Non-binary Turbo Codes Research Articles

Union Bound Evaluation for Non-Binary Turbo Coded Modulations

A method to compute the truncated union bound of non-binary turbo codes mapped to high order modulations is proposed in this letter. It calls for the estimate of the truncated Euclidean distance spectrum. To this end, we identify the error events that limit the Euclidean distance of non-binary turbo codes based on memory-1 convolutional codes defined over GF $(q)$ , $q>2$ . Application examples are elaborated for codes over GF(64). The resulting bounds are found to accurately predict the asymptotic performance of the coded modulation scheme.

Performance of Hybrid Binary and Non-Binary Turbo Decoding Schemes for LTE and DVB-RCS Standards


 Binary and Non-Binary Turbo codes have been deployed in several digital communication standards to perform error correction. In order to enhance their error performance, several schemes such as Joint Source Channel Decoding (JSCD), extrinsic information scaling mechanisms, and prioritized QAM constellation mapping have been proposed for improving the error performance of error correcting codes. In this paper, hybrid schemes comprising of JSCD, regression based extrinsic information scaling, and prioritized 16-Quadrature Amplitude Modulation (QAM) with binary and non-binary Turbo codes have been presented. Significant improvement in error performance has been observed with the proposed scheme as compared to the conventional one. The hybrid scheme in the case of binary symmetric and asymmetric LTE Turbo codes, and triple binary Turbo codes outperform the conventional scheme by 0.8 dB on average. With duo-binary Turbo codes for the DVB-RCS standard, the hybrid scheme outperforms the conventional one with an average gain of 0.9 dB in BER performance.

Capacity-Approaching Non-Binary Turbo Codes: A Hybrid Design Based on EXIT Charts and Union Bounds

In this paper, we introduce a novel design approach for capacity-approaching non-binary turbo codes. There are two important factors that impact the performance of turbo codes in general: 1) the convergence behavior of iterative decoding in the low signal-to-noise ratio (SNR) and 2) the error-floor effect in the high SNR. We thus design the non-binary turbo codes by means of the EXIT charts and truncated union bounds. We first reduce the search space of component recursive convolutional codes by the analysis based on the truncated union bounds in conjunction with the uniform interleaver, followed by its optimization through the EXIT chart analysis. The construction of the EXIT chart for non-binary turbo codes with fixed code coefficients is a non-trivial task by the fact that these messages have multiple parameters to identify. Therefore, we develop a new EXIT chart analysis for non-binary messages which does not rely on any specific message model. It is demonstrated through computer simulations that the well-designed non-binary turbo codes achieve a better performance than their binary counterparts as well as the conventional non-binary LDPC codes of the same field size. Furthermore, the code design is extended to high-order modulation, and our turbo codes designed for quadrature amplitude modulation are shown to outperform the conventional turbo trellis coded modulation schemes.

Non‐binary turbo‐coded physical‐layer network coding on impulsive noise channels

Non-binary turbo codes promise excellent performance for a wide range of applications and environments, but research in this area is sparse. The performance of a non-binary turbo code defined in GF(4) on a two-way wireless relay channel (TWRC) employing physical-layer network coding, which is affected by impulsive noise is investigated. Simulation results for binary and non-binary turbo codes are presented and validated with an error floor analysis at the relay of the TWRC and it is observed that non-binary turbo codes significantly outperform binary turbo codes at low signal-to-noise ratios.

Physical Layer Deterministic Network Coding Using PUM Turbo Codes over AWGN Channel, N Nodes through a Base Station Scenario

Network Coding (NC) is a recent technique which is used to improve the transmission data rate and the power efficiency. These goals are obtained by combining data together before transmitting them, resulting to less transmitted data that carry the same amount of information. NC research work over the physical layer and the upper layers are popular and needed to be more investigated. In this paper, we propose a practical system of large-number of connected multi-source network coding (LMSNC), at the physical layer that exploits the broadcast nature of the wireless channel, using the practical and bandwidth-efficient schemes decode-and-forward (DF) and then compare it with Amplify and Forward (AF). The theoretical analysis and the simulation results show the effect of the noise when it cumulates in AF system and how DF is solving this severe default. Moreover, we consider the MSNC for Small-number of connected sources (SMSNC) and the two-way communication setup where two users exchange their information over an intermediate network node (ideally called Base Station), as two reference cases to compare with. With SMSNC, the number of necessary downlink transmissions from the intermediate node to the users is reduced, and thus the throughput is increased. Simulation results obtained using high-performance non-binary turbo codes, based on Partial Unit Memory (PUM) codes (4, 2, 1, 4) and (8, 4, 3, 8); confirm that combining PUM Turbo Code (PUMTC) and NC in the proposed MSNC setup gives almost the same BER performance as that for SMSNC at the small number of processing steps mainly when PUMTC (8, 4, 3, 8) is performed, which is required to retrieve the received coded messages. In the scenario of AF, combining packets results to cumulate the noise, which justifies the reason we decided to increase the number of transmitted coded messages in the network, i.e., the BER performance improves when sending extra coded messages. Finally, the possibility for a trade-off among BER, data rate and the number of transmitted coded messages is shown for LMSNC through graphics and simulation results.

