A novel class of bit-flipping (BF) algorithm for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are referred to as gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. The proposed algorithms exhibit better decoding performance than known BF algorithms, such as the weighted BF algorithm or the modified weighted BF algorithm for several LDPC codes.

Gradient descent bit flipping algorithms for decoding LDPC codes

A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon's visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon's capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated space-time and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted.

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Turbo Decoding and Detection for Wireless Applications

A novel class of bit-flipping (BF) algorithms for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are called gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. Based on gradient descent formulation, the proposed algorithms are naturally derived from a simple nonlinear objective function.

It was recently shown that the reliability ratio based bit-flipping (RRWBF) decoding algorithm for low-density parity-check (LDPC) codes performs best among existing bit-flipping-based algorithms. A new version of this algorithm is proposed such that decoding time is significantly reduced, especially when the iteration number is small and the code length is large. Simulation results showed the proposed version has up to 2322.39%, 823.90%, 511.79%, and 261.92% speedup compared to the original algorithm on a UNIX workstation for 10, 30, 50, and 100 iterations. It is thus much more efficient to adopt this version for simulation and hardware implementation. Moreover, this version of the RRWBF algorithm provides a more intuitive way of interpreting its superior performance over other bit-flipping-based algorithms.

Implementation-efficient reliability ratio based weighted bit-flipping decoding for LDPC codes

In this paper, the characteristics of irregular quasicyclic-low-density parity check (QC-LDPC) codes are examined when they are applied on a highly impulsive noise channel, such as the power-line-communications (PLC) channel. We study two decoding algorithms: 1) the sum product and 2) the bit-flipping algorithm, and how they affect the system's performance. LDPC codes are introduced in combination with other coding schemes, such as Reed-Solomon and convolutional codes. We propose irregular QC-LDPC codes as outer codes for the PLC channel in combination with Reed-Solomon codes, due to their decoding characteristics. In addition, various code rates are used for each different coding scenario. We also test how common Reed-Solomon codes affect the system's performance, such as the RS(63, 53), RS(511, 431), RS(127, 107), and RS(255, 239) codes. Furthermore, we propose an altered version of the sum-product decoding algorithm to enable its operation when QC-LDPC codes are used as the outer coding scheme in combination with Reed-Solomon codes. Regarding the system's design, the orthogonal frequency-division multiplexing transmission technique is utilized. We also take Zimmermann's model into consideration for the PLC channel and Middleton's noise model.

Mitigation of Impulsive Noise Effect on the PLC Channel With QC–LDPC Codes as the Outer Coding Scheme

A novel reliability ratio based weighted bit-flipping decoding scheme is proposed for low-density parity-check codes. A coding gain of 1 dB is achieved in comparison to the weighted bit-flipping scheme, when communicating over an AWGN channel, while maintaining the same decoding complexity.

/pdf/reliability-ratio-based-weighted-bit-flipping-decoding-for-2244abrida.pdf

Reliability ratio based weighted bit-flipping decoding for low-density parity-check codes

Joint source-coding, channel-coding and modulation schemes based on variable length codes, inphase-quadrature phase interleaved trellis coded modulation (TCM) and turbo TCM (TTCM) schemes are proposed. A significant coding gain and a lower error floor are achieved without bandwidth expansion.

/pdf/joint-source-coding-channel-coding-and-modulation-schemes-22hdgvti8b.pdf

F. Guo

Papers

Reliability ratio based weighted bit-flipping decoding for low-density parity-check codes

Joint source-coding, channel-coding and modulation schemes for AWGN and Rayleigh fading channels