Permutation codes are error-correcting codes over symmetric groups. We focus on permutation codes under Chebyshev (l∞) distance. A permutation code invented by Kløve et al. is of length n, size 2n-d and, minimum distance d. We denote the code by φn,d. This code is the largest known code of length n and minimum Chebyshev distance d > n/2 so far, to the best of the authors knowledge. They also devised efficient encoding and hard-decision decoding (HDD) algorithms that outperform the bounded distance decoding. In this paper, we derive a tight upper bound of decoding error probability of HDD. By factor graph formalization, we derive an efficient maximum a-posterior probability decoding algorithm for φn,d. We explore concatenating permutation codes of φn,d=0 with binary outer codes for more robust error correction. A naturally induced pseudo distance over binary outer codes successfully characterizes Chebyshev distance of concatenated permutation codes. Using this distance, we upper-bound the minimum Chebyshev distance of concatenated codes. We discover how to concatenate binary linear codes to achieve the upper bound. We derive the distance distribution of concatenated permutation codes with random outer codes. We demonstrate that the sum-product decoding performance of concatenated codes with outer low-density parity-check codes outperforms conventional schemes.

A high-rate coding scheme that polar codes are concatenated with low density generator matrix (LDGM) codes is proposed in this paper. The scheme, referred to as polar-LDGM (PLG) codes, can boost the convergence speed of polar codes and eliminate the error floor behavior of LDGM codes significantly, while retaining the low encoding and decoding complexity. With a sensibly designed Gaussian approximation (GA), we can accurately predict the theoretical performance of PLG codes. The numerical results show that PLG codes have the potential to approach the capacity limit and avoid error floors effectively. Moreover, the encoding complexity is lower than the existing LDPC coded system. This motives the application of powerful PLG codes to satellite communications in which message transmission must be extremely reliable. Therefore, an adaptive relaying protocol (ARP) based on PLG codes for the relay satellite system is proposed. In ARP, the relay transmission is selectively switched to match the channel conditions, which are determined by an error detector. If no errors are detected, the relay satellite in cooperation with the source satellite only needs to forward a portion of the decoded message to the destination satellite. It is proved that the proposed scheme can remarkably improve the error probability performance. Simulation results illustrate the advantages of the proposed scheme

The bit-error-rate (BER) performance predicted by the semi-analytical evolution technique proposed by Li Ping et al. becomes inaccurate for parallel concatenated coded interleave-division multiple-access (PCC-IDMA) systems. To solve this problem, we develop a novel evolution technique of such systems. Numerical results show that the predicted performance agrees well with the simulation results, and that this technique is useful for system optimization.

In this paper we look at the serial concatenation of short linear block codes with a rate-1 recursive convolutional encoder, with a goal of designing high-rate codes with low error floor. We observe that under turbo-style decoding the error floor of the concatenated codes with extended Hamming codes is due to detectable errors in many cases. An interleaver design addressing this is proposed in this paper and its effectiveness is verified numerically. We next examine the use of extended BCH codes of larger minimum distance, resulting in an improved weight spectrum of the overall code. Reduced complexity list decoding is used to decode the BCH codes in order to obtain low decoding complexity for a negligible loss in performance.

The history of forward error correction in optical communications is reviewed. The various types of FEC are classified as belonging to three generations. The first generation FEC represents the first to be successful in submarine systems, when the use of RS(255, 239) became widespread as ITU-T G.975, and also as G.709 for terrestrial systems. As WDM systems matured, a quest began for a stronger second generation FEC. Several types of concatenated code were proposed for this, and were installed in commercial systems. The advent of third-generation FEC opened up new vistas for the next generation of optical communication systems. Thanks to soft decision decoding and block turbo codes, a net coding gain of 10.1 dB has been demonstrated experimentally. That brought us a number of positive impacts on existing systems. Each new generation of FEC was compared in terms of the ultimate coding gain. The Shannon limit was discussed for hard or soft decision decoding. Several functionalities employing the FEC framing were introduced, such as overall wrapping by the FEC frame enabling the asynchronous multiplexing of different clients' data. Fast polarization scrambling with FEC was effective in mitigating polarization mode dispersion, and the error monitor function proved useful for the adaptive equalization of both chromatic dispersion and PMD.

