Recent Advances in Turbo Code Design and Theory

Abstract

The interleaver, which combines the outputs of turbo decoders, is essential in determining the performance of turbo codes and is the main source of decoder computation and implementation complexity. ABSTRACT | The discovery of turbo codes and the subsequent rediscovery of low-density parity-check (LDPC) codes represent major milestones in the field of channel coding. Recent advances in the design and theory of turbo codes and their relationship to LDPC codes are discussed. Several new interleaver designs for turbo codes are presented which illustrate the important role that the interleaver plays in these codes. The relationship between turbo codes and LDPC codes is explored via an explicit formulation of the parity-check matrix of a turbo code, and simulation results are given for sum product decoding of a turbo code.

EXIT Charts for System Design and Analysis

“…be independent [61]. Furthermore, using longer interleavers typically leads to more Gaussian-like LLR distributions and hence the system's performance may approach Shannon's capacity limit more closely [25].…”

“…Furthermore, using longer interleavers typically leads to more Gaussian-like LLR distributions and hence the system's performance may approach Shannon's capacity limit more closely [25]. The interleaver has been shown to be an essential component of iterative decoding and its length is the dominant factor in determining the code's distance properties, which in turn determines the asymptotic performance of iteratively decoded systems [61][62][63]. The goal of the interleaver is to improve the distance properties of the code [64].…”

“…In summary, the interleaver design substantially affects both the BER "turbo cliff" as well as the error floor. Several interleaver designs were proposed in [61] for increasing the minimum Hamming distance of parallel concatenated codes. According to [61], at high SNR values, the asymptotic BER of a turbo code decreases linearly upon increasing the interleaver length.…”

Iterative Decoding for Redistributing Energy Consumption in Wireless Sensor Networks

“…The above-mentioned re-arrangement operations are necessary because the achievable iterative decoding performance and, hence, the achieveable PER performance are commensurate with the degree to which the chip ordering in c appears to be randomized [13]. Note that an improved PER performance can be expected for longer PHY payloads, since the interleaver's ability to pseudo-randomly re-arrange the order of the chips in the sequence c is commensurate with its length N p .…”

“…This motivates the use of so-called deterministic interleavers [13] in the augmented PHY. Rather than using raw interleaver mappings Π, deterministic interleavers require the storage of only a small number of parameters, which unambiguously describe a particular way of re-arranging the chips in the sequence c. Deterministic interleavers therefore require less ROM than random interleavers.…”