Cyclic Low-Density MDS Array Codes

We construct two infinite families of low density MDS array codes which are also cyclic. One of these families includes the first such sub-family with redundancy parameter r > 2. The two constructions have different algebraic formulations, though they both have the same indirect structure. First MDS codes that are not cyclic are constructed and then by applying a certain mapping to their parity check matrices, non-equivalent cyclic codes with the same distance and density properties are obtained. Using the same proof techniques, a third infinite family of quasi-cyclic codes can be constructed

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

Delay-insensitive pipelined communication on parallel buses

Consider a communication channel that consists of several subchannels transmitting simultaneously and asynchronously. As an example of this scheme, we can consider a board with several chips. The subchannels represent wires connecting between the chips where differences in the lengths of the wires might result in asynchronous reception. In current technology, the receiver acknowledges reception of the message before the transmitter sends the following message. Namely, pipelined utilization of the channel is not possible. Our main contribution is a scheme that enables transmission without an acknowledgment of the message, therefore enabling pipelined communication and providing a higher bandwidth. However, our scheme allows for a certain number of transitions from a second message to arrive before reception of the current message has been completed, a condition that we call skew. We have derived necessary and sufficient conditions for codes that can tolerate a certain amount of skew among adjacent messages (therefore, allowing for continuous operation) and detect a larger amount of skew when the original skew is exceeded. These results generalize previously known results. We have constructed codes that satisfy the necessary and sufficient conditions, studied their optimality, and devised efficient decoding algorithms. To the best of our knowledge, this is the first known scheme that permits efficient asynchronous communications without acknowledgment. Potential applications are in on-chip, on-board, and board to board communications, enabling much higher communication bandwidth

Increasing the Information Density of Storage Systems Using the Precision-Resolution Paradigm

Arguably, the most prominent constrained system in storage applications is the (d, k)-RLL (Run-Length Limited) system, where every binary sequence obeys the constraint that every two adjacent 1's are separated by at least d consecutive 0's and at most k consecutive 0's, namely, runs of 0's are length limited. The motivation for the RLL constraint arises mainly from the physical limitations of the read and write technologies in magnetic and optical storage systems. We revisit the rationale for the RLL system and reevaluate its relationship to the physical media. As a result, we introduce a new paradigm that better matches the physical constraints. We call the new paradigm the Precision-Resolution (PR) system, where the write operation is limited by precision and the read operation is limited by resolution. We compute the capacity of a general PR system and demonstrate that it provides a significant increase in the information density compared to the traditional RLL system (for identical physical limitations). For example, the capacity of the (2, 10)-RLL used in CD-ROMs and DVDs is approximately 0.5418, while our PR system provides the capacity of about 0.7725, resulting in a potential increase of about 40% in information density

Analysis of checkpointing schemes for multiprocessor systems

Parallel computing systems provide hardware redundancy that helps to achieve low cost fault-tolerance, by duplicating the task into more than a single processor, and comparing the states of the processors at checkpoints. This paper suggests a novel technique, based on a Markov Reward Model (MRM), for analyzing the performance of checkpointing schemes with task duplication. We show how this technique can be used to derive the average execution time of a task and other important parameters related to the performance of checkpointing schemes. Our analytical results match well the values we obtained using a simulation program. We compare the average task execution time and total work of four checkpointing schemes, and show that generally increasing the number of processors reduces the average execution time, but increases the total work done by the processors. However, in cases where there is a big difference between the time it takes to perform different operations, those results can change

Decoding the Golay code with Venn diagrams

A decoding algorithm, based on Venn diagrams, for decoding the [23, 12, 7] Golay code is presented. The decoding algorithm is based on the design properties of the parity sets of the code. As for other decoding algorithms for the Golay code, decoding can be easily done by hand

Network coding for non-uniform demands

Non-uniform demand networks are defined as a useful connection model, in between multicasts and general connections. In these networks, each sink demands a certain number of messages, without specifying their identities. We study the solvability of such networks and give a tight bound on the number of sinks for which the min cut condition is sufficient. This sufficiency result is unique to the non-uniform demand model and does not apply to general connection networks. We propose constructions to solve networks at, or slightly below capacity, and investigate the effect large alphabets have on the solvability of such networks. We also show that our efficient constructions are suboptimal when used in networks with more sinks, yet this comes with little surprise considering the fact that the general problem is shown to be NP-hard

How does the pitch and pattern of a signal affect auditory arousal thresholds?

How arousal thresholds vary with different sounds is a critical issue for emergency awakenings, especially as sleepers are dying in fires despite having a working smoke alarm. Previous research shows that the current high pitched (3000+ Hz) smoke alarm signal is significantly less effective than an alternative signal, the 520 Hz square wave, in all populations tested. However, as the number of sounds tested has been small further research is needed. Here we measured auditory arousal thresholds (AATs) across signals with a range of characteristics to determine the most effective waking signal. Thirty nine young adults participated over three nights. In Part A, nine signals were presented in stage 4 sleep with ascending decibel levels. Signals were short beeps in the low to mid frequency range with different spectral complexities: square waves, pure tones, whoops and white noise. Part B manipulated temporal patterns, inserting silences of 0, 10 and 21 seconds after each 12 seconds of beeps. It was found that the low frequency (400 and 520 Hz) square waves yielded significantly lower AATs than the alternatives. A trend was found across the three temporal manipulations, with a 10 second intervening silence showing some advantage. These findings support earlier research indicating that the best sound for awakening from deep sleep is a low frequency square wave. It is argued that the signal with the lowest response threshold when awake may be the same as the most arousing signal when asleep, especially where the sleeper processes the signal as meaningful