Implementing the Han–Kobayashi Scheme Using Low Density Parity Check Codes Over Gaussian Interference Channels

Abstract

We focus on Gaussian interference channels (GICs) and study the Han-Kobayashi (HK) coding strategy for the twouser case with the objective of designing implementable (explicit) channel codes. Specifically, low-density parity-check (LDPC) codes are adopted for use over the channel, their benefits are studied and suitable codes are designed. Iterative joint decoding is used at the receivers, where independent and identically distributed (i.i.d.) channel adapters are used to prove that loglikelihood-ratios (LLRs) exchanged among the nodes of the Tanner graph enjoy symmetry when BPSK or QPSK with Gray coding is employed. This property is exploited in the proposed code optimization algorithm adopting a random perturbation technique. Code optimization and convergence threshold computations are carried out for different GICs employing finite constellations by tracking the average mutual information. Furthermore, stability conditions for the admissible degree distributions under strong and weak interference levels are determined. Via examples, it is observed that the optimized codes using BPSK or QPSK with Gray coding operate close to the capacity boundary for strong interference. For the case of weak interference, it is shown that nontrivial rate pairs are achievable via the newly designed codes which are not possible by single user codes with time-sharing. Performance of the designed codes is also studied for finite block lengths through simulations of specific codes picked with the optimized degree distributions with random constructions, where, for one instance, the results are compared with those of some structured designs.

Soft-Decoding-Based Strategies for Relay and Interference Channels: Analysis and Achievable Rates Using LDPC Codes

“…Theoretical results on the HK strategy involve randomly-generated, unstructured component codes (within the rate-splitting framework), whose decoding requires high-complexity algorithms. To reduce complexity, these codes could be replaced by lower-complexity ones (e.g., LDPC codes [66]), effectively introducing a second form of structure, beyond rate splitting (which facilitates partial decoding). However, it is likely that soft-IC-BP, whose LDPC codes contribute their structure simultaneously to partial decoding and low-complexity algorithms, enjoys a practical advantage.…”

LDPC Code Design for Fading Interference Channels

“…At receiver j, the outgoing LLR from the state node corresponding to the ith bit of the message k is calculated as [5]…”

“…Stability condition characterizes the convergence behavior of iterative decoders under the assumption that a low error probability has already been achieved. It is essentially utilized for eliminating error floors [14], and it has been studied previously for joint iterative decoding in multiuser scenarios [10] and [5] for broadcast and unfaded IC with real channel gains, respectively. Here, we extend the results to fading ICs under joint iterative decoding.…”

“…In [4], the authors present a concrete coding scheme to approach the theoretically achievable rate pairs by using LDPC codes concatenated with convolutional codes. Implementation of the HK coding scheme for a general GIC based on LDPC codes is studied in [5] where the authors perform decoding threshold analysis by utilizing Monte Carlo simulations, and show that with their proposed code design method, rate pairs close to the HK inner bounds can be attained. Furthermore, the authors in [6] propose a polar coding scheme for ICs, and show theoretically that fully joint decoder for the HK coding scheme can be simplified by employing partial joint decoders at the receivers, which is more favorable to polar coding.…”

Code design for binary energy harvesting channel

“…We terminate the optimization procedure if no improvement can be obtained after a predetermined number of iterations. Further details about the LDPC code design by using random perturbation technique can be found in [11], [15].…”