Turbo codes-based image transmission for channels with multiple types of distortion

Product codes are generally used for progressive image transmission when random errors and packet loss (or burst errors) co-exist. However, the optimal rate allocation considering both component codes gives rise to high-optimization complexity. In addition, the decoding performance may be degraded quickly when the channel varies beyond the design point. In this paper, we propose a new unequal error protection (UEP) scheme for progressive image transmission by using rate-compatible punctured Turbo codes (RCPT) and cyclic redundancy check (CRC) codes only. By sophisticatedly interleaving each coded frame, the packet loss can be converted into randomly punctured bits in a Turbo code. Therefore, error control in noisy channels with different types of errors is equivalent to dealing with random bit errors only, with reduced turbo code rates. A genetic algorithm-based method is presented to further reduce the optimization complexity. This proposed method not only gives a better performance than product codes in given channel conditions but is also more robust to the channel variation. Finally, to break down the error floor of turbo decoding, we further extend the above RCPT/CRC protection to a product code scheme by adding a Reed-Solomon (RS) code across the frames. The associated rate allocation is discussed and further improvement is demonstrated.     

Probabilistic crisscross error correction

The crisscross error model in data arrays is considered, where the corrupted symbols are confined to a prescribed number of rows or columns (or both). Under the additional assumption that the corrupted entries are uniformly distributed over the channel alphabet, and by allowing a small decoding error probability, a coding scheme is presented where the redundancy can get close to one half the redundancy required in minimum-distance decoding of crisscross errors     

Performance of Forward-Error Correction Code in 10-Gb/s RSOA-Based WDM PON

We investigate the performance of the forward-error correction (FEC) code for the 10-Gb/s wavelength-division- multiplexed passive optical network (WDM PON) implemented by using reflective semiconductor optical amplifiers (RSOAs) with extremely limited modulation bandwidth and the electronic equalizers to compensate for the degradations resulting from the use of such RSOAs. We show that the error occurrences in this network strongly depend on the bit pattern and the burst errors are likely to occur. Thus, it is important to use the FEC code capable of correcting the burst errors such as Reed–Solomon (RS) code. In addition, since a significant penalty can be induced by the increased line rate resulting from the use of the FEC code, it is necessary to find the optimum redundancy required to minimize the bit-error rate. We also evaluate the tolerance to the chromatic dispersion of the proposed 10-Gb/s WDM PON implemented by using the RS code with the optimum redundancy.      

Enhanced Low Complex Double Error Correction Coding with Crosstalk Avoidance for Reliable On-Chip Interconnection Link

As the technology scales down, shrinking geometry and layout dimension, on- chip interconnects are exposed to different noise sources such as crosstalk coupling, supply voltage fluctuation and temperature variation that cause random and burst errors. These errors affect the reliability of the on-chip interconnects. Hence, error correction codes integrated with noise reduction techniques are incorporated to make the on-chip interconnects robust against errors. The proposed error correction code uses triplication error correction scheme as crosstalk avoidance code (CAC) and a parity bit is added to it to enhance the error correction capability. The proposed error correction code corrects all the error patterns of one bit error, two bit errors. The proposed code also corrects 7 out of 10 possible three bit error patterns and detects burst errors of three. Hybrid Automatic Repeat Request (HARQ) system is employed when burst errors of three occurs. The performance of the proposed codec is evaluated for residual flit error rate, codec area, power, delay, average flit latency and link energy consumption. The proposed codec achieves four magnitude order of low residual flit error rate and link energy minimization of over 53 % compared to other existing error correction schemes. Besides the low residual flit error rate, and link energy minimization, the proposed codec also achieves up to 4.2 % less area and up to 6 % less codec power consumption compared to other error correction codes. The less codec area, codec power consumption, low link energy and low residual flit error rate make the proposed code appropriate for on chip interconnection link.     

Analysis of recurrent codes

A definition of a recurrent code is given in a framework which renders it amenable to mathematical analysis. Recurrent codes for both independent and burst errors are considered, and a necessary and sufficient condition for either type of error correction is established. For burst-error-correcting codes, the problem treated is (for a fixed burst length and redundancy) the minimization of the error-free distance ("guard space") required between bursts. A lower bound is obtained on the guard space, and in certain cases, codes which realize this bound are given. A general code which is close to the lower bound in many cases is also given. For independent errors, a code which will correct any error, provided that no consecutive "n" positions have more than "e" digits in error, is discussed. Fore = 1, a necessary and sufficient condition onnis derived; fore > 1, a lower bound onnis obtained, and for the case of redundancy1/2, an upper bound onnis also derived.     

