Abstract: This paper studies the application of convolutional coding to Constant Envelope Orthogonal Frequency Division Multiplexing (CE-OFDM). The noise at the output of the phase demodulator (in the CE-OFDM receiver) is shown to be approximately Gaussian at high SNR and relatively low modulation indices. This allows the use of the conventional metric in the Viterbi decoding algorithm. A bound on the performance of convolutionally coded CE-OFDM is derived and is plotted along side the performance curves obtained through simulation. Both the cases with and without a phase unwrapper are studied. The phase unwrapper results in large bursts of errors at moderate to high modulation indices due to cycle slips. Such burst errors overwhelm the convolutional code and render it useless. Fewer burst errors are generated in the absence of a phase unwrapper. Further adding a simple interleaver is beneficial to counter the burst errors. It is shown that channel coding with interleaving provides good performance for CE-OFDM for low to moderate modulation indices while correcting burst errors due to phase wrapping.

Abstract: We study a modification method for constructing low-density parity-check (LDPC) codes for solid burst erasures. Our proposed modification method is based on a column permutation technique for a parity-check matrix of the original LDPC codes. It can change the burst erasure correction capabilities without degradation in the performance over random erasure channels. We show by simulation results that the performance of codes permuted by our method are better than that of the original codes, especially with two or more solid burst erasures.

Abstract: Apparatus and methods are provided to correct burst errors from a communication channel. Embodiments may include correcting burst errors in received data using a decoder configured as a Meggitt decoder with an additional selection criterion to correct a burst error having a length larger than the code error correction capability.

Abstract: Two-dimensional array codes correcting rectangular burst errors are considered. We give a construction and examples of linear two-dimensional array codes correcting rectangular burst errors of size b 1 × b 2 with minimum redundancy r = 2b 1 b 2. We present constructions of cyclic two-dimensional array codes correcting phased and arbitrary rectangular burst errors; their encoding and decoding algorithms are also given. A class of cyclic two-dimensional array codes correcting rectangular burst errors with asymptotically minimal redundancy is described. We construct a class of linear two-dimensional array codes correcting cyclic rectangular b 1 × b 2 burst errors with asymptotic excess redundancy $$\tilde r_C (b_1 ,b_2 ) = 2b_1 b_2 - 3$$ .

Abstract: Some well-known real-number codes are DFT codes. Since these codes are cyclic, they can be used to correct erasures (errors at known positions) and detect errors, using the locator polynomial via the syndrome, with efficient algorithms. The stability of such codes are, however, very poor for burst error patterns. In such conditions, the stability of the system of equations to be solved is very poor. This amplifies the rounding errors inherent to the real number field. In order to improve the stability of real-number error-correcting codes, other types of coding matrices were considered, namely random orthogonal matrices. These type of codes have proven to be very stable, when compared to DFT codes. However, the problem of detecting errors (when the positions of these errors are not known) with random codes was not addressed. Such codes do not possess any specific structure which could be exploited to create an efficient algorithm. In this paper, we present an efficient method to locate errors with codes based on random orthogonal matrices.

Abstract: This paper investigates cyclic codes for correcting bursts of errors from a new point of view. A simple iterative algorithm for correcting bursts of errors is developed. This algorithm is optimal in the sense that it corrects burst of errors of lengths up to the burst-error-correction limit of a cyclic code. Also included in the paper is an iterative process for correcting bursts of erasures.

Abstract: Low density parity check (LDPC) codes have the ability to transmit data at rates approaching channel capacity with very low error probability. Our study of LDPC codes on JPEG2000-compressed ultraspectral sounder data shows that for an LDPC encoder designed with certain input parameters, the LDPC decoder is able to correct all single errors and two-bit burst errors. Furthermore, our analysis on a massive variety of 3- and 4-bit burst error scenarios indicates that the locations of LDPC-uncorrected errors for 3- and 4-bit burst errors appear to be fixed, regardless of the content of the input data. We propose a look-up table based error correction method to correct errors surviving from the LDPC decoder for 3- and 4-bit burst errors.

Abstract: Three types of errors occur in satellite communications: random bit errors, burst errors, and synchronization errors. Random bit errors are randomly distributed in a block of data, and are always present (i.e., constant error). Random bit errors are caused by atmosphere or electronic equipment. Burst errors are localized, and are created by some sudden change in the communications channel (e.g., antenna pointing errors). Synchronization errors are caused by the failure of the receiver to detect the block boundaries. Burst noise with low signal-to-noise-ratio (SNR) can cause long localized burst errors. Long burst errors can lead to synchronization errors. Many communication channels contain both random and burst noise. In many communication systems where the bandwidth is fixed, coding rate is an important factor. Our research is unique because it compares an erasure correction code, such as the Information Dispersal Algorithm (IDA), with Turbo Product Codes (TPC) where coding rate is high and burst errors are long. Coding rate of TPC is f; therefore, it must be heavily punctured to obtain a high coding rate. We set coding rate for both TPC and IDA at 0.875. Most of the work in the area of burst error correction considers only short burst errors or low coding rates (e.g., f) where our research assumes high coding rate and long burst errors. Presented here is IDA, a product code with a high coding rate, that is capable of correcting both random bit errors and long burst errors. The product code uses two different Forward-Error-Correction-Codes (FECC). One for random bit error correction and the other for burst error correction. In the horizontal direction (i.e., inner code), we use any FECC to correct random bit errors. In the vertical direction (i.e., outer code), we use any erasure correction code, such as IDA, to correct long burst errors. The IDA can be implemented using Reed Solomon (RS) codes. Faster and more efficient codes can be used to implement IDA, but they are not currently implemented in hardware. The IDA can be used to design bandwidth-efficient FECC for a channel with burst noise. Our research presents the analysis, design, implementation, and testing of IDA. The IDA has been implemented in software using the RS codes. We compared its performance with that of TPC. Assuming a well-defined channel with long burst noise (i.e., many bit errors) and a large block size, we showed that if symbol-by-symbol reliability is not available (i.e., unable to detect burst noise boundaries), then IDA will perform better than TPC in terms of bit and block error rates. However, if symbol-by-symbol reliability is available, then IDA may perform as well as TPC in terms of block error rate, while TPC will always have a lower bit error rate.

Abstract: In this paper we compare some aspects of the design and analysis of one-dimensional (1-D) and two-dimensional (2-D) storage systems. We show that for modulation codes and for the detection of signals corrupted by intersymbol interference and additive white Gaussian noise, the design and analysis is much more complicated in the 2-D case as compared with the 1-D case. However, we show that the reverse is true for the design of burst error correcting cyclic codes. That is, we show that one must carefully choose the generator polynomial to obtain a good 1-D burst error correcting code but using a cyclic product code, any arbitrary generator polynomials for the row code and for the column code can produce a good 2-D burst error correcting code.

Abstract: In this paper, it is shown that under very mild assumptions, practically any binary linear block code of length N and dimension K is able to correct any burst of length up to N - K with probability of success Pc = 1 for erasures, and any burst of length up to N - K - m with probability of success Pc ges 1 - N2-m for errors. In both cases, the decoding is based on identifying a string of zeroes in an extended syndrome corresponding to a particular representation of the parity check matrix of the code and its complexity is O(N2) binary operations