Dmitri V. Truhachev

An analysis of the block error probability performance of iterative decoding

Asymptotic iterative decoding performance is analyzed for several classes of iteratively decodable codes when the block length of the codes N and the number of iterations I go to infinity. Three classes of codes are considered. These are Gallagers regular low-density parity-check (LDPC) codes, Tanners generalized LDPC (GLDPC) codes, and the turbo codes due to Berrou et al. It is proved that there exist codes in these classes and iterative decoding algorithms for these codes for which not only the bit error probability P/sub b/, but also the block (frame) error probability P/sub B/, goes to zero as N and I go to infinity.

To the Theory of Low-Density Convolutional Codes. II

A theoretical and experimental analysis of iterative decoding of low-density convolutional (LDC) codes is given. Two families are investigated: homogeneous LDC codes and a convolutional code version of turbo-codes.

Some Results Concerning the Design and Decoding of Turbo-Codes

We consider the following problems related to the construction and analysis of turbo-codes: asymptotic behavior of interleavers (permutors), asymptotic behavior of the minimum distance, and also some examples of practical application of the developed methods to concrete turbo-codes.

A Two-Stage Capacity-Achieving Demodulation/Decoding Method for Random Matrix Channels

Iterative processing for linear matrix channels, aka turbo equalization, turbo demodulation, or turbo code-division multiple access (CDMA), has traditionally been addressed as the concatenation of conventional error control codes with the linear (matrix) channel. However, in several situations, such as CDMA, multiple-input-multiple-output (MIMO) channels, orthogonal frequency-division multiplexing (OFDM), and intersymbol-interference (ISI) channels, the channel itself either contains inherent signal redundancy or such redundancy can readily be introduced at the transmitter. For such systems, iterative demodulation of the linear channel exploiting this redundancy using simple iterative cancellation demodulators, followed by conventional feedforward error control decoding, provides a low-complexity, but extremely efficient decoding alternative. This two-stage demodulator/decoder outperforms more complex turbo CDMA methods for equal power modes (users). Furthermore, it is shown that arbitrary numbers of modes can be supported if an unequal power distribution is adopted. These power distributions are nested, which means that additional modes can be added without disturbing an existing mode population. The main result shows that these nested power distributions enable the two-stage receiver to approach the Shannon capacity of the channel to within less than one bit for any signal-to-noise ratio (SNR).

Multiple Access Demodulation in the Lifted Signal Graph With Spatial Coupling

Demodulation in a random multiple access channel is considered where the signals are chosen uniformly randomly with unit energy. It is shown that by lifting (replicating) the graph of this system and randomizing the graph connections, a simple iterative cancellation demodulator achieves the same performance as an optimal symbol-by-symbol detector of the original system. The iterative detector has a complexity that is linear in the number of users, while the direct optimal approach is known to be NP-hard. However, the maximal system load of this lifted graph is limited to

A portable MIMO testbed and selected channel measurements

\alpha , even for large signal-to-noise ratios (SNRs)—the system is interference limited. Spatial coupling between subsequent lifted graphs is introduced, and anchoring the initial graphs, the achievable system load

Distance Bounds for Periodically Time-Varying and Tail-Biting LDPC Convolutional Codes

\alpha

Analysis of a Random Channel Access Scheme with Multi-Packet Reception

can go to infinity as the SNR goes to infinity. Our results apply to several well-documented system proposals, such as interleave-division multiple access, partitioned spreading, and certain forms of multiple-input multiple-output communications.

Generalized superposition modulation and iterative demodulation: a capacity investigation

A portable multiple-input multiple-output (MIMO) testbed that is based on field programmable gate arrays (FPGAs) and which operates in the 902–928 MHz industrial, scientific, and medical (ISM) band has been developed by the High Capacity Digital Communications (HCDC) Laboratory at the University of Alberta. We present a description of the HCDC testbed along with MIMO channel capacities that were derived from measurements taken with the HCDC testbed for three special locations: a narrow corridor, an athletics field that is surrounded by a metal fence, and a parkade. These locations are special because the channel capacities are different from what is expected for a typical indoor or outdoor channel. For two of the cases, a ray-tracing analysis has been performed and the simulated channel capacity values closely match the values calculated from the measured data. A ray-tracing analysis, however, requires accurate geometrical measurements and sophisticated modeling for each specific location. A MIMO testbed is ideal for quickly obtaining accurate channel capacity information.

On the minimum distance of low-density parity-check codes with parity-check matrices constructed from permutation matrices

Existence type lower bounds on the free distance of periodically time-varying LDPC convolutional codes and on the minimum distance of tail-biting LDPC convolutional codes are derived. It is demonstrated that the bound on free distance of periodically time-varying LDPC convolutional codes approaches the bound on free distance of general (nonperiodic) time-varying LDPC convolutional codes as the period increases. The proof of the bound is based on lower bounding the minimum distance of corresponding tail-biting LDPC convolutional codes, which is of interest in its own right.