Raptor Codes in the Low SNR Regime

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise (BIAWGN) channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.Comment: Submitted to the IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:1510.0772

On a Low-Rate TLDPC Code Ensemble and the Necessary Condition on the Linear Minimum Distance for Sparse-Graph Codes

This paper addresses the issue of design of low-rate sparse-graph codes with linear minimum distance in the blocklength. First, we define a necessary condition which needs to be satisfied when the linear minimum distance is to be ensured. The condition is formulated in terms of degree-1 and degree-2 variable nodes and of low-weight codewords of the underlying code, and it generalizies results known for turbo codes [8] and LDPC codes. Then, we present a new ensemble of low-rate codes, which itself is a subclass of TLDPC codes [4], [5], and which is designed under this necessary condition. The asymptotic analysis of the ensemble shows that its iterative threshold is situated close to the Shannon limit. In addition to the linear minimum distance property, it has a simple structure and enjoys a low decoding complexity and a fast convergence.Comment: submitted to IEEE Trans. on Communication

Efficient fault-tolerant quantum computing

Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible quantum codes are obtained, and good candidates exhibited. This permits a new analysis of the permissible error rates and minimum overheads for robust quantum computing. It is found that, under the standard noise model of ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an order of magnitude larger than the logical machine contained within it in order to be reliable. For example, a scale-up by a factor of 22, with gate error rate of order $10^{-5}$, is sufficient to permit large quantum algorithms such as factorization of thousand-digit numbers.Comment: 21 pages plus 5 figures. Replaced with figures in new format to avoid problem

High-Rate Regenerating Codes Through Layering

In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff, and compare very well in comparison to scheme that employs space-sharing between MSR and MBR codes. For the parameter set $(n,k,d=k)$ with $n < 2k-1$, we construct a class of codes with an auxiliary parameter $w$, referred to as canonical codes. With $w$ in the range $n-k < w < k$, these codes operate in the region between the MSR point and the MBR point, and perform significantly better than the space-sharing line. They only require a field size greater than $w+n-k$. For the case of $(n,n-1,n-1)$, canonical codes can also be shown to achieve an interior point on the line-segment joining the MSR point and the next point of slope-discontinuity on the storage-repair-bandwidth tradeoff. Thus we establish the existence of exact-repair codes on a point other than the MSR and the MBR point on the storage-repair-bandwidth tradeoff. We also construct layered regenerating codes for general parameter set $(n,k<d,k)$, which we refer to as non-canonical codes. These codes also perform significantly better than the space-sharing line, though they require a significantly higher field size. All the codes constructed in this paper are high-rate, can repair multiple node-failures and do not require any computation at the helper nodes. We also construct optimal codes with locality in which the local codes are layered regenerating codes.Comment: 20 pages, 9 figure

ChitChat: Making Video Chat Robust to Packet Loss

Video chat is increasingly popular among Internet users. Often, however, chatting sessions suffer from packet loss, which causes video outage and poor quality. Existing solutions however are unsatisfying. Retransmissions increase the delay and hence can interact negatively with the strict timing requirements of interactive video. FEC codes introduce extra overhead and hence reduce the bandwidth available for video data even in the absence of packet loss. This paper presents ChitChat, a new approach for reliable video chat that neither delays frames nor introduces bandwidth overhead. The key idea is to ensure that the information in each packet describes the whole frame. As a result, even when some packets are lost, the receiver can still use the received packets to decode a smooth version of the original frame. This reduces frame loss and the resulting video freezes and improves the perceived video quality. We have implemented ChitChat and evaluated it over multiple Internet paths. In comparison to Windows Live Messenger 2009, our method reduces the occurrences of video outage events by more than an order of magnitude

Randomized Differential DSSS: Jamming-Resistant Wireless Broadcast Communication

Abstract—Jamming resistance is crucial for applications where reliable wireless communication is required. Spread spectrum techniques such as Frequency Hopping Spread Spectrum (FHSS) and Direct Sequence Spread Spectrum (DSSS) have been used as countermeasures against jamming attacks. Traditional antijamming techniques require that senders and receivers share a secret key in order to communicate with each other. However, such a requirement prevents these techniques from being effective for anti-jamming broadcast communication, where a jammer may learn the shared key from a compromised or malicious receiver and disrupt the reception at normal receivers. In this paper, we propose a Randomized Differential DSSS (RD-DSSS) scheme to achieve anti-jamming broadcast communication without shared keys. RD-DSSS encodes each bit of data using the correlation of unpredictable spreading codes. Specifically, bit “0 ” is encoded using two different spreading codes, which have low correlation with each other, while bit “1 ” is encoded using two identical spreading codes, which have high correlation. To defeat reactive jamming attacks, RD-DSSS uses multiple spreading code sequences to spread each message and rearranges the spread output before transmitting it. Our theoretical analysis and simulation results show that RD-DSSS can effectively defeat jamming attacks for anti-jamming broadcast communication without shared keys. I