Turbo codes with symmetric and asymmetric component codes defined over finite fields of integers

Binary asymmetric turbo codes and non-binary turbo codes have been proposed to improve the bit error rate (BER) performance of parallel concatenated coding schemes. Both strategies have certain advantages that can be exploited when they are put together. This paper investigates turbo codes based on two component recursive systematic convolutional (RSC) codes defined over a finite field of integers. Symmetric and asymmetric non-binary turbo codes are obtained and their BER performance in both the ‘waterfall’ and the ‘error-floor’ regions is analysed. The results show good performance improvements when compared to binary and quaternary turbo codes with same throughput.

Bit-Level Extrinsic Information Exchange Method for Double-Binary Turbo Codes

Nonbinary turbo codes have many advantages over single-binary turbo codes, but their decoder implementations require much more memory, particularly for storing symbolic extrinsic information to be exchanged between two soft-input-soft-output (SISO) decoders. To reduce the memory size required for double-binary turbo decoding, this paper presents a new method to convert symbolic extrinsic information to bit-level information and vice versa. By exchanging bit-level extrinsic information, the number of extrinsic information values to be exchanged in double-binary turbo decoding is reduced to the same amount as that in single-binary turbo decoding. A double-binary turbo decoder is designed for the WiMAX standard to verify the proposed method, which reduces the total memory size by 20%.

Distributed source coding using symbol-based and non-binary turbo codes – applications to wireless sensor networks

A simple but powerful scheme for distributed source coding (DSC) based on the concept of binning and syndromes and non traditional turbo codes is proposed. The previous works on the compression with side information using turbo codes and the binning technique are focused on binary turbo codes. The source is considered to be binary or is converted to a binary stream. This conversion, however, reduces the redundancy that could be exploited by the compression algorithm. To achieve higher compression efficiency, the authors propose using a scheme based on a turbo decoder that decides over symbols rather than bits. In the same direction and for further performance improvement, at the cost of increased encoder complexity, they also present a DSC scheme based on non-binary turbo codes. The results demonstrate improved performance. Based on the suggested algorithms, a scheme for gathering real data in wireless sensor networks and assess the corresponding energy savings is proposed.

Double-Binary Circular Turbo Decoding Based on Border Metric Encoding

This brief presents an energy-efficient soft-input soft-output (SISO) decoder based on border metric encoding, which is especially suitable for nonbinary circular turbo codes. In the proposed method, the size of the branch memory is reduced to half and the dummy calculation is removed at the cost of a small-sized memory that holds encoded border metrics. Due to the infrequent accesses to the border memory and its small size, the energy consumed for SISO decoding is reduced by 26.2%. Based on the proposed SISO decoder and the dedicated hardware interleaver, a double-binary tail-biting turbo decoder is designed for the WiMAX standard using a 0.18-mum CMOS process, which can support 24.26 Mbps at 200 MHz.

Soft multiuser demodulation and iterative decoding for FH/SSMA with a block turbo code

The number of users that can be supported by frequency-hopped, spread-spectrum multiple-access systems can be increased greatly by using multiuser demodulation and iterative decoding. In the receiver employed hard-decision multiuser demodulation followed by iterative decoding, users exchange decoded information with each other. Additional information from multiuser demodulation in the first decoding iteration is limited by the hard-decision output of the multiuser demodulator. The error-correction used was an errors-and-erasures Reed-Solomon (RS) decoder. We revisit hard-decision demodulation and conventional RS decoding. Hard-decision multiuser demodulation is modified to provide a soft output, which is then given to a nonbinary block turbo code with shortened RS codes as the constituent codes. An iterative multiuser decoding algorithm is developed to do soft multiuser interference cancellation. This soft receiver with soft demodulation and decoding is shown to be more resistant to multiuser interference and channel noise, especially at lower values of signal-to-noise ratio. The results show a great improvement in the ability of the system to support more users (more than three times in some cases), as compared with systems that erase all hits or employ hard-decision multiuser demodulation followed by RS code. We examine the proposed method for synchronous as well as asynchronous frequency-hopped systems in both AWGN and fading channels.

A distributed source coding technique for correlated images using turbo-codes

The Slepian-Wolf (1973) theorem states that the output of two correlated sources can be compressed to the same extent without loss, whether they communicate with each other or not, provided that decompression takes place at a joint decoder. We present a distributed source coding scheme for correlated images which uses modulo encoding of pixel values and encoding (compression) of the resulting symbols with binary and nonbinary turbo-codes, so that larger rate savings than using modulo encoding. alone are achieved, practically without loss.