Error control codes have extensively been applied to semiconductor memories using high density RAM chips with wide I/O data, e.g., with 8-bit or 16-bit I/O data. Recently, spotty byte errors called s-spotty byte errors are newly defined as t or fewer bits errors in a byte having length b bits, where 1 ≤ t ≤ b. This paper proposes another type of spotty byte errors, i.e., m-spotty byte errors, where more than t bits errors in a byte may occur due to hit by high energetic particles. For these errors, this paper presents generalized m-spotty byte error control codes with minimum m-spotty distance d.

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.

Packet loss and delay cause degradation in the quality of real-time, interactive applications such as video conferencing. Forward error correction (FEC) schemes have been proposed to make the applications more resilient to packet loss, because the time required to recover the lost packets is shorter than that required to retransmit the lost packets. On the other hand, the codec generally used in real-time applications like MPEG4 has the feature that the sending bit rate and the packet size of the traffic vary significantly according to the motion of an object in a video. If the traditional FEC coding, which is calculated on the basis of a fixed-size block, is applied to such applications, a waste of bandwidth and a delay variation are caused and the quality is degraded. In this paper, we propose suitable FEC schemes for visual communication systems using variable bit-rate (VBR) codec and evaluate the effectiveness of these schemes using our prototype implementation and experimental network.

The Reed-Solomon code is a versatile channel code pervasively used for communication and storage systems. The bit-serial Reed-Solomon encoder has a simple structure, although it is somewhat difficult to understand the algorithm without considerable theoretical background. Some professionals and students, not able to understand the algorithm thoroughly, might need to implement the bit-serial encoder for themselves. In this letter, a step-by-step method is presented for the implementation of the bit-serial encoder even without understanding the internal algorithm, which would be helpful for VHDL, DSP, and simulation programming.

This paper examines a coded Gaussian Minimum Shift Keying (GMSK) system which uses Reed-Solomon (RS) codes both in Additive White Gaussian Noise (AWGN) channels and Rayleigh fading channels. The performance of GMSK and RS code combinations is compared with the constraint that the transmitted signal bandwidth is constant. The coding gains were obtained using simulations and the best combination of GMSK and RS codes was found. The optimal code rates over AWGN and Rayleigh fading channels were also compared.

This paper proposes a reconfigurable adaptive FEC system based on Reed-Solomon (RS) code with interleaving. In adaptive FEC schemes, error correction capability t is changed dynamically according to the communication channel condition. For given error correction capability t, we can implement an optimal RS decoder composed of minimum hardware units for each t. If the hardware units of the RS decoder can be reduced for any given error correction capability t, we can embed as large deinterleaver as possible into the RS decoder for each t. Reconfiguring the RS decoder embedded with the expanded deinterleaver dynamically for each error correction capability t allows us to decode larger interleaved codes which are more robust error correction codes to burst errors. In a reliable transport protocol, experimental results show that our system achieves up to 65% lower packet error rate and 5.9% higher data transmission throughput compared to the adaptive FEC scheme on a conventional fixed hardware system. In an unreliable transport protocol, our system achieves up to 76% better bit error performance with higher code rate compared to the adaptive FEC scheme on a conventional fixed hardware system.

In this paper, an efficient architecture for an adaptive Reed-Solomon decoder is presented, where the block length n and the message length k can be varied from their minimum allowable values up to their selected values. This eliminates the need of inserting zeros before decoding shortened RS codes. And the error-correcting capability t can be changed adaptively to channel state at every codeword block. The decoder allows efficient decoding in both burst mode and continuous mode, and it permits 3-step pipelined processing based on the modified Euclid's algorithm. Each step in decoding is designed to be clocked by a separate clock. Thus, each step can be efficiently pipelined with no help of multiplexing. Also, it makes it possible to employ no additional buffer even when the decoder input and output clocks are different. The adaptive RS decoder over GF(28) having the error-correcting capability of upto 10 has been designed in VHDL, and successfully synthesized in an FPGA chip. It can be used in a wide range of applications because of its versatility.

One of the categories of decoding techniques for DFT codes in erasure channels is the class of iterative algorithms. Iterative algorithms can be considered as kind of alternating mapping methods using the given information in a repetitive way. In this paper, we propose a new iterative method for decoding DFT codes. It will be shown that the proposed method outperforms the well-known methods such as Wiley/Marvasti, and ADPW methods in the decoding of DFT codes in erasure channels.

We propose multibits/sequence-period optical code division multiple access (MS-OCDMA) systems with double optical hardlimiters (DHL) in the presence of APD noise, thermal noise, and channel interference. We apply Reed-Solomon (RS) codes to MS-OCDMA to further improve the error rate performance. We show that the MS-OCDMA receiver with DHL improves the bit error probability of MS-OCDMA systems when the received laser power is large. We also show that the performance of RS coded MS-OCDMA system is better than that of on-off keying OCDMA (OOK-OCDMA) system at the same bit rate and at the same chip rate, respectively.

Based on a modified step-by-step decoding procedure, a high-speed pipelined Reed-Solomon decoder is presented. The decoder requires only the delay time of three 2-input XOR gates for decoding each coded symbol. The decoder can be operated in a bit rate of Gbits/sec order and thus suitable for the very high speed data transmission systems.

