This paper presents new encoding and decoding methods for Berlekamp-Preparata convolutional codes (BPCCs) based on tail-biting technique. The proposed scheme can correct a single block of n bit errors relative to a guard space of m error-free blocks while no fractional rate loss is incurred. The proposed tail-biting BPCCs (TBBPCCs) can attain optimal complete burst error correction bound. Therefore, they have the optimal phased-burst-error-correcting capability for convolutional codes. Compared with the previous scheme, the proposed scheme can also improve error correcting capability.

In the future, 5G radio access and support for the internet of things (IoT) is becoming more important, which is called machine type communications. Different from current mobile communication systems, machine type communications generates relatively small packets. In order to support such small packets with high reliability, channel coding techniques are inevitable. One of the most effective channel codes in such conditions is the tail-biting convolutional code, since it is used in LTE systems due to its good performance for small packet sizes. By employing a list Viterbi algorithm for the tail-biting convolutional code, the block error rate (BLER) performances is further improved. Therefore, this paper evaluates the BLER performances of several list Viterbi algorithms, i.e., circular parallel list Viterbi algorithm (CPLVA), per stage CPLVA (PSCPLVA), and successive state and sequence estimation (SSSE). In the evaluation, computational complexity is also taken into account. It is shown that the performance of the CPLVA is better in the wide range of computational complexity defined in this paper.

Nonprimitive non-narrow-sense BCH codes have been studied by many scholars. In this paper, we utilize nonprimitive non-narrow-sense BCH codes to construct a family of asymmetric quantum codes and two families of quantum convolutional codes. Most quantum codes constructed in this paper are different from the ones in the literature. Moreover, some quantum codes constructed in this paper have good parameters compared with the ones in the literature.

In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes based on circulant matrices of quasi-cyclic codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as the original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.

In this paper, we clarify the relationship between an initial (final) state in a tail-biting error-trellis and the obtained syndromes. We show that a final state is dependent on the first M syndromes as well, where M is the memory length of the parity-check matrix. Next, we calculate the probability of an initial (final) state conditioned by the syndromes. We also apply this method to concrete examples. It is shown that the initial (final) state in a tail-biting error-trellis is well estimated using these conditional probabilities.

In this paper, we present a construction method of non-binary low-density parity-check (LDPC) convolutional codes. Our construction method is an extension of Felstrom and Zigangirov construction [1] for non-binary LDPC convolutional codes. The rate-compatibility of the non-binary convolutional code is also discussed. The proposed rate-compatible code is designed from one single mother (2,4)-regular non-binary LDPC convolutional code of rate 1/2. Higher-rate codes are produced by puncturing the mother code and lower-rate codes are produced by multiplicatively repeating the mother code. Simulation results show that non-binary LDPC convolutional codes of rate 1/2 outperform state-of-the-art binary LDPC convolutional codes with comparable constraint bit length. Also the derived low-rate and high-rate non-binary LDPC convolutional codes exhibit good decoding performance without loss of large gap to the Shannon limits.

This paper presents hybrid type-II automatic repeat request (H-ARQ) for wireless wearable body area networks (BANs) based on ultra wideband (UWB) technology. The proposed model is based on three schemes, namely, high rate optimized rate compatible punctured convolutional codes (HRO-RCPC), Reed Solomon (RS) invertible codes and their concatenation. Forward error correction (FEC) coding is combined with simple cyclic redundancy check (CRC) error detection. The performance is investigated for two channels: CM3 (on-body to on-body) and CM4 (on-body to a gateway) scenarios of the IEEE802.15.6 BAN channel models for BANs. It is shown that the improvement in performance in terms of throughput and error protection robustness is very significant. Thus, the proposed H-ARQ schemes can be employed and optimized to suit medical and non-medical applications. In particular we propose the use of FEC coding for non-medical applications as those require less stringent quality of service (QoS), while the incremental redundancy and ARQ configuration is utilized only for medical applications. Thus, higher QoS is guaranteed for medical application of BANs while allowing coexistence with non-medical applications.

We newly design time-varying low-density parity-check convolutional codes (LDPC-CCs) based on parity check polynomials of the convolutional codes with a time period of 3, and show that BER (Bit Error Rate) performance in the time-varying LDPC-CCs with a time period of 3 is better than that in the conventional time-varying LDPC-CCs with a time period of 2 in the same coding rate with the nearly equal constraint length.

In the modern day, MPEG-4 image compression technique have been commonly applied in various indoor wireless communication systems. The efficient system design mostly relies on the joint source channel coding algorithms, which aim to reduce the complexity of channel coding process, while maintaining the quality of the receiving images. In this paper, we design the MAP source-controlled channel decoders with both random and semirandom interleavers for Rician slow flat block-fading channels. The MAP-Viterbi decoder employs the residual redundancy from zerotree symbol sequences of MPEG-4 HFS packets. The interleaving processes are done after the overall channel coding process to combat the block-fading effects. The computer simulations summarize the system performance in terms of average WER and PSNR (dB). With the interleavers, the significant improvement in PSNR of about 15-17 dB is obtained for both ML and MAP decoding. Also in many cases, we obtain more improvement of about 0.2-0.4 dB for using MAP decoding with the interleavers.

This letter proposes a simple combined coding and modulation based on super-orthogonal convolutional codes (SOCs) in order to support both coherent and non-coherent ultra-wideband (UWB) receivers. In the proposed scheme, the coherent receivers obtain a coding gain as large as the SOC while simultaneously supporting non-coherent receivers. In addition, their performance can be freely adapted by changing the encoder constraint length and the number of PPM slots according to its application. Thus, the proposal enables a more flexible system design for low data-rate UWB systems.

