Direct Space-Time GF(q) LDPC Modulation
ABSTRACT Wireless communication using multiple-input multiple-output (MIMO) systems improves throughput and enhances reliability for a given total transmit power. In this paper, potential performance gains are investigated via a direct Galois field [GF(q)] low-density parity-check (LDPC) space-time coding and modulation scheme. The field order q is chosen such that the number of bits per GF(q) LDPC symbol matches the number of bits per space-time symbol. The result is an elegant coding and decoding scheme that leverages the powerful LDPC iterative decoding technique. Results for 2, 3, and 4 transmitter systems with relatively short block lengths of around 2000 bits are provided, demonstrating frame-error- rate performances as close as 0.5 dB to the probability of outage upper bound.
Conference Paper: Rate adaptive non-binary LDPC codes with low encoding complexity[Show abstract] [Hide abstract]
ABSTRACT: For error-correction codes, the optimal coding rate can vary and depend on factors including channel, time-varying fading, environmental interference, power, bandwidth allocation, communication content, and application. Rate adaptive coding schemes are thus important for robust communications. This writeup proposes and studies a rate adaptive low density parity check (LDPC) coding scheme using non-binary Galois fields (GF). The algorithm uses a single low complexity encoding structure, but maintains strong near-capacity performance at arbitrary rational rates. The rate adaptive encoder can be used in a space-time code for multiple-input multiple-output (MIMO) communication systems and is shown to achieve near capacity performance at various rates and different MIMO configurations.Signals, Systems and Computers (ASILOMAR), 2011 Conference Record of the Forty Fifth Asilomar Conference on; 01/2011
Conference Paper: Joint decoding of multiple non-binary LDPC codewords[Show abstract] [Hide abstract]
ABSTRACT: We develop a belief-propagation (BP) decoder for the joint decoding of multiple codewords which belong to the same non-binary LDPC code. Decoding is based on soft information in form of joint channel-posterior probabilities of all codeword symbols. We extend the BP algorithm for q-ary LDPC codes such that the FFT-based check node processing is preserved and the complexity remains manageable. This joint decoding is useful in settings in which multiple codewords are transmitted in a non-orthogonal way over the same channel, including multiple-access with packet collisions, physical-layer network coding and multi-resolution broadcasting. We show in an example that joint decoding can be far superior to separate decoding.2014 ICC - 2014 IEEE International Conference on Communication Workshop (ICC); 06/2014
Conference Paper: Efficiently encodable non-binary generalized LDPC codes[Show abstract] [Hide abstract]
ABSTRACT: This writeup examines the construction and performance of non-binary generalized low-density parity-check (GLDPC) codes. Recently, binary GLDPC coding techniques have been shown to improve upon conventional low-density parity-check (LDPC) codes by increasing the minimum codeword length, reducing error floors, and improving performance at lower coding rates. GLDPC codes replace the parity-check constraints of a standard LDPC code with stronger codes, e.g. short linear block codes. At the same time, non-binary LDPC codes have been shown to outperform their binary LDPC counterpart for shorter codeword lengths and for space-time coding applications in multiple-input multiple-output (MIMO) systems. Therefore, in contrast to previous works which have examined binary GLDPC codes, this paper explores non-binary GLDPC codes to combine all of the aforementioned benefits of non-binary LDPC and binary GLDPC codes. Additionally, non-binary GLDPC codes can attain higher coding rates than the counterpart binary GLDPC codes. We first propose a class of GLDPC codes with low encoding complexity, where the number of encoding operations scales linearly with the codeword length. An example is provided to illustrate the performance and complexity benefits of GLDPC codes over non-binary LDPC codes at lower coding rates. In particular, a GF(4) GLDPC code is shown to outperform a strong GF(256) LDPC code while requiring approximately 9x less operations per information bit. It is also demonstrated that with the appropriate parameters, the non-binary GLDPC codes outperform non-binary LDPC codes with respect to both the error floor and waterfall performance. Furthermore, it is shown that performance remains strong for the same coding rate as the constellation changes; this result contrasts previous works which have demonstrated that for non-binary LDPC codes, optimal parameters such as the column weight need to be adjusted for different constellations.2013 Asilomar Conference on Signals, Systems and Computers; 11/2013