The maximum a posteriori (MAP) algorithm is the optimum solution for decoding concatenated codes, such as turbo codes. Since the MAP algorithm is computationally complex, more efficient algorithms, such as the Max-Log-MAP algorithm and the soft-output Viterbi algorithm (SOVA), can be used as suboptimum solutions. Especially, the Max-Log-MAP algorithm is widely used, due to its near-optimum performance and lower complexity compared with the MAP algorithm. In this paper, we propose an efficient algorithm for decoding concatenated codes by modifying the Max-Log-MAP algorithm. The efficient implementation of the backward recursion and the log-likelihood ratio (LLR) update in the proposed algorithm improves its computational efficiency. Memory is utilized more efficiently if the sliding window algorithm is adopted. Computer simulations and analysis show that the proposed algorithm requires a considerably lower number of computations compared with the Max-Log-MAP algorithm, while providing the same overall performance.

This letter presents a new concatenated code and a new criterion for the new concatenated code in fast Rayleigh fading channel. The new concatenated code consists of the cascade of a new space-time trellis code (STTC) as an inner code and a new convolutional code as an outer code. The new criterion maximizes the minimum free distance for the new convolutional code and both the minimum trace and the average trace of distance matrix for the new STTC. The new concatenated code improves the frame error rate (FER) performance significantly with low complexity. The new STTC and convolutional code are designed so as to satisfy the new criterion for 4-state 4 phase shift keying (PSK). The results of the suggested concatenated code are obtained using two transmit antennas, and shown to be significantly superior to the new and existing STTCs. As the number of receive antennas increases, the performance of the new concatenated code significantly improves, for instance, reaches FER = 10-3 at signal-to-noise ratio (SNR) = 5.2 dB for four receive antennas. Note that the proposed concatenated code also improves significant FER performance by using only one receive antenna for high SNR.

The use of concatenated codes in non-coherent synchronous optical fiber CDMA networks is proposed. The concatenated code sequences are generated using Walsh code sequences and balanced Walsh code sequences, which are selected from Walsh code sequences. The selection of balanced Walsh code sequences is presented and the design of fully programmable electro-optical transmitter and receiver is reported. In the proposed network, sequence-inversion keying of intensity modulated unipolar concatenated code sequences is employed at the transmitter and unipolar-bipolar correlation is implemented at the receiver. The analysis of the system BER performance is presented and it is proved that multiple-access interference is completely eliminated. It is also shown that the BER performance of the proposed system is better than that of non-coherent synchronous optical fiber CDMA system using optical orthogonal codes with double hard-limiters.

In this letter, we introduce a two-state turbo-TCM scheme based on the concatenated tree codes. The proposed scheme can achieve near capacity performance yet has considerably lower decoding complexity compared with other existing turbo-TCM codes.

An upper bound on frame error rate (FER) for generalized concatenated convolutional codes (GCCC's) with iterative decoding is presented. The GCCC is a generalized concatenated code which consists of an inner binary convolutional code and outer Reed-Solomon codes. The FER bound is derived from the average weight enumerator of the inner code. We can optimize the configuration of the outer code since the FER bound can be easily computed. Some optimum outer code profiles will be shown. The results show that combination of GCCC and iterative decoding attains fairly small frame error probability (PB 10-13, Eb/N0 = 6 dB) with relatively simple component code (16-state convolutional code and Reed-Solomon code of length 32).

Concatenated codes have many remarkable properties from both the theoretical and practical viewpoints. The minimum distance of a concatenated code is at least the product of the minimum distances of an outer code and an inner code. In this paper, we shall examine some cases that the minimum distance of concatenated codes is beyond the lower bound and get the tighter bound or the true minimum distance of concatenated codes by using the complete weight enumerator of the outer code and the Hamming weight enumerator of the inner code. Furthermore we propose a new decoding method based on Reddy-Robinson algorithm by using the decoding method beyond the BCH bound.

This paper presents a new upper bound on overall bit error rate (BER) for a concatenated code which consists of an inner convolutional code and an outer interleaved Reed-Solomon code. The upper bound on BER is derived based on a lower bound on the effective minimum distance of the concatenated code. This upper bound can be used for the cases when the interleaver size is small such that the conventional upper bound is not applicable.

Concatenated codes have many remarkable properties from both the theoretical and practical viewpoints. The minimum distance of a concatenated code is at least the product of the minimum distances of an outer code and an inner code. In this paper, we shall study on a condition that the minimum distance of concatenated codes is beyond the lower bound.