A method for constructing low-density convolutional (LDC) codes with the degree distribution optimized for block low-density parity-check (LDPC) codes is presented. If the degree distribution is irregular, the constructed LDC codes are also irregular. In this letter we give the encoding and decoding method for LDC codes, and study how to avoid the short cycles of LDC codes. Some simulation results are also presented.

Fading in mobile satellite communications severely degrades the performance of data transmission. It is commonly modeled with non-frequency selective Rayleigh fading. For this type of channel, a new structure for a bit-interleaved coded modulation (BICM) scheme is presented and evaluated to determine its effectiveness compared to previously proposed schemes. This scheme is referred to as rate-compatible punctured BICM (RCP-BICM), in that its BICM encoder is able to yield a wide range of data rates by using a punctured convolutional code obtained by periodically perforating parity bits from the output of a low-rate-1/2 systematic convolutional code. A trellis-coded modulation (TCM) scheme and a turbo TCM (TTCM) scheme are discussed and evaluated for comparison with the RCP-BICM scheme. Simulation results demonstrate that the RCP-BICM scheme with hard-decision iterative decoding is superior to the TCM scheme by 3 dB at a bit error rate (BER) of 10-5 over an Rayleigh fading channel, and comes at a BER of 10-5 within 1 dB of the TCM scheme over an additive white Gaussian noise (AWGN) channel.

This paper addresses a novel scheme for variable rate error correction coding with interleavered puncturing serially concatenated convolutional code. In order to obtain a variable coding rate, the bits of the outer coder are perforated with a given puncturing pattern, and randomly interleaved. The effect of interleavered puncturing on the overall coding performance is analyzed, and the upper bound to the bit error probability of the proposed coder is derived. Moreover, to evaluate the effectiveness of the proposed scheme some simulation results are presented with the iterative decoding procedure, in which the channel models of Rayleigh fading and additive white Gaussian noises are assumed.

In this paper, we propose and analytically evaluate the use of punctured convolutional codes for recovering packets lost in multicast transmission. An independent erasure channel is assumed for packets transmission over a star topology. The analysis provides a method for determining the recoverability and the post-reconstruction receiving rate for a given convolutional code. We theoretically evaluate the effectiveness of the proposed approach taking into account two different parameters: the number of transmissions per packet and the number of packets needed to be sent to guarantee the reception of data. Finally, we compare the proposed approach with the scheme when parity packets are generated based on Reed-Solomon codes.

This paper considers a high-rate turbo code which employs high-rate convolutional codes as component codes, and presents a novel method of reducing the decoding complexity of the codes. By eliminating some of branches that have the lowest reliabilities among all the branches entering each node, the proposed algorithm reduces the complexity in the process of the add-compare-select (ACS) between the consecutive stages of iterative decoding. That is, the complexity gradually decreases as the number of iterations increases. We compare the unpunctured high-rate turbo code with a classical punctured high-rate turbo code in terms of performance/complexity trade-off under the same code rate. Simulation results show that the proposed approach with a good trade-off provides an alternative coding scheme to the classical punctured high-rate turbo coding for the application to high-data-rate wireless communication systems.

This paper presents the generator polynomial matrices and the upper bound on the constraint length of punctured convolutional codes (PCCs), respectively. By virtue of these properties, we provide the puncturing realizations of the good known nonsystematic and systematic high rate CCs.

We propose using punctured convolutional code for a Discrete Multitone (DMT) Asymmetric Digital Subscriber Line (ADSL) system to improve the data rate performance of ADSL. The theoretical performance of the systems with single coding rate for all subchannels, and with adaptive coding rate for each subchannel are presented respectively. It is found that the data rate performance of the proposed system is higher than the uncoded system.

In this paper, we study unequal error protection (UEP) capabilities of punctured convolutional codes. For constructing the good UEP convolutional codes, the conditional weight distributions of UEP convolutional codes are defined and evaluated. The conditional weight distributions are computed by using the transfer functions of time-varying trellis structures of punctured convolutional codes. The best UEP convolutional codes from the viewpoint of the weight distributions are listed.

A punctured convolutional coded PR4ML system for digital magnetic recording, which applies a punctured coding method to the convolutional code and records the punctured code sequences on two tracks, is proposed. In this study, the bit error rate performance of the proposed system is obtained by computer simulation taking account of partial erasure, which is one of the nonlinear distortions at high densities, and it is compared with those of a conventional 8/9 coded PR4ML system and an I-NRZI coded PR4ML system. The results show that the proposed system is hardly affected by partial erasure and exhibits good performance in high-density recording. A bit error rate of 10-4 can be achieved with SNR's of approximately 13.2 dB and 9.1 dB less than those of the conventional 8/9 coded and I-NRZI coded PR4ML systems, respectively, at a normalized linear density of 3.

This paper proposes an adaptive modulation system with a punctured convolutional code for land mobile communications to achieve high quality, high bit rate, and high spectral efficient data transmission in multipath fading environments. The proposed system adaptively controls the coding rate of the punctured convolutional code, symbol rate, and modulation level according to the instantaneous fading channel conditions. During good channel conditions, the modulation parameters are selected to increase the transmission rate as much as possible with satisfying a certain transmission quality. As channel conditions become worse, lower rate modulation parameters are applied or transmission is stopped. The performances in fading environments are evaluated theoretically and by computer simulations. The results show that the proposed system can realize higher quality transmission without the degradation in average bit rate compared to conventional adaptive modulation systems.