Research Interests

My research interests lie in the following broad areas

  • Digital Communications
  • Information Theory
  • Data Compression
  • Coding Theory and Practice



Spatially Coupled LDPC (SC-LDPC) Codes

Recently, iterative processing on spatially coupled sparse graphs has received a lot of attention in the literature. The concept of coupling a sequence of identical small structured graphs into a chain of length L with improved properties, first demonstrated in the context of low-density parity-check (LDPC) convolutional codes, has been shown to be applicable to a diverse list of topics, such as compressed sensing, multiuser communication, quantum codes, relay channels, wiretap channels, and models in statistical physics.

In this project, we showed that SC-LDPC codes have a unique combination of capacity approaching thresholds and linear growth of minimum distance with constraint length, thereby promising excellent performance at low and high signal-to-noise ratios. The figure to the right shows the remarkable “wave-like decoding” characteristics of SC-LDPC codes - as we iterate the decoder (curves from top to bottom) the probability of error decays rapidly from the ends of the chain to the center.

Selected publications:

  • D. G. M. Mitchell, M. Lentmaier, and D. J. Costello, Jr., “Spatially Coupled LDPC Codes Constructed from Protographs,” IEEE Transactions on Information Theory, vol. 61, no. 9, pp. 4866-4889, Sep. 2015.
  • K. Huang, D. G. M. Mitchell, L. Wei, X. Ma, and D. J. Costello, Jr., “Performance Comparison of LDPC Block and Spatially Coupled Codes over GF(q),” IEEE Transactions on Communications, vol. 63, no. 3, pp. 592-604, Mar. 2015.
  • D. J. Costello, Jr., L. Dolecek, T. E. Fuja, J. Kliewer, D. G. M. Mitchell, and R. Smarandache, “Spatially Coupled Sparse Codes on Graphs - Theory and Practice,” IEEE Communications Magazine, vol. 52, no. 7, pp. 168-176, July 2014.
  • D. G. M. Mitchell, M. Lentmaier, and D. J. Costello Jr., “On the Minimum Distance of Generalized Spatially Coupled LDPC Codes”, Proc. IEEE International Symposium on Information Theory, Istanbul, Turkey, July 2013.
  • L. Wei, D. G. M. Mitchell, T. E. Fuja, and D. J. Costello, Jr., “Design of Spatially Coupled LDPC Codes Over GF(q) for Windowed Decoding,” IEEE Transactions on Information Theory, vol. 62, no. 9, pp. 4781-4800, Sept. 2016.


Lossy Source Coding

Lossy coding of speech, high quality audio and video, and so on, is widespread today. Compared to lossless compression, where the source must be reconstructed identically from its compressed version, the lossy source compression problem requires the reconstructed data to be correct only up to some specified distortion measure. In this project, we investigate the distortion performance of a practical class of protograph-based, spatially coupled low density generator matrix (SC-LDGM) codes and show that they have distortion performance very close to the rate-distortion (RD) limit, as the “coupling length” L grows, with low-to-moderate encoding latency.

Selected publications:

  • A. Golmohammadi, J. Kliewer, D. J. Costello, Jr., and D. G. M. Mitchell, “On the Windowed Encoding Complexity of SC-LDGM Codes for Lossy Source Compression,” Proc. International Symposium on Information Theory and Its Applications, Monterey, CA, Oct. 2016.
  • A. Golmohammadi, D. G. M. Mitchell, J. Kliewer, and D. J. Costello, Jr., “Windowed Encoding of Spatially Coupled LDGM Codes for Lossy Source Compression,” Proc. IEEE International Symposium on Information Theory, Barcelona, Spain, July 2016.


Low-Complexity Implementation of LDPC Decoders

Quasi-cyclic (QC) low-density parity-check (LDPC) codes are of great interest to code designers, since they can be encoded with low complexity using simple feedback shift-registers and their structure leads to efficiencies in decoder design. Moreover, QC codes can be shown to perform well compared to random codes for moderate block lengths. The conventional algorithms for decoding LDPC codes rely on (various forms of) the belief-propagation (BP) algorithm and involve iterative message-passing (MP) on the code’s bipartite Tanner graph, consisting of check nodes and variable nodes. In a hardware implementation of any MP algorithm, messages are inevitably quantized, i.e., represented with a fixed number of bits. As a result, a practical implementation may experience performance that is inferior to models in which quantization is not considered.

Some of the results published in this project include: 1) A code-independent performance bound for quantized low-density parity-check (LDPC) decoders; 2) a method for constructing QC-LDPC codes using a two-step lifting procedure based on a protograph, that results in provably improved minimum distance and girth properties; and 3) techniques to construct high-rate efficiently encodable LDPC codes with improved optimized absorbing set spectrum by “breaking” problematic substructures (see figure on right).

