We propose a coding/decoding strategy that surpasses the symmetric information rate of a binary insertion/deletion (ID) channel and approaches the Markov capacity of the channel. The proposed codes comprise inner trellis codes and outer irregular low-density parity-check (LDPC) codes. The trellis codes are designed to mimic the transition probabilities of a Markov input process that achieves a high information rate, whereas the LDPC codes are designed to maximize an iterative decoding threshold in the superchannel (concatenation of the ID channels and trellis codes).

This letter presents numerical results of lossy source coding for non-uniformly distributed binary source with trellis codes. The results show how the performance of trellis codes approaches the rate-distortion function in terms of the number of states.

Trellis coded modulation (TCM) concept is applied to the mode constellation points of orbital angular momentum (OAM) modulation. OAM modulation considers the multiple OAM modes as additional constellation points and maps a first part of a block of information bits to the transmitting OAM modes. Therefore, spatial multiplexing gains are retained and spectral efficiency is boosted. The second part of the block of information bits is mapped to a complex symbol using conventional digital modulation schemes. At any particular time instant, only one OAM mode is active. The receiver estimates the transmitted symbol and the active OAM mode, then uses the two estimates to retrieve the original block of data bits. Simulation reveals that with the TCM employed both for the OAM constellation points and the signal constellation points, a considerable bit error rate (BER) gain can be obtained under all turbulence conditions, compared with that of the no coding scheme.

Efficient detection schemes for an overloaded multiple-input multiple-output (MIMO) system have been investigated recently. The literature shows that trellis coded modulation (TCM) is able to enhance a system's capability to separate signal streams in the detection process of MIMO systems. However, the computational complexity remains high as a maximum likelihood detection (MLD) algorithm is used in the scheme. Thus, a sphere decoding (SD) algorithm with a pseudo distance (PD) is proposed in this paper. The PD maintains the coding gain advantage of the TCM by keeping some potential paths connected unlike conventional SD which truncates them. It is shown that the proposed scheme can reduce the number of distance calculations by about 98% for the transmission of 3 signal streams. In addition, the proposed scheme improves the performance by about 2dB at the bit error rate of 10-2.

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 focus on the multi-way relaying channel where K users wish to exchange information with each other within two phases. Precoding at each user and the relay is carefully constructed to ensure that the signals from the same user pair are grouped together and cross-pair interference can be cancelled. Reliable detection is challenging at the relay since the observation constellation is no longer one of the regular ones, due to the fact that a relay observation is the superposition of the messages from one of the $rac{1}{2}K(K-1)$ user pairs. When the trellis coded modulation is used at each node, a simple constellation mapping function and a reduced-states decoding scheme can be applied at the relay, which result in much lower complexity. Furthermore, a modified version of the decoding method is also developed which is called the re-encoding-avoidance scheme at the relay. Monte-Carlo simulation results are provided to demonstrate the performance of the proposed scheme.

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.

Physical-layer network coding with binary turbo coding in a two-way relay channel is considered. A two-user turbo decoding scheme is proposed with a simplified sum trellis. For two-user iterative decoding at a relay, the component decoder with its simplified sum trellis decodes the superimposed signal to the arithmetic sum of two users' messages. The simplified sum trellis is obtained by removing one of the states in a pair of mutual symmetrical states from a sum trellis. This removal reduces the decoding complexity to half of that with the sum trellis, and does not degrade decoding performance over AWGN channel since two output sequences from the pair of mutual symmetrical states are the same.

In this paper, a block-constrained trellis coded vector quantization (BC-TCVQ) algorithm is combined with an algebraic codebook to produce an algebraic trellis vector code (ATVC) to be used in ACELP coding. ATVC expands the set of allowed algebraic codebook pulse position, and the trellis branches are labeled with these subsets. The Viterbi algorithm is used to select the excitation codevector. A fast codebook search method using an efficient non-exhaustive search technique is also proposed to reduce the complexity of the ATVC search procedure while maintaining the quality of the reconstructed speech. The ATVC block code is used as the fixed codebook of AMR-NB (12.2 kbps), which reduces the computational complexity compared to the conventional algebraic codebook.

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 propose a new method to estimate and effectively reduce the effect of thermal asperity (TA) in the perpendicular magnetic recording (PMR) channels with the state trellis. The TA is estimated from the state trellis, then its average is used to modify the equalized signal entering the Viterbi detector. For the partial response (PR) targets with DC component, the proposed method with a maximum-likelihood detector can improve the bit error rate performance by more than an order of magnitude when TA occurs and degrades when the giant magneto-resistive (GMR) nonlinearity and base line wander (BLW) effects are present. Unlike the previous studies, this method allows the use of PR targets with DC component under the presence of TA.