Burst-trapping techniques for a compound channel

An adaptive decoding technique called burst trapping is presented to correct both random and burst errors. Two decoding algorithms are used, one for random errors, and the other for bursts. The former is based on a conventional correction technique, the latter utilizes an encoding procedure for which each information digit appears twice in the data stream, first unchanged, and second combined with (addition modulo2) a check digit of a widely separated later block. Whenever the number of errors within a code block are detected to be too large to correct with the random-error-correcting algorithm, the burst-correcting algorithm corrects these errors by recovering the information from later blocks where it appears in combination with check digits. It is shown that the scheme requires very limited guard space and has limited error propagation. Furthermore, the storage requirement is even smaller than the guard space. This is the only known coding system that has this desirable feature. Results of simulation of such codes over telephone channels indicate that the performance of such codes, when compared with interleaved block codes, offers better results at significantly lower cost.     

Wireless image transmission using turbo codes and optimal unequal error protection.

A novel image transmission scheme is proposed for the communication of set partitioning in hierarchical trees image streams over wireless channels. The proposed scheme employs turbo codes and Reed-Solomon codes in order to deal effectively with burst errors. An algorithm for the optimal unequal error protection of the compressed bitstream is also proposed and applied in conjunction with an inherently more efficient technique for product code decoding. The resulting scheme is tested for the transmission of images over wireless channels. Experimental evaluation clearly demonstrates the superiority of the proposed transmission system in comparison to well-known robust coding schemes.     

Pseudo-analog speech transmission in mobile radio communicationsystems

A low-complexity pseudo-analog speech transmission scheme is proposed for portable communications. It uses a speech coder based on adaptive differential pulse code modulation (ADPCM) in combination with a multilevel digital modulation technique such as M-ary DPSK or M-ary FSK and features low quantization noise, bandwidth efficiency, and robustness to transmission errors. A nonsymmetric M -ary DPSK scheme called skewed M-ary DPSK is proposed to enhance the noisy channel performance. Comparison to conventional analog FM and a digital speech transmission scheme using adaptive predictive coding and forward error correction (FEC) based on convolutional coding shows that the pseudo-analog system has the best objective signal-to-noise ratio performance under most channel conditions. Informal subjective evaluations rate the digital system superior to the pseudo-analog scheme for bad channels and conversely for good channels. It is concluded that the pseudo-analog system can be designed with low delay and high speech quality for good channels with high spectral efficiency     

Hybrid Error Control Using Retransmission and Generalized Burst-Trapping Codes

On most real channels hybrid error control schemes are expected to provide a throughput higher than that of automatic repeatrequest (ARQ) systems and a reliability better than forward error correction (FEC) systems. On compound channels, channels with a mixture of random and burst errors, generalized burst-trapping (GBT) codes seem to be quite effective for FEC. In this paper, a hybrid scheme with Go BackNARQ as the retransmission component and GBT code as the FEC component, is described. Its performance is analyzed in terms of throughput efficiency and undetected error probability and is compared with that of a forward-acting GBT code. Numerical calculations of the parameters are presented to illustrate the performance.     

Direct sequence spread spectrum scheme for an unmanned aerial vehicle PPM control signal protection

In this letter, a new direct sequence spread spectrum scheme for protection of an unmanned aerial vehicle (UAV) binary pulse-position modulated (PPM)control signal is proposed. The UAV PPM control signal consists of data frames. Each of them contains a synchronizing pulse followed by a number of shorter pulses equal to the number of channels N. At the beginning of any pulse is the pause long 0.3 ms. The proposed scheme uses (N + 1) pseudonoise (PN) codes: one of them (PN₀) is assigned to the synchronizing pulse while the each of the remaining N codes (PN₁, PN₂, ... PN_N) corresponds to the appropriate channel. The same PN code is transmitted during the pause and the pulse which follows the pause. At the receiving side, the set of (N + 1) passive correlators is used to detect respective PN codes. Proposed scheme requires neither PN code tracking process nor data demodulation, so is resistant to timing jitter. Performance measures of the proposed scheme are calculated.     

