When residual belief-propagation (RBP), which is a kind of informed dynamic scheduling (IDS), is applied to low-density parity-check (LDPC) codes, the convergence speed in error-rate performance can be significantly improved. However, the RBP decoders presented in previous literature suffer from poor convergence error-rate performance due to the two phenomena explored in this paper. The first is the greedy-group phenomenon, which results in a small part of the decoding graph occupying most of the decoding resources. By limiting the number of updates for each edge message in the decoding graph, the proposed Quota-based RBP (Q-RBP) schedule can reduce the probability of greedy groups forming. The other phenomenon is the silent-variable-nodes issue, which is a condition where some variable nodes have no chance of contributing their intrinsic messages to the decoding process. As a result, we propose the Silent-Variable-Node-Free RBP (SVNF-RBP) schedule, which can force all variable nodes to contribute their intrinsic messages to the decoding process equally. Both the Q-RBP and the SVNF-RBP provide appealing convergence speed and convergence error-rate performance compared to previous IDS decoders for both dedicated and punctured LDPC codes.

This paper presents a practical technique that uses Ping's interleave(r)-division multiple access and single-user decoding to provide uncoordinated access for a family of binary-input binary-output multiple-access channels (MACs) including the OR-MAC where users' binary transmissions are combined with the logical OR operation. Information theoretic calculations provide the achievable sum-rates and optimal ones densities for these MACs. Because the required ones densities are significantly less than 50%, new nonlinear trellis code analysis and design techniques are introduced to provide the needed codes. Union bound techniques that predict the performance of these codes are also presented. Simulation results and a working FPGA implementation verify the performance and feasibility of the proposed nonlinear codes and overall multiple access scheme.

This paper describes and analyzes low-density parity-check code families that support variety of different rates while maintaining the same fundamental decoder architecture. Such families facilitate the decoding hardware design and implementation for applications that require communication at different rates, for example to adapt to changing channel conditions. Combining rows of the lowest-rate parity-check matrix produces the parity-check matrices for higher rates. An important advantage of this approach is that all effective code rates have the same blocklength. This approach is compatible with well known techniques that allow low-complexity encoding and parallel decoding of these LDPC codes. This technique also allows the design of programmable analog LDPC decoders. The proposed design method maintains good graphical properties and hence low error floors for all rates.

This paper presents serially concatenated trellis coded modulations (SCTCMs) that perform consistently close to the available mutual information for periodic erasure channel (PEC), periodic fading channel (PFC) and the 2 times 2 compound matrix channel. We use both the maximum-likelihood decoding criteria and iterative decoding criteria to design universal SCTCMs for the PEC and the PFC. For the space-time channel, by demultiplexing the symbols across the antennas, the proposed universal SCTCMs for the period-2 PFC deliver consistent performance over the eigenvalue skew of the matrix channel. Within the family of channels having the same eigenvalue skew, a time-varying linear transformation (TVLT) is used to mitigate the performance variation over different eigenvectors. The proposed space-time SCTCMs of 1.0, 2.0 and 3.0 bits per transmission require excess mutual information in the ranges 0.11-0.15, 0.23- 0.26 and 0.35-0.53 bits per antenna, respectively. Because of their consistent performance over all channels, the proposed codes will have good frame-error-rate (FER) performance over any quasi-static fading distribution. In particular, the codes provide competitive FER performance in quasi-static Rayleigh fading.

In this paper, we propose serially concatenated trellis coded modulations (SCTCMs) that perform consistently close to the available mutual information for the 2-by-2 compound matrix channel. The proposed SCTCMs use universal SCTCMs for the period-2 periodic fading channel in order to deliver consistent performance over eigenvalue skew. Within the family of channels having the same eigenvalue skew, a time-varying linear transformation (TVLT) is used to mitigate the performance variation over different eigenvectors. The proposed SCTCMs of 1, 2 and 3 bits per transmission require excess mutual information in the ranges 0.11- 0.15, 0.23-0.26 and 0.35-0.53 bits per antenna, respectively. Because of their consistent performance over all channels, the proposed codes will have good frame-error-rate (FER) performance over any quasi- static fading distribution. In particular, the codes provide competitive FER performance in quasi-static Rayleigh fading.

This paper presents trellis codes for the Z channel designed to maintain a relatively low ones density. These codes have applications in pulse-position modulation systems and as a solution for uncoordinated communication on the binary OR multiple-access channel (MAC). In this paper we consider the latter application to demonstrate the performance of the codes. The OR channel provides an unusual opportunity where single-user decoding permits operation at about 70% of the full multiple-access channel sum capacity. The interleaver-division multiple access technique applied in this paper should approach that performance with turbo solutions. However, the current paper focuses on very low latency codes with simple decoding, intended for very high speed (gigabits per second) applications. Namely, it focuses on nonlinear trellis codes that provide about 30% of the full multiple-access sum capacity at high speeds and with very low latency. These trellis codes are designed specifically for the Z-Channel that arises in a multiple-user OR channel, when the other users are treated as noise. In order to optimize the sum-capacity of the OR-MAC, the trellis code transmits codewords with a ones density much less than 50%. Also, a union bound technique that predicts the performance of these codes is presented. Results from simulations and a working FPGA implementation are shown.

This paper extends the near-capacity performance of serially-concatenated convolutional codes under AWGN to periodically time-varying channels. In particular, we propose serially-concatenated trellis-coded modulations (SCTCMs) that perform consistently close to channel capacity under periodic erasures as well as under AWGN, without sacrificing AWGN channel performance. The proposed 0.5 bits/symbol and 1.5 bits/symbol SCTCM schemes are robust with respect to periodic time-variations with a period of two-symbols.