In this letter, a circulation-based distributed space time trellis code (DSTTC) technique for amplify-and-forward (AF) relaying is proposed. The proposed circulation technique is a method of configuring new protocols from the existing protocols of which the performance is dependent on specific source to relay links. The simulation results show that the newly developed protocol is less dependent on weak conditions of specific links and a performance gain in frame error rate (FER) can be obtained over the original protocol.

A major drawback with linear precoding in a downlink multi-user MIMO system is the increase in the transmit power when a channel is correlated. On the other hand, nonlinear trellis precoding in downlink multi-user MIMO systems is capable of minimizing the transmit power by adding a shaping sequence to the original transmit sequence. However, conventional trellis precoding cannot be directly applied to existing bit-interleaved coded MIMO-OFDM systems since the trellis precoding and error correcting codes should be designed separately. In this paper, we proposed to embed trellis precoding into the error correcting codes that are used in the original multi-user MIMO-OFDM system employing linear precoding. Major advantage of this approach is that the receiving procedure at user terminals designed for the original system need not be changed up to the error correcting decoder to support our trellis precoding. Computer simulations show that the proposed trellis precoding provides improvements of 2 dB and 2.5 dB in 22 and 33 MIMO configurations, respectively.

Transmission of convolutionally encoded source-codec parameters over noisy channels can benefit from the turbo principle through iterative source-channel decoding. We first formulate a recursive implementation based on sectionalized code trellises for MAP symbol decoding of binary convolutional codes. Performance is further enhanced by the use of an interpolative softbit source decoder that takes into account the channel outputs within an interleaving block. Simulation results indicate that our proposed scheme allows to exchange between its constituent decoders the symbol-level extrinsic information and achieves high robustness against channel noises.

In this paper an algebraic trellis vector quantization (ATVQ) that introduces algebraic codebooks into trellis coded vector quantization (TCVQ) structure is presented. Low encoding complexity and minimum memory storage requirements are achieved using the proposed approach. It exploits advantages of both the TCVQ and the algebraic codebooks to know the delayed decision, the codebook widening, the low computational complexity and the no storage of codebook. This novel vector quantization scheme is used to encode the wideband speech line spectral frequencies (LSF) parameters. Experimental results on wideband speech have shown that ATVQ yields the same performance as the traditional split vector quantization (SVQ) and the TCVQ in terms of spectral distortion (SD). It can achieve a transparent quality at 47 bits/frame with a considerable reduction of memory storage and computation complexity when compared to SVQ and TCVQ.

A Generalized Symbol-rate-increased (GSRI) Pragmatic Adaptive Trellis Coded Modulation (ATCM) is applied to a Multi-carrier CDMA (MC-CDMA) system with bi-orthogonal keying is analyzed. The MC-CDMA considered in this paper is that the input sequence of a bi-orthogonal modulator has code selection bit sequence and sign bit sequence. In, an efficient error correction code using Reed-Solomon (RS) code for the code selection bit sequence has been proposed. However, since BPSK is employed for the sign bit modulation, no error correction code is applied to it. In order to realize a high speed wireless system, a multi-level modulation scheme (e.g. MPSK, MQAM, etc.) is desired. In this paper, we investigate the performance of the MC-CDMA with bi-orthogonal keying employing GSRI ATCM. GSRI TC-MPSK can arbitrarily set the bandwidth expansion ratio keeping higher coding gain than the conventional pragmatic TCM scheme. By changing the modulation scheme and the bandwidth expansion ratio (coding rate), this scheme can optimize the performance according to the channel conditions. The performance evaluations by simulations on an AWGN channel and multi-path fading channels are presented. It is shown that the proposed scheme has remarkable throughput performance than that of the conventional scheme.

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.

Space-time trellis coding systems employing orthogonal frequency division multiplexing technique over frequency-selective channels is considered, where fading gains vary within a frame interval. The channel time-evolution of each sub-carrier is modeled by an autoregressive process, while the receiver utilizing a recursive technique combining Kalman filtering with per-survivor processing is studied.

In this paper, a block-constrained trellis coded quantization (BC-TCQ) algorithm is combined with an algebraic codebook to produce an algebraic trellis code (ATC) to be used in ACELP coding. In ATC, the set of allowed algebraic codebook pulse positions is expanded, and the expanded set is partitioned into subsets of pulse positions; the trellis branches are labeled with these subsets. The list Viterbi algorithm (LVA) is used to select the excitation codevector. The combination of an ATC codebook and LVA trellis search algorithm is denoted as an ATC-LVA block code. The ATC-LVA block code is used as the fixed codebook of the AMR-WB 8.85 kbps mode, reducing complexity compared to the conventional algebraic codebook.

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.