Turbo-principle-based decoding in LDPC and turbo codes

Channel coding is a powerful technique to get reliable communication over noisy channels. The performance of the coding system is bounded by Shannon limit. Lately, the proposal of parallel-concatenated convolutional code (PCCC), called turbo codes, has increased the interest in the coding area since these codes give most of the gain promised by the channel-coding theorem. Because turbo codes did not actually results from applying a pre existing theory, most of their outstanding features remain to be explained. The objective of this paper is to introduce turbo codes and the key elements to their superiority. Open problems and unresolved issues will be highlighted.

2008 5th International Symposium on Turbo Codes and Related Topics, 2008

The convergence of iterative decoding schemes is considered. The class of dually coupled codes is recalled, being a super class to both Turbo and LDPC codes. It is proven that the output L-values of a Turbo decoder cannot grow to infinity, while those of an LDPC decoder can. Finally, a new decoder parameter is introduced by which the convergence behavior can be controlled.

This paper introduces the effect of decoding iterations on the performance of a new class of convolutional codes called Turbo Code. Turbo Code encoder is built using a parallel concatenation of two Recursive Systematic Convolutional (RSC) codes. The associated decoder is implemented using a feedback-decoding rule in an iterative manner.

Turbo codes play a major role in channel error correction schemes used in wireless communications. Turbo codes emerged in 1993 and since that time they dominate the research in error control coding together with low-density parity-check codes. Due to their remarkable performances, turbo code and low density parity check code have been accepted to a number of standards by many organizations which decide to include turbo code and low density parity check into their new standards after these codes were proven successful in a many of missions. In this paper, the calculation and comparison of performance versus complexity for those two techniques of channel coding was done. For a fair comparison, the performance and complexity should be compared together. The complexity was calculated by counting the number of clock cycles need to complete the decoding algorithm. This comparison is used as a guiding lines of using either turbo code or the low density parity check in specific communicatio...

6th Joint IFIP Wireless and Mobile Networking Conference (WMNC), 2013

This work considers the bit error rate (BER) performance of turbo product codes (TPC) constituted from low density parity check (LDPC) codes with non-sequential decoding (NSD). The BER of the TPC-LDPC is evaluated for LDPC codes with various rates and sizes using the bit f lipping (BF) and sum product (SP) algorithms. Monte Carlo simulation results demonstrate that NSD can provide a remarkable additional coding gain of about 35 dB using the BF algorithm as compared to sequential decoding. Moreover, simulation results confirmed that the order of the turbo and LDPC decoding iterations can have a noticeable impact on the BER. Similarly, the NSD of TPC-LDPC codes using the SP algorithm offered noticeable improvement for particular codes.

Turbo codes are becoming a widespread and mature coding scheme, as they are included in the standards of the third generation of mobile communication systems [1]. They were originally shown to perform very well from long to medium sizes of blocks [2] thanks to their good codewords weight distribution – i.e. good free distance and low multiplicity of low weight codewords -and to the ability of iterative decoding to perform near optimum decoding in the sense of Maximum Likelihood (ML). However in recent releases of the standards they are also intended to be used for short sizes of blocks, down to 40 bits, and in those cases turbo decoding no longer provides ML decoding. The aim of this paper is first to quantify the suboptimality of turbo decoding when applied to short Parallel Concatenated Convolutional Codes as compared to ML decoding, and then to provide a way to improve the turbo decoding process in those cases. In this view the ML bounds of the considered short turbo codes are de...

IEEE Transactions on Communications, 2000

In this letter, we propose a new decoding algorithm to improve the bit error rate performance of the hard-input hard-output (HIHO) turbo product codes (TPC) with hard iterative decoding. The proposed algorithm iteratively, but not sequentially, decodes the received TPC blocks based on the reliability of the constituent codes. Simulation results confirm a noticeable coding gain improvement using the proposed decoding process with respect to standard HIHO TPC decoding. An efficient implementation of the new technique offers a negligible additional complexity when the channel-bit error probability is less than 10 −2 .

