Can Punctured Rate-1/2 Turbo Codes Achieve a Lower Error Floor than their Rate-1/3 Parent Codes?

In this paper we concentrate on rate-1/3 systematic parallel concatenated convolutional codes and their rate-1/2 punctured child codes. Assuming maximum-likelihood decoding over an additive white Gaussian channel, we demonstrate that a rate-1/2 non-systematic child code can exhibit a lower error floor than that of its rate-1/3 parent code, if a particular condition is met. However, assuming iterative decoding, convergence of the non-systematic code towards low bit-error rates is problematic. To alleviate this problem, we propose rate-1/2 partially-systematic codes that can still achieve a lower error floor than that of their rate-1/3 parent codes. Results obtained from extrinsic information transfer charts and simulations support our conclusion.Comment: 5 pages, 7 figures, Proceedings of the 2006 IEEE Information Theory Workshop, Chengdu, China, October 22-26, 200

Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes

In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is proper and $C$-symmetric, and make a connection to finite graph covers of the 3D-TC factor graph. This connection is used to show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum a posteriori constituent decoders on the binary erasure channel. Furthermore, we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a finite-length minimum pseudoweight analysis for small cover degrees. Also, an explicit description of the fundamental cone of the 3D-TC polytope is given. Finally, we present an extensive numerical study of small-to-medium block length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the minimum distance $d_{\rm min}$ and/or the stopping distance $h_{\rm min}$ is high, the minimum pseudoweight (on the additive white Gaussian noise channel) is strictly smaller than both the $d_{\rm min}$ and the $h_{\rm min}$, and 2) the minimum pseudoweight grows with the block length, at least for small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication

The Error-Pattern-Correcting Turbo Equalizer

The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of its matching Viterbi detector. By targeting the low Hamming-weight interleaved errors of the outer convolutional code, which are responsible for low Euclidean-weight errors in the Viterbi trellis, the turbo equalizer with an error-pattern correcting code (TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the conventional non-precoded TE, especially for high rate applications. A maximum-likelihood upper bound is developed on the BER floor of the TE-EPCC for a generalized two-tap ISI channel, in order to study TE-EPCC's signal-to-noise ratio (SNR) gain for various channel conditions and design parameters. In addition, the SNR gain of the TE-EPCC relative to an existing precoded TE is compared to demonstrate the present TE's superiority for short interleaver lengths and high coding rates.Comment: This work has been submitted to the special issue of the IEEE Transactions on Information Theory titled: "Facets of Coding Theory: from Algorithms to Networks". This work was supported in part by the NSF Theoretical Foundation Grant 0728676

Turbo Detection of Space-time Trellis-Coded Constant Bit Rate Vector-Quantised Videophone System using Reversible Variable-Length Codes, Convolutional Codes and Turbo Codes

In this treatise we characterise the achievable performance of a proprietary video transmission system, which employs a Constant Bit Rate (CBR) video codec that is concatenated with one of three error correction codecs, namely a Reversible Variable-Length Code (RVLC), a Convolutional Code (CC) or a convolutional-based Turbo Code (TC). In our investigations, the CBR video codec was invoked in conjunction with Space-Time Trellis Coding (STTC) designed for transmission over a dispersive Rayleigh fading channel. At the receiver, the channel equaliser, the STTC decoder and the RVLC, CC or TC decoder, as appropriate, employ the Max-Log Maximum A-Posteriori (MAP) algorithm and their operations are performed in an iterative 'turbo-detection' fashion. The systems were designed for maintaining similar error-free video reconstruction qualities, which were found to be subjectively pleasing at a Peak Signal to Noise Ratio (PSNR) of 30.6~dB, at a similar decoding complexity per decoding iteration. These design criteria were achieved by employing differing transmission rates, with the CC- and TC-based systems having a 22% higher bandwidth requirement. The results demonstrated that the TC-, RVLC- and CC-based systems achieve acceptable subjective reconstructed video quality associated with an average PSNR in excess of 30~dB for $E_b/N_0$ values above 4.6~dB, 6.4~dB and 7.7~dB, respectively. The design choice between the TC- and RVLC-based systems constitutes a trade-off between the increased error resilience of the TC-based scheme and the reduced bandwidth requirement of the RVLC-based scheme

Turbo Decoding and Detection for Wireless Applications

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 spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted

Turbo-Coded Adaptive Modulation Versus Space-Time Trellis Codes for Transmission over Dispersive Channels

Decision feedback equalizer (DFE)-aided turbocoded wideband adaptive quadrature amplitude modulation (AQAM) is proposed, which is capable of combating the temporal channel quality variation of fading channels. A procedure is suggested for determining the AQAM switching thresholds and the specific turbo-coding rates capable of maintaining the target bit-error rate while aiming for achieving a highly effective bits per symbol throughput. As a design alternative, we also employ multiple-input/multiple-output DFE-aided space–time trellis codes, which benefit from transmit diversity and hence reduce the temporal channel quality fluctuations. The performance of both systems is characterized and compared when communicating over the COST 207 typical urban wideband fading channel. It was found that the turbo-coded AQAM scheme outperforms the two-transmitter space–time trellis coded system employing two receivers; although, its performance is inferior to the space–time trellis coded arrangement employing three receivers. Index Terms—Coded adaptive modulation, dispersive channels, space–time trellis codes

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