In this letter, we investigate tight analytical and asymptotic upper bounds for bit error rate (BER) of constitutional codes over exponentially correlated Nakagami-m fading channels. Specifically, we derive the BER expression depending on an exact closed-form formula for pairwise error event probabilities (PEEP). Moreover, the corresponding asymptotic analysis in high signal-to-noise ratio (SNR) regime is also explored, which is verified via numerical results. This allows us to have explicit insights on the achievable coding gain and diversity order.

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.

This letter presents ternary convolutional codes and their punctured codes with optimum distance spectrum.

We present numerical results on the rate-distortion performance of convolutional coding for the binary symmetric source, and show how convolutional codes approach the rate-distortion bound by increasing the trellis states.

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.

We propose a quasi-linear trellis-coded modulation (TCM) using nonbinary convolutional codes for quadrature amplitude modulation (QAM). First, we study a matched mapping which is able to reduce the computational complexity of the Euclidean distances between signal points of MQAM. As an example, we search for rate R=1/2 convolutional codes for coded 64QAM by this method. The symbol error rates of the proposed codes are estimated by the distance properties theoretically and they are verified by simulation. In addition, we compare the minimum free Euclidean distances of these new codes with their upper bounds. Finally, the bit error probabilitiy of the proposed coded modulation is compared with uncoded signal constellations and a conventional TCM code proposed by Ungerboeck. The result shows the proposed scheme outperform them on the AWGN channels.

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 letter, we show that the code-trellis and the error-trellis for a convolutional code can be reduced simultaneously, if reduction is possible. Assume that the error-trellis can be reduced by shifting particular error-subsequences. In this case, if the identical shifts occur in the corresponding subsequences of each code-path, then the code-trellis can also be reduced. First, we obtain pairs of transformations which generate the identical shifts both in the subsequences of the code-path and in those of the error-path. Next, by applying these transformations to the generator matrix and the parity-check matrix, we show that reduction of these matrices is accomplished simultaneously, if it is possible. Moreover, it is shown that the two associated trellises are also reduced simultaneously.

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.

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.

In this paper, we extend the conventional error-trellis construction for convolutional codes to the case where a given check matrix H(D) has a factor Dl in some column (row). In the first case, there is a possibility that the size of the state space can be reduced using shifted error-subsequences, whereas in the second case, the size of the state space can be reduced using shifted syndrome-subsequences. The construction presented in this paper is based on the adjoint-obvious realization of the corresponding syndrome former HT(D). In the case where all the columns and rows of H(D) are delay free, the proposed construction is reduced to the conventional one of Schalkwijk et al. We also show that the proposed construction can equally realize the state-space reduction shown by Ariel et al. Moreover, we clarify the difference between their construction and that of ours using examples.

Yamada, Harashima, and Miyakawa proposed to use a trellis constructed based on a syndrome former for the purpose of Viterbi decoding of rate-(n-1)/n convolutional codes. In this paper, we extend their code-trellis construction to general rate-k/n convolutional codes. We show that the extended construction is equivalent to the one proposed by Sidorenko and Zyablov. Moreover, we show that the proposed method can also be applied to an error-trellis construction with minor modification.

Soft-decision decoding techniques are applied to asynchronous frequency-hop/spread-spectrum multiple-access (FH/SSMA) networks, where M-ary frequency shift keying (MFSK) is employed to transmit one modulated symbol per hop. Coding schemes using soft-decision decoded binary convolutional codes or turbo codes are considered, both with or without bit-interleaving. Performances of several soft metrics are examined for each coding scheme. It is shown that when multiple access interference is the main source of errors, the product metric offers the best performance among the soft metrics considered for all coding schemes. Furthermore, the application of soft-decision decoded convolutional codes or turbo codes without bit-interleaving is shown to allow for a much larger number of simultaneously transmitting users than hard-decision decoded Reed-Solomon codes. Finally, it is observed that when soft-decision decoding techniques are employed, synchronous networks attain better performance than asynchronous networks.

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.

This paper proposes a butterfly structure for Viterbi decoders, which works for convolutional codes of all rates k/n. The proposed butterfly structure can exploit the inherent symmetry of trellis branches, so that only some branch metrics need to be computed, while the others can be derived from the computed branches. Consequently, the computational complexity of the Viterbi decoder can be significantly reduced without any error performance loss. The applicability of the butterfly structure is validated by the best codes of rates 1/2, 2/3, and 3/4. Most of the best codes can apply the butterfly structure to reduce their branch metric computation complexity by a factor of 2 or 4. This study also reports a number of new codes with high branch symmetry under the symmetry consideration. Their branch metric computation can be reduced by a factor of 4, 8 or 16 with the similar performance to the best codes.

Assume that G(D) is a k0n0 canonical generator matrix. Let G(L)(D) be the generator matrix obtained by integrating L consecutive trellis-modules associated with G(D). We also consider a modified version of G(L)(D) using a column permutation. Then take notice of the corresponding minimal trellis-module T(L). In this paper, we show that there is a case where the minimum number of states over all levels in T(L) is less than the minimum attained for the minimal trellis-module associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellis-module with further reduced number of states. We actually present such an example. We also clarify the mechanism of state-space reduction. That is, we show that trellis-module integration combined with an appropriate column permutation and a shifted sectionalization of the trellis is equivalent to shifting some particular bits of the original code bits by L time units.

Efficient real-time contents distribution services on the Internet are only possible by suppressing the influence of packet losses. One solution for UDP transmission is the use of Forward Error Correction (FEC) based on Reed-Solomon codes. However, a more efficient method is required since this causes the increase of network traffic and includes the weakness to burst packet losses. In this paper, we propose a data recovery method that generates redundant data with the combination of Reed-Solomon codes and convolution of neighboring blocks. We realize the small amount of redundancy and the high reliability in data transmission compared with using only Reed-Solomon codes in the environment that burst packet losses are occurred frequently. We implement proposal method into the network bridge and confirm its efficiency from the viewpoint of data reconstruction from burst packet losses.

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.