Spatially Coupled Turbo Codes: Principles and Finite Length Performance

In this paper, we give an overview of spatially coupled turbo codes (SC-TCs), the spatial coupling of parallel and serially concatenated convolutional codes, recently introduced by the authors. For presentation purposes, we focus on spatially coupled serially concatenated codes (SC-SCCs). We review the main principles of SC-TCs and discuss their exact density evolution (DE) analysis on the binary erasure channel. We also consider the construction of a family of rate-compatible SC-SCCs with simple 4-state component encoders. For all considered code rates, threshold saturation of the belief propagation (BP) to the maximum a posteriori threshold of the uncoupled ensemble is demonstrated, and it is shown that the BP threshold approaches the Shannon limit as the coupling memory increases. Finally we give some simulation results for finite lengths.Comment: Invited paper, IEEE Int. Symp. Wireless Communications Systems (ISWCS), Aug. 201

Turbo-Detected Unequal Error Protection Irregular Convolutional Codes Designed for the Wideband Advanced Multirate Speech Codec

Abstract—since the different bits of multimedia information, such as speech and video, have different error sensitivity, efficient unequalprotection channel coding schemes have to be used to ensure that the perceptually more important bits benefit from more powerful protection. Furthermore, in the context of turbo detection the channel codes should also match the characteristics of the channel for the sake of attaining a good convergence performance. In this paper, we address this design dilemma by using irregular convolutional codes (IRCCs) which constitute a family of different-rate subcodes. we benefit from the high design flexibility of IRCCs and hence excellent convergence properties are maintained while having unequal error protection capabilities matched to the requirements of the source. An EXIT chart based design procedure is proposed and used in the context of protecting the different-sensitivity speech bits of the wideband AMR speech codec. As a benefit, the unequalprotection system using IRCCs exhibits an SNR advantage of about 0.4dB over the equal-protection system employing regular convolutional codes, when communicating over a Gaussian channel

Turbo-Detected Unequal Protection MPEG-4 Wireless Video Telephony using Multi-Level Coding, Trellis Coded Modulation and Space-Time Trellis Coding

Most multimedia source signals are capable of tolerating lossy, rather than lossless delivery to the human eye, ear and other human sensors. The corresponding lossy and preferably low-delay multimedia source codecs however exhibit unequal error sensitivity, which is not the case for Shannon’s ideal entropy codec. This paper proposes a jointly optimised turbo transceiver design capable of providing unequal error protection for MPEG-4 coding aided wireless video telephony. The transceiver investigated consists of space-time trellis coding (STTC) invoked for the sake of mitigating the effects of fading, in addition to bandwidth efficient trellis coded modulation or bit-interleaved coded modulation, combined with a multi-level coding scheme employing either two different-rate non-systematic convolutional codes (NSCs) or two recursive systematic convolutional codes for yielding a twin-class unequal-protection. A single-class protection based benchmark scheme combining STTC and NSC is used for comparison with the unequal-protection scheme advocated. The video performance of the various schemes is evaluated when communicating over uncorrelated Rayleigh fading channels. It was found that the proposed scheme requires about 2.8 dBs lower transmit power than the benchmark scheme in the context of the MPEG-4 videophone transceiver at a similar decoding complexity

A unary error correction code for the near-capacity joint source and channel coding of symbol values from an infinite set

A novel Joint Source and Channel Code (JSCC) is proposed, which we refer to as the Unary Error Correction (UEC) code. Unlike existing JSCCs, our UEC facilitates the practical encoding of symbol values that are selected from a set having an infinite cardinality. Conventionally, these symbols are conveyed using Separate Source and Channel Codes (SSCCs), but we demonstrate that the residual redundancy that is retained following source coding results in a capacity loss, which is found to have a value of 1.11 dB in a particular practical scenario. By contrast, the proposed UEC code can eliminate this capacity loss, or reduce it to an infinitesimally small value. Furthermore, the UEC code has only a moderate complexity, facilitating its employment in practical low-complexity applications

MIMO-aided near-capacity turbo transceivers: taxonomy and performance versus complexity