A new design method, which is referred to as the matched design method, for concatenated trellis-coded modulation (TCM) is presented. Most of the conventional concatenated TCM employs TCM designed to maximize the minimum squared Euclidean free distance, d2free. With the matched design method, we maximize d21(t) instead of d2free, where d21(t) is the effective minimum squared Euclidean distance (MSED) when the outer code has a t-error correcting capability. The effective MSED is derived from the Euclidean/Hamming (E/H) joint weight distribution of terminated TCM. We here assume the concatenated TCM whose transmitted symbol corresponds to a symbol of outer code. The new classes of 2-dimensional (2D) and 4-dimensional (4D) codes are found by a computer search. Under the performance measures of the effective MSED or the effective multiplicity, these codes are superior to the conventional codes such as the Ungerboeck's 2D-codes when those are used as an inner code. We disclose an interesting fact that the new class of codes using rate-1/2 encoder is superior to the class of codes using rate-2/3 encoder. This fact implies that the codes using rate-1/2 encoder have two advantages: 1) better overall decoding performance and 2) less decoding complexity.

An adaptive decoding scheme for a concatenated code used in the frequency-hopped spread-spectrum communication system in the presence of a pulse-burst jammer is proposed and its performance is analyzed. Concatenated coding schemes employing binary inner-code and Reed-Solomon outer code are investigated and the use of side information is allowed to decode both erasures and errors. The proposed scheme makes the decoder enable to adapt to the jamming level by switching between two decoding modes such that the decoded bit error rate can be reduced. The optimal threshold value for switching in this proposed scheme is derived. It has been shown that the proposed decoding scheme yields a significant performance improvement over a conventional decoding scheme. In addition, performance analysis and its variation of adaptive decoding scheme with the imperfect side information are also presented.

This paper investigates the error correcting capabilities of concatenated codes employing algebraic geometry codes as outer codes and time-varying randomly selected inner codes, used on discrete memoryless channels with maximum likelihood decoding. It is proved that Gallager's random coding error exponent can be obtained for all rates by such codes. Further, it is clarified that the error exponent arbitrarily close to Gallager's can be obtained for almost all random selections of inner codes with a properly chosen code length, provided that the length of the outer code is sufficiently large. For a class of regular channels, the result is also valid for linear concatenated codes, and Gallager's expurgated error exponent can be asymptotically obtained for all rates.

High rate binary coset codes are investigated. The binary coset (BC) code is a binary convolutional code with parallel path. In our previous research of concatenated trelliscoded modulation (TCM) scheme, we have found that the effective minimum distance of inner code is more important than the minimum free distance when TCM is used as inner code. In this paper, for inner code, we construct the high rate BC codes by maximizing the effective minimum distance. With the new inner codes, we can decrease the decoding complexity of the inner code compared with conventional best convolutional code while maintaining the overall decoding performance.

The Consultative Committee of Space Data Systems (CCSDS) proposes a packetized telemetry scheme for the convenience of data exchange and networking in space activity. This paper describes the outline of the telemetry scheme and the on-orbit experiment which was carried out to show the applicability of the proposed CCSDS packet telemetry scheme using the Japan's satellite "Hiten" in a highly elliptical orbit. The telemetry data which are generated by the onboard instruments are packetized in Hiten, and reformed to the original data in earth stations successfully. The experimental results show that the standardized scheme is helpful for tracking cross-support between organizations, and that the concatenated code is quite effective to transmit data in a low C/N condition.

The DSD (Double Soft Decision) concatenated forward error correction scheme is proposed to realize a higher-coding-gain forward error correction system with simple hardware. The novel scheme soft decision decodes inner codes as well as outer codes. In this scheme, likelihood information from an inner Viterbi decoder is used for the decoding of outer codes. Path memory circuit status 1,0 ratio is newly proposed as a measure of likelihood information and it is shown that this method is the most reliable even though it has the simplest hardware among the alternative likelihood information extracting methods. Computer simulation clarifies that the proposed DSD scheme improves Pe performance to one-third that of the conventional hard decision outer decoding.

In this letter, we consider a magnetic or optical recording system employing a concatenated code that consists of a runlength-limited (d, k) block code as an inner code and a byte-error-correcting code as an outer code. (d, k) means that any two consecutive ones in the code bit stream are separated by at least d zeros and by at most k zeros. The minimum separation d and the maximum separation k are imposed in order to reduce intersymbol interference and extract clock control from the received bit stream, respectively. This letter recommends to use as the outer code a unidirectional-byte-error-correcting code instead of an ordinary byte-error-correcting code. If we devise the mapping of the code symbols of the outer code onto the codewords of the inner code, we may improve the error performance. Examples of the mappings are described.