An efficient convolutional coding/decoding strategy for channelswith memory

Many digital communication channels are affected by errors that tend to occur in bursts. A great deal of work has been devoted to finding good burst-error-correcting codes and developing burst-error-correcting schemes. However, burst-error-correcting codes are generally not effective for long bursts. Some burst-error-correcting schemes suffer long delay in decoding. Others are very sensitive to random errors in the guard space. Most of these schemes are not adaptive to channel conditions. A new adaptive scheme is proposed to overcome these drawbacks. The scheme employs a combination of two complementary punctured convolutional (CPC) codes. One of the codes is used for burst detection and for channel state estimation, and both codes are used for error correction. The proposed scheme is analyzed over a two state Markov chain channel model. Unlike existing burst-error-correcting schemes, it is shown that the proposed scheme is adaptive to channel conditions and less sensitive to errors in the guard space. For the same delay, the proposed scheme offers better performance than the interleaving schemes. When the channel is heavily corrupted by bursts, the improvement is even more pronounced     

Performance of H.263 video transmission over wireless channelsusing hybrid ARQ

This paper proposes a hybrid ARQ error control scheme based on the concatenation of a Reed-Solomon (RS) code and a rate compatible punctured convolutional (RCPC) code for low-bit-rate video transmission over wireless channels. The concatenated hybrid ARQ scheme we propose combines the advantages of both type-I and type-II hybrid ARQ schemes. Certain error correction capability is provided in each (re)transmitted packet, and the information can be recovered from each transmission or retransmission alone if the errors are within the error correction capability (similar to type-I hybrid ARQ). The retransmitted packet contains redundancy bits which, when combined with the previous transmission, result in a more powerful RS/convolutional concatenated code to recover information if error correction fails for the individual transmissions (similar to type-II hybrid ARQ). Bit-error rate (BER) or signal-to-noise ratio (SNR) of a radio channel changes over time due to mobile movement and fading. The channel quality at any instant depends on the previous channel conditions. For the accurate analysis of the performance of the hybrid ARQ scheme, we use a multistate Markov chain (MSMC) to model the radio channel at the data packet level. We propose a method to partition the range of the received SNR into a set of states for constructing the model so that the difference between the error rate of the real radio channel and that of the MSMC model is minimized. Based on the model, we analyze the performance of the concatenated hybrid ARQ scheme. The results give valuable insight into the effects of the error protection capability in each packet, the mobile speed, and the number of retransmissions. Finally, the transmission of H.263 coded video over a wireless channel with error protection provided by the concatenated hybrid ARQ scheme is studied by means of simulations     

Hybrid ARQ schemes for point-to-multipoint communication overnonstationary broadcast channels

Hybrid automatic-repeat-request (ARQ) error control schemes make use of both error detection and error correction in order to achieve high throughput and low undetected error probabilities on two way channels. Two hybrid ARQ schemes, termed hybrid go-back-N (HGB- N) and hybrid selective-repeat (HSR), are proposed for point-to-multipoint communications over broadcast channels. Both schemes incorporate a concatenated code for error correction and error detection. The performance study of the hybrid schemes is based on a two-state Markov model of a burst noise channel. An analytic solution is derived for the throughput efficiency of the HSR scheme, while approximations and computer simulation are used to evaluate the throughput efficiency of the HGB-N scheme. It is shown that the schemes perform considerably better than the corresponding pure ARQ schemes in which a block code is used for error detection only, especially in environments with a large number of receivers and large channel roundtrip delays, such as satellite broadcast links     

A note on burst-error correction using the check polynomial (Corresp.)

When decoding a cyclic code, an alternative to computing the syndrome by dividing the receivedn-tupleW(x)by the generator polynomialG(x)is to compute the productH(x)W(x), modx^n - 1, with the check polynomialH(x). It is shown in this paper that the form of the product can be predicted in terms of general code parameters and corresponds closely to the burst error from which it is derived. By using the properties of the product sequence, a burst-error decoder is derived in such a way that a family of potentially fast burst-error decoders can be constructed. Another important application of the proposed technique concerns decoder implementation for the correction of a synchronization error (slip) when the coset code technique is used. It is shown that slip correction can be implemented so that both the magnitude and direction of slip are determined by examining only one receivedn-tuple.     