In this treatise, we firstly review the associated Multiple-Input Multiple-Output (MIMO) system theory and review the family of hard-decision and soft-decision based detection algorithms in the context of Spatial Division Multiplexing (SDM) systems. Our discussions culminate in the introduction of a range of powerful novel MIMO detectors, such as for example Markov Chain assisted Minimum Bit-Error Rate (MC-MBER) detectors, which are capable of reliably operating in the challenging high-importance rank-deficient scenarios, where there are more transmitters than receivers and hence the resultant channel-matrix becomes non-invertible. As a result, conventional detectors would exhibit a high residual error floor. We then invoke the Soft-Input Soft-Output (SISO) MIMO detectors for creating turbo-detected two- or three-stage concatenated SDM schemes and investigate their attainable performance in the light of their computational complexity. Finally, we introduce the powerful design tools of EXtrinsic Information Transfer (EXIT)-charts and characterize the achievable performance of the diverse near- capacity SISO detectors with the aid of EXIT charts

Evolutionary Algorithm Aided Interleaver Design for Serially Concatenated Codes

In this paper, we propose an algorithm for designing the interleavers of Serially Concatenated Codes (SCCs), in order to increase the Minimum Hamming Distance (MHD) between the legitimate permutations of the encoded bit sequence and hence to improve the corresponding error floor. Unlike previous so-called Code Matched Interleaver (CMI) designs, our approach is capable of creating interleavers for serial concatenations of both irregular and non-linear codes, as well as achieving MHDs that are arbitrarily close to the maximum possible, provided that a sufficiently high off-line complexity is affordable. However, owing to the efficiency of the proposed approach, only a relatively low number of algorithm generations are required to achieve significant improvements to the error floor of low-delay wireless sensor network, speech and audio schemes, for example. Indeed, we demonstrate that our interleavers are capable of completely eradicating the error floors that would otherwise be apparent, if classic random or S-random interleavers were employed

On The Design Of Physical Layer Rateless Codes

Codes that are capable of generating any number of encoded symbols from a given number of source symbols are called rateless codes. Luby transform (LT) codes are the first practical realization of rateless codes while Raptor codes are constructed by serially concatenating LT codes with high-rate outer low-density parity-check (LDPC) codes. Although these codes were originally developed for binary erasure channel (BEC), due to their rateless feature, they are being investigated and designed for their use in noisy channels. It is known that LT codes are the irregular non-systematic rateless counterpart of low-density generator-matrix (LDGM) codes. Therefore, the first part of our work is focused on LDGM codes and their serially concatenated scheme called serially concatenated LDGM (SCLDGM) codes. Though single LDGM codes are asymptotically bad codes, the SCLDGM codes are known to perform close to the Shannon limit. We first study the asymptotic behaviour of LDGM codes using a discretized density evolution method. We then show that the DDE method can be used in two-steps to provide the detailed asymptotic performance analysis of SCLDGM codes. We also provide the detailed error-floor analysis of both the LDGM and SCLDGM codes. We also prove a necessary condition for the successful decoding of such concatenated codes under sum-product (SP) decoding in binary input additive white Gaussian noise (BIAWGN) channels. Based on this necessary condition, we then develop a DDE-based optimization approach which can be used to optimize such concatenated codes in general. We present both the asymptotic performance and simulation results of our optimized SCLDGM codes that perform within 0.26 dB to the Shannon limit in BIAWGN channels. Secondly, we focus on the asymptotic analysis and optimization design of LT and Raptor codes over BIAWGN channels. We provide the exact asymptotic performance of LT codes using the DDE method. We apply the concept of the two-step DDE method to the Raptor codes and obtain their exact asymptotic performance in BIAWGN channels. We show that the existing Raptor codes using solely the same output degree distribution can perform within 0.4 dB to the Shannon limit for various realized code-rates. We then develop a DDE-based optimization technique to optimally design such physical layer Raptor codes. Our optimized Raptor codes are shown to perform within 0.2 dB to the Shannon limit for most of the realized code-rates. We also provide the asymptotic curves, decoding thresholds, and simulation results showing that our optimized Raptor codes outperform the existing Raptor codes in BIAWGN channels. Finally, we present the asymptotic analysis and optimization design of systematic version of these codes namely systematic LT and systematic Raptor codes as well