We propose a method to represent non-binary error patterns for Reed-Solomon codes using a trellis. All error patterns are sorted according to their Euclidean distances from the received vector. The decoder searches through the trellis until it finds a codeword. This results in a soft-decision maximum likelihood algorithm with lower complexity compared to other known MLD methods. The proposed MLD algorithm is subsequently modified to further simplify complexity, reflecting in a slight reduction in the error performance.

GSRI Pragmatic TCM, which is a Pragmatic Trellis Coded Modulation allowing bandwidth expansion, has been proposed. In [1], it is shown that this scheme can achieve higher performance than conventional Pragmatic TCM scheme. On the other hand, a real-time video multimedia communication is one of the possible applications for the third generation mobile communication systems. This video multimedia communication system needs a multiplexer which mixes various types of media such as video, voice and data into a single bitstream. ITU-T has standardized H.223 Annex A, B, C and D multimedia multiplexing protocols for low bit-rate mobile communications. This paper evaluates the performance of the GSRI Pragmatic TCM with an application of a mobile multimedia system using H.223 Annex D multiplexing scheme and MPEG-4 video coding.

This paper presents a new technique for the synthesis of sets of low-peak sequences exhibiting low peak cross correlation. The sequences also have flat power spectra and are suitable for many applications requiring such sets of uncorrelated pseudo-white-noise sources. This is a new application of the ta-sequence (trigonometric function aliasing sequence), which itself is a very new technique that uses the well-known "Reed-Solomon code" or "One coincident code" to generate these sets of low-peak-factor pseudo-white-noise exhibiting low peak cross correlation. The ta sequence method presented here provides the means for generating various sequences at the lengths required for such applications as system measurement (needing uncorrelated test signals), pseudo-noise synthesis (for spread spectrum communication), and audio signal processing for sound production (for enhancing spatial imagery in stereo signals synthesized from mono sources) and sound reproduction (for controlling unwanted interference effects in multiple-loudspeaker arrays).

In this paper, we introduce a lower bound for the generalized Hamming weights, which is applicable to arbitrary linear code, in terms of the notion of well-behaving. We also show that any [n,k] linear code C over a finite field F is the t-th rank MDS for t such that g(C)+1 t k where g(C) is easily calculated from the basis of Fn so chosen that whose first n-k elements generate C. Finally, we apply our result to Reed-Solomon, Reed-Muller and algebraic geometry codes on Cab, and determine g(C) for each code.

In this paper, we consider the applicability of turbo code for future third generation (3G) mobile telecommunication systems. Futhermore, we propose a simple method of estimating the channel variance which is necessary for the MAP (Maximum A Posteriori) decoding algorithm. We compare the performance of turbo code with a known channel variance, conventional variance estimate and variance estimated by our proposed technique. We show that our variance estimation scheme is adequate for 3G WB-CDMA mobile systems without degradation of turbo code performance.

A simple near-orthogonal code is used as frequency-hopping patterns for the frequency-hopped multiple access systems. Extended RS code is used as channel coding to deplete the effects of hits from simultaneous users. Packet error probability and channel throughput for the system utilizing the near-orthogonal code are evaluated and compared to the corresponding values obtained from the system utilizing random patterns. Results show that the former can provide substantial improvement over the latter. In our illustrated examples, we also show that under the constraint of packet error probability PE 10-2, the maximum achievable number of users with most (n,k) RS codes of interest is less than the number of distinct codewords in the near-orthogonal code. Thus, the number of codewords of the near-orthogonal code is large enough to support the practical application.

The DC component suppressing method, called Guided Scrambling (GS), has been proposed, where a source bit stream within a data block is subjected to several kinds of scrambling and a RLL (Run Length Limited) coding to make the selection set of channel bit streams, then the one having the least DC component is selected. Typically, this technique uses a convolutional operation or GF (Galois field) conversion. A review of their respective symbol error properties has revealed important findings. In the former case, the RS (Reed-Solomon) decoding capability is reduced because error propagation occurs in descrambling. In the latter case, error propagation of a data block length occurs when erroneous conversion data occurs after RS decoding. This paper introduces expressions for determining the decoded symbol error probabilities of the two schemes based on these properties. The paper also discusses the difference in code rates between the two schemes on the basis of the result of calculation using such expressions.

Generalized minimum-distance (GMD) decoding is well-known as a soft decision decoding technique for such linear block codes as BCH and RS codes. The GMD decoding algorithm generates a set of candidate codewords and selects as a decoded codeword that candidate with the smallest reliable distance. In this paper, for a GMD decoder of RS and BCH codes, we present a new sufficient condition for the decoded codeword to be optimal, and we show that this sufficient condition is less stringent than the one presented by Taipale and Pursely.

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.

A Reed-Solomon coded Type-I Hybrid ARQ scheme based on a Selective-Repeat (SR) ARQ with multicopy retransmission is proposed for mobile/personal satellite communication systems of a transmitter and a receiver both with the finite buffer. The performance of the proposed scheme on fading channels is analyzed. The basic idea of the strategy is the use of two modes; the SR mode and the multicopy mode. In the latter mode, erroneous blocks stored in the transmitter buffer are alternatively retransmitted multiple times when ν consecutive retransmissions in the SR mode are received in error. Numerical and simulation results for ν1 show that the proposed scheme presents better performance than the conventional SR+ST scheme 2 of the 2N block buffer by Miller and Lin.