The burst error correcting capabilities of a simple array code

We propose a simple decoder for a widely used array code, known as the EVENODD code, which is originally designed to correct phased burst errors, to make it useful for correcting nonphased errors. The proposed scheme is capable of correcting almost all bursts up to a certain length. We show that the failure rate is sufficiently small and approaches zero as the block length increases. The redundancy of the code is twice the maximal burst length, which is a lower bound for the redundancy of a true burst-error-correcting code. Both the encoder and the decoder have very low complexity, both in terms of number of operations and in terms of computer code size     

An error control system with multiple-stage forward errorcorrections

A robust error control coding system is presented. This system is a cascaded FEC (forward error control) scheme supported by parity retransmissions for further error correction in the erroneous data words. The error performance and throughput efficiency of the system are analyzed. Two specific examples of the error control system are studied. The first example does not use an inner code, and the outer code, which is not interleaved, is a shortened code of the NASA standard RS code over GF(2⁸). The second example, as proposed for NASA uses the same shortened RS code as the base outer code C₂, except that it is interleaved to a depth of 2. It is shown that both examples provide high reliability and throughput efficiency even for high channel bit-error rates in the range of 10^-2     

Iterative joint source-channel decoding of variable-length codes using residual source redundancy

We present a novel symbol-based soft-input a posteriori probability (APP) decoder for packetized variable-length encoded source indexes transmitted over wireless channels where the residual redundancy after source encoding is exploited for error protection. In combination with a mean-square or maximum APP estimation of the reconstructed source data, the whole decoding process is close to optimal. Furthermore, solutions for the proposed APP decoder with reduced complexity are discussed and compared to the near-optimal solution. When, in addition, channel codes are employed for protecting the variable-length encoded data, an iterative source-channel decoder can be obtained in the same way as for serially concatenated codes, where the proposed APP source decoder then represents one of the two constituent decoders. The simulation results show that this iterative decoding technique leads to substantial error protection for variable-length encoded correlated source signals, especially, when they are transmitted over highly corrupted channels.     

Reed-Solomon codes for correcting phased error bursts

A code structure is introduced that represents a Reed-Solomon (RS) code in two-dimensional format. Based on this structure, a novel approach to multiple error burst correction using RS codes is proposed. For a model of phased error bursts, where each burst can affect one of the columns in a two-dimensional transmitted word, it is shown that the bursts can be corrected using a known multisequence shift-register synthesis algorithm. It is further shown that the resulting codes posses nearly optimal burst correction capability, under certain probability of decoding failure. Finally, low-complexity systematic encoding and syndrome computation algorithms for these codes are discussed. The proposed scheme may also find use in decoding of different coding schemes based on RS codes, such as product or concatenated codes.     

Introduction to redundancy coding

An introduction to redundancy encoding as used in digital data communications is described. The need for redundancy is first addressed, followed by a discussion of the binary symmetric channel, burst noise channels, and the use of interleaving to randomize burst errors. The concept of redundancy is presented next, showing how it is used to supply the highest possible degree of error detection or how it can be applied to provide for the detection and correction of a lesser number of errors. The use of some codes to correct some errors and also to detect, but not correct, additional errors is discussed. The properties of block codes are developed beginning with repetition codes then covering single-parity check codes, Hamming (single-error detection) codes, and Bose-Chadhuri-Hocquenghem (BCH)codes. The basic properties and structures of these codes are emphasized with examples of implementation procedures for both encoding and decoding.     

The (d,k) subcode of a linear block code

A simple technique employing linear block codes to construct (d,k) error-correcting block codes is considered. This scheme allows asymptotically reliable transmission at rate R over a BSC channel with capacity C_BSC provided R ⩽C_d,k-(1+C_BSC), where C_d,k is the maximum entropy of a (d,k ) source. For the same error-correcting capability, the loss in code rate incurred by a multiple-error correcting (d,k) code resulting from this scheme is no greater than that incurred by the parent linear block code. The single-error correcting code is asymptotically optimal. A modification allows the correction of single bit-shaft errors as well. Decoding can be accomplished using off-the-shelf decoders. A systematic (but suboptimal) encoding scheme and detailed case studies are provided