Miscorrection probability beyond the minimum distance

The miscorrection probability of a list decoder is the probability that the decoder will have at least one non-causal codeword in its decoding sphere. Evaluating this probability is important when using a list-decoder as a conventional decoder since in that case we require the list to contain at most one codeword for most of the errors. A lower bound on the miscorrection is the main result. The key ingredient in the proof is a new combinatorial upper bound on the list-size for a general q−ary block code. This bound is tighter than the best known on large alphabets, and it is shown to be very close to the algebraic bound for Reed-Solomon codes. Finally we discuss two known upper bounds on the miscorrection probability and unify them for linear MDS codes

A Combinatorial Bound on the List Size

In this paper we study the scenario in which a server sends dynamic data over a single broadcast channel to a number of passive clients. We consider the data to consist of discrete packets, where each update is sent in a separate packet. On demand, each client listens to the channel in order to obtain the most recent data packet. Such scenarios arise in many practical applications such as the distribution of weather and traffic updates to wireless mobile devices and broadcasting stock price information over the Internet. To satisfy a request, a client must listen to at least one packet from beginning to end. We thus consider the design of a broadcast schedule which minimizes the time that passes between a clients request and the time that it hears a new data packet, i.e., the waiting time of the client. Previous studies have addressed this objective, assuming that client requests are distributed uniformly over time. However, in the general setting, the clients behavior is difficult to predict and might not be known to the server. In this work we consider the design of universal schedules that guarantee a short waiting time for any possible client behavior. We define the model of dynamic broadcasting in the universal setting, and prove various results regarding the waiting time achievable in this framework

Improved Decoding of Staircase Codes: The Soft-aided Bit-marking (SABM) Algorithm

Staircase codes (SCCs) are typically decoded using iterative bounded-distance decoding (BDD) and hard decisions. In this paper, a novel decoding algorithm is proposed, which partially uses soft information from the channel. The proposed algorithm is based on marking certain number of highly reliable and highly unreliable bits. These marked bits are used to improve the miscorrection-detection capability of the SCC decoder and the error-correcting capability of BDD. For SCCs with $2$-error-correcting Bose-Chaudhuri-Hocquenghem component codes, our algorithm improves upon standard SCC decoding by up to $0.30$~dB at a bit-error rate (BER) of $10^{-7}$. The proposed algorithm is shown to achieve almost half of the gain achievable by an idealized decoder with this structure. A complexity analysis based on the number of additional calls to the component BDD decoder shows that the relative complexity increase is only around $4\%$ at a BER of $10^{-4}$. This additional complexity is shown to decrease as the channel quality improves. Our algorithm is also extended (with minor modifications) to product codes. The simulation results show that in this case, the algorithm offers gains of up to $0.44$~dB at a BER of $10^{-8}$.Comment: 10 pages, 12 figure

Improved Soft-Aided Decoding of Product Codes With Dynamic Reliability Scores

Products codes (PCs) are conventionally decoded with efficient iterative bounded-distance decoding (iBDD) based on hard-decision channel outputs which entails a performance loss compared to a soft-decision decoder. Recently, several hybrid algorithms have been proposed aimed to improve the performance of iBDD decoders via the aid of a certain amount of soft information while keeping the decoding complexity similarly low as in iBDD. We propose a novel hybrid low-complexity decoder for PCs based on error-and-erasure (EaE) decoding and dynamic reliability scores (DRSs). This decoder is based on a novel EaE component code decoder, which is able to decode beyond the designed distance of the component code but suffers from an increased miscorrection probability. The DRSs, reflecting the reliability of a codeword bit, are used to detect and avoid miscorrections. Simulation results show that this policy can reduce the miscorrection rate significantly and improves the decoding performance. The decoder requires only ternary message passing and a slight increase of computational complexity compared to iBDD, which makes it suitable for high-speed communication systems. Coding gains of up to 1.2 dB compared to the conventional iBDD decoder are observed

AN INTERESTING AND EFFECTIVE CODE FOR ERROR-CORRECTING IN MASS-STORAGE DEVICES

We present an interesting version of error correcting codes that makes use of the idea of multi-dimensional coding and is able to make very large data total error-free even if the ratio of the number of erroneous characters to the total amount of characters is about 0.1 - 0.2. The encoding and decoding mechanisms are very simple to do. Because of these properties it can be used when transferring very large data through a noisy channel or storing in a shoddy memory-device even if the data is required to be transferred or stored intactly, which means to obtain it after decoding total error-free. Noisy channels can be e.g. phone lines transferring facsimile data (Doong, 1992), and as a 'shoddy' memory- device can be regarded any kind of standard-quality ones when counting on the worst case in a system to accomplish the requirement of high-reliability (e.g. a stable storage device), mainly when using cheaper kinds of mass storage devices (e.g. Hard Disks, Optical Disks)