Selected publications:

  • H. Hatami, D. G. M. Mitchell, D. J. Costello, Jr., and T. Fuja, “Performance bounds for Quantized LDPC Decoders based on Absorbing Sets,” Proc. IEEE International Symposium on Information Theory, Barcelona, Spain, July 2016.
  • D. G. M. Mitchell and E. Rosnes, “Edge Spreading Design of High Rate Array-Based SC-LDPC Codes,” Proc. IEEE International Symposium on Information Theory, pp. 2950-2954, Aachen, Germany, June 2017.
  • L. Chen, S. Mo, D. J. Costello, Jr., D. G. M. Mitchell, and R. Smarandache, “A Protograph-Based Design of Quasi-Cyclic Spatially Coupled LDPC Codes,” Proc. IEEE International Symposium on Information Theory, pp. 1683-1687, Aachen, Germany, June 2017.
  • D. G. M. Mitchell, R. Smarandache, and D. J. Costello, Jr., “Quasi-Cyclic LDPC Codes Based on Pre-lifted Protographs,” IEEE Transactions on Information Theory, vol. 60, no. 10, pp. 5856-5874, Oct. 2014.


Robust Error Control for Time-Varying Channels

It is often desirable in applications that experience changing channel conditions to be able to employ a variety of code rates with the same decoding hardware. One method to achieve this is to puncture a low rate mother code. In this scheme, the transmitter punctures coded symbols, and, as a result of having fewer transmitted code symbols, the code rate is increased. Coding schemes that use this technique are known as rate-compatible punctured codes.

In this project, we perform a random puncturing analysis of low-density parity-check (LDPC) code ensembles, deriving a simple analytic expression for the iterative belief propagation (BP) decoding threshold of a randomly punctured LDPC code ensemble on the binary erasure channel (BEC) and show that, with respect to the BP threshold, the strength and suitability of an LDPC code ensemble for random puncturing is completely determined by a single constant. We also construct codes that show remarkably robust performance over a variety of coding rates (see the figure on the right).

Selected publications:

  • D. G. M. Mitchell, M. Lentmaier, A. E. Pusane, and D. J. Costello, Jr., “Randomly Punctured LDPC Codes,” IEEE Journal on Selected Areas in Communications, vol. 34, no. 2, pp. 408-421, Feb. 2016.
  • H. Zhou, D. G. M. Mitchell, N. Goertz, and D. J. Costello, Jr., “Robust Rate-Compatible Punctured LDPC Convolutional Codes,” IEEE Transactions on Communications, vol. 61, no. 11, pp. 4428-4439, Nov. 2013.
  • H. Zhou, D. G. M. Mitchell, N. Goertz, and D. J. Costello Jr., “A Puncturing Algorithm for Rate-Compatible LDPC Convolutional Codes”, winner of best student paper, Proc. International Symposium on Turbo Codes and Iterative Information Processing, Gothenburg, Sweden, Aug. 2012.


High-rate Coupled Turbo/LDPC Codes for Optical/Streaming Applications

Braided convolutional codes (BCCs) are a type of parallel-concatenated convolutional code in which the parity outputs of one component encoder are fed back and used as inputs to the other component encoder at the succeeding time unit (see the figure on the right). Blockwise BCCs have the advantage that both the encoding and decoding can be performed in a fashion similar to turbo codes for which efficient hardware implementations exist. Based on their excellent performance in both the waterfall and error-floor regions, the robustness of this performance to puncturing, and the ability to employ a low-complexity soft decision decoding algorithm at high code rates, blockwise BCC codes appear to be worthy competitors to the product-like codes that have recently been proposed for high-speed optical communication.

Selected publications:

  • M. Zhu, D. G. M. Mitchell, M. Lentmaier, D. J. Costello, Jr., and B. Bai, “Braided Convolutional Codes with Sliding Window Decoding,” IEEE Transactions on Communications, vol. 65, no. 9, pp. 3645-3658, Sept. 2017.
  • D. J. Costello, Jr., M. Lentmaier, and D. G. M. Mitchell, “New Perspectives on Braided Convolutional Codes,” Proc. International Symposium on Turbo Codes and Iterative Information Processing, Brest, France, Sept. 2016.
  • D. G. M. Mitchell, A. E. Pusane, M. Lentmaier, and D. J. Costello, Jr., “On the Block Error Rate Performance of Spatially Coupled LDPC Codes for Streaming Applications,” Proc. IEEE Information Theory Workshop, Cambridge, UK, Sept. 2016.
  • M. Zhu, D. G. M. Mitchell, M. Lentmaier, D. J. Costello, Jr., and B. Bai, “Window Decoding of Braided Convolutional Codes”, Proc. IEEE Information Theory Workshop, Jeju Island, Korea, Oct. 2015.


Acknowledgements

The material described above is based upon work supported in part by the National Science Foundation under Grant Nos. CCF-1161754 and ECCS-1710920, and in part by the National Aeronautics and Space Administration (NASA) Training Grant NNX15AL51H.