2010 National Conference On Communications (NCC), 2010

Turbo codes and Low Density Parity Check (LDPC) codes have been shown to be practical codes that can approach Shannon capacity in several communication systems. In terms of performance and implementation complexity, LDPC codes and turbo codes are highly comparable, especially at coding rates around 1/2. In many recent wireless standards such as 3GPP LTE and WiMax, both turbo and LDPC codes have been recommended at the encoder. However, the decoder for turbo codes involves trellises and the BCJR algorithm, while the decoder for LDPC codes uses sparse graphs and the message passing algorithm. Therefore, in several implementations, a designer is forced to implement either the turbo decoder or the LDPC decoder. The main idea behind this work is to enable the implementation of both decoders using a common architecture. We view the constituent convolutional code in a turbo code as a block code, and construct a sparse parity check matrix for it. Then, the sparse matrix and the associated bipartite graph are used for decoding the convolutional code by soft message passing algorithms. Simulation results show a manageable degradation in performance with a reduction in complexity.

2013

Use of turbo codes is more popular in most of the wireless applications, because of its greater Error control ability. The BER performance reaches to the Shannon's channel capacity limit. Turbo code implementation using SISO decoders with iterative MAP decoding algorithms introduces large time delay to recover the transmitted information bits. This results in increasing Wi-Max system complexity and storage requirement (Memory size). In this paper, the efforts have been made to propose the methods for effective termination of iterations to make the decoder efficient, in terms of reduction in the time delay and the requirement of memory size while maintaining the BER performance. Authors have propose various termination techniques which help in reducing the complexity as compare to conventional MAP decoding algorithm for same BER performance.

2006

The convergence rate of LDPC decoding is comparatively slower than turbo code decoding: 25 LDPC iterations versus 8-10 iterations for turbo codes. Recently, Mansour proposed a 'turbo-schedule' to improve the convergence rate of LDPC decoders. In this letter, we first extend the turbo-scheduling principle to the check messages. Second, we show analytically that the convergence rate of both turbo-schedules is about twice as fast as the standard message passing algorithm for most LDPC codes.

In this paper, the sub-optimality of iterative decoding of BCH product codes also called Block Turbo Codes (BTC) is investigated. Lower bounds on Maximum Likelihood (ML) decoding performances for Packet Error Rate (PER) and Bit Error Rate (BER) are given in order to evaluate the optimality of the iterative decoding algorithm. On an AWGN (Additive White Gaussian Noise) channel, simulations show that the turbo decoding of product code is sub-optimal for long codes, even when the elementary codes are decoded in an optimal way. We propose to apply after turbo decoding a scheme to combat this sub-optimality. This scheme is described, the performance gain is then evaluated on Gaussian and Rayleigh channels.

JPL TDA Progress …, 1996

2010

Turbo coding is the most commonly used error correcting scheme in wireless systems resulting in maximum coding gain. In this paper, a comparative study of the symbol-bysymbol maximum a posteriori (MAP) algorithm, its logarithmic versions, namely, Log-MAP and Max-Log-MAP decoding algorithms used in SISO Turbo Decoders are analyzed. The performance of Turbo coding algorithms are carried out in terms of bit error rate (BER) by varying parameters such as Frame size, number of iterations and choice of interleaver. Keywords-: Iterative decoding; MAP decoding; Turbo Codes.

Elsevier eBooks, 2014

This chapter is a general introduction to the original turbo codes discovered in the early 1990s and also known as convolutional turbo codes or parallel concatenated convolutional codes. It presents the main concepts of coding theory introduced with the invention of turbo codes, put in an historical perspective. The overall structures of the encoder and decoder are analyzed and some fundamental guidelines for the design of turbo codes with good performance are provided. Then, the basics of turbo decoding are introduced and the main component decoding algorithms are briefly described. Finally, the very first proof-of-concept implementations are described and the pioneer telecommunication applications and current transmission standards using turbo codes are reviewed.