multilevel 2-cell t-write codes

We consider t-write codes for write-once memories with cells that can store multiple levels. Using worst-case sum-rate optimal 2-cell t-write code constructions for the asymptotic case of continuous levels, we derive 2-cell t-write code constructions that give good sum-rates for cells that support q discrete levels. A general encoding scheme for q-level 2-cell t-write codes is provided.

Windowed decoding of spatially coupled codes

Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach the Shannon limit, as well as for finite lengths, since degree-2 variable nodes that result in high error floors can be completely avoided. However, to realize the promised good performance, one needs large blocklengths. This in turn implies a large latency and decoding complexity. For the memoryless binary erasure channel, we consider the decoding of spatially coupled codes through a windowed decoder that aims to retain many of the attractive features of belief propagation, while trying to reduce complexity further. We characterize the performance of this scheme by defining thresholds on channel erasure rates that guarantee a target erasure rate. We give analytical lower bounds on these thresholds and show that the performance approaches that of belief propagation exponentially fast in the window size. We give numerical results including the thresholds computed using density evolution and the erasure rate curves for finite-length spatially coupled codes.