Code Design for Iterative Decoding of Multilevel Codes

Abstract

The code design problem for multilevel coded modulation with iterative decoding (MLCM-ID) has been left unsolved over a decade. In this paper, we define the code design criterion for MLCM-ID based on a novel concept-parametrically-mapped EXIT (PM-EXIT) function. We derive the EXIT functions for MLCM-ID, and present the mathematical work by which the three area theorems of PM-EXIT function are proved. This gives theoretical support of the curve-fitting techniques used in MLCM-ID, and also provides firm proof that the PM-EXIT function design rule allows in principle capacity-achieving code assignment. The simulation results perfectly match the theoretical analysis, and also confirm that the design rule proposed fully exploits the flexibility of MLCM-ID in the choice of codes. Both in theory and simulations, our code design is verified.

Parity Information Aided Iterative Multistage Decoding for Multilevel LDPC Codes

“…MSD-ID [2] consists in passing soft extrinsic information among all L decoding levels, then starting over the process by sending the = L − 1 level's soft extrinsic information to the first level = 0, which will pass the new level = 0 extrinsic information forward. The decoding is finalized when a desired number of iterations T is completed.…”

“…Iterative demodulation and decoding (ID) schemes for many coded modulations have been proven to decrease error probability rates in comparison to the conventional decoding procedures [2] [3]. Wang and Burr [2] proposed the union of multilevel codes and iterative decoding.…”

“…Iterative demodulation and decoding (ID) schemes for many coded modulations have been proven to decrease error probability rates in comparison to the conventional decoding procedures [2] [3]. Wang and Burr [2] proposed the union of multilevel codes and iterative decoding. They have obtained promising results regarding error probability performance when applying multistage iterative demodulation and decoding (MSD-ID) to multilevel convolutional and turbo codes.…”

Simultaneous packet transmission (SPT) using multiple streams

“…A SPT scheme employs a ‐ary overall constellation for transmission with . The proposed SPT technique partitions the overall constellation similar to Ungerboeck set partitioning [19] and employs multiple streams similar to multi‐level codes (MLCs) [20, 21]. However, as explained later, the SPT significantly differs from Ungerboeck codes and traditional MLCs [20, 21].…”

“…The proposed SPT technique partitions the overall constellation similar to Ungerboeck set partitioning [19] and employs multiple streams similar to multi‐level codes (MLCs) [20, 21]. However, as explained later, the SPT significantly differs from Ungerboeck codes and traditional MLCs [20, 21]. It is demonstrated here that the SPT is capable of significantly increasing the throughput of a communication system.…”