Bella Bose

Wireless Broadcast Using Network Coding

Traditional approaches to reliably transmit information over an error-prone network employ either forward error correction (FEC) or retransmission techniques. In this paper, we propose some network coding schemes to reduce the number of broadcast transmissions from one sender to multiple receivers. The main idea is to allow the sender to combine and retransmit the lost packets in a certain way so that with one transmission, multiple receivers are able to recover their own lost packets. For comparison, we derive a few theoretical results on the bandwidth efficiency of the proposed network coding and traditional automatic repeat-request (ARQ) schemes. Both simulations and theoretical analysis confirm the advantages of the proposed network coding schemes over the ARQ ones.

Lee distance and topological properties of k-ary n-cubes

In this paper, we consider various topological properties of a k-ary n-cube (Q/sub n//sup k/) using Lee distance. We feel that Lee distance is a natural metric for defining and studying a Q/sub n//sup k/. After defining a Q/sub n//sup k/ graph using Lee distance, we show how to find all disjoint paths between any two nodes. Given a sequence of radix k numbers, a function mapping the sequence to a Gray code sequence is presented, and this function is used to generate a Hamiltonian cycle. Embedding the graph of a mesh and the graph of a binary hypercube into the graph of a Q/sub n//sup k/ is considered. Using a k-ary Gray code, we show the embedding of a k(n/sub 1/)/spl times/k(n/sub 2/)/spl times/.../spl times/k(n/sub m/)-dimensional mesh into a Q/sub n//sup k/ where n=/spl Sigma//sub i=l//sup m/n/sub i/. Then using a single digit, 4-ary reflective Gray code, we demonstrate embedding a Q/sub n/ into Q/sub [n/2]//sup 4/. We look at how Lee distance may be applied to the problem of resource placement in a Q/sub n//sup k/ by using a Lee distance error-correcting code. Although the results in this paper are only preliminary, Lee distance error-correcting codes have not been applied previously to this problem. Finally, we consider how Lee distance can be applied to message routing and single-node broadcasting in a Q/sub n//sup k/. In this section we present two single-node broadcasting algorithms that are optimal when single-port and multi-port I/O is used. >

On unordered codes

By extending the results obtained by D. E. Knuth (1986), a parallel unordered coding scheme with 2/sup r/ information bits is described. Balanced codes in which each codeword contains equal amounts of zeros and ones, with r check bits and up to 2/sup r+1/-(r+2) information bits, are constructed. Unordered codes with r check bits and up to 2/sup r/+2/sup r-1/-1 information bits are designed. Codes capable of detecting 2/sup r-1/+(2/sup r//2)-1 unidirectional errors using r check bits are also described. A review of previous work is presented. >

Edge disjoint Hamiltonian cycles in k-ary n-cubes and hypercubes

Solutions for decomposing a higher dimensional torus to edge disjoint lower dimensional tori, in particular, edge disjoint Hamiltonian cycles are obtained based on the coding theory approach. First, Lee distance Gray codes in Z/sub k//sup n/ are presented and then it is shown how these codes can directly be used to generate edge disjoint Hamiltonian cycles in k-ary n-cubes. Further, some new classes of binary Gray codes are designed from these Lee distance Gray codes and, using these new classes of binary Gray codes, edge disjoint Hamiltonian cycles in hypercubes are generated.

A hybrid network coding technique for single-hop wireless networks

In this paper, we investigate a hybrid network coding technique to be used at a wireless base station (BS) or access point (AP) to increase the throughput efficiency of single-hop wireless networks. Traditionally, to provide reliability, lost packets from different flows (applications) are retransmitted separately, leading to inefficient use of wireless bandwidth. Using the proposed hybrid network coding approach, the BS encodes these lost packets, possibly from different flows together before broadcasting them to all wireless users. In this way, multiple wireless receivers can recover their lost packets simultaneously with a single transmission from the BS. Furthermore, simulations and theoretical analysis showed that when used in conjunction with an appropriate channel coding technique under typical channel conditions, this approach can increase the throughput efficiency up to 3.5 times over the automatic repeat request (ARQ), and up to 1.5 times over the HARQ techniques.

A Joint Network-Channel Coding Technique for Single-Hop Wireless Networks

Reliable transmission over an error-prone channel is typically accomplished via channel coding or retransmission of the lost information. In this paper, we investigate a joint network-channel coding technique to increase the bandwidth efficiency of wireless networks. In particular, we show that the proposed joint network-channel coding approach which combines the recent network coding (NC) concept with the traditional forward error correction (FEC) technique, can increase the bandwidth efficiency in single-hop wireless networks such as WLAN or WiMAX networks. We present some analytical results on the bandwidth efficiency for both broadcast and unicast scenarios. Based on these theoretical results, we provide a heuristic algorithm that dynamically selects the optimal level of FEC to be used with network coding technique for given channel conditions. For typical channel characteristics, both simulations and theoretical results confirm that the proposed joint network channel coding approach can reduce the bandwidth usage up to five times over the automatic repeat request (ARQ) technique and up to two times over the HARQ technique.

Fault-tolerant ring embedding in de Bruijn networks

A method of embedding a ring in a d-ary de Bruijn multiprocessor network in the event of multiple node (processor) failures is presented. In particular, the algorithm guarantees that a (2/sup n/-n-1)-node ring will be found in a binary de Bruijn network with a single faulty node, where 2/sup n/ is the total number of nodes in the network. It is also shown that a (d/sup n/-1)-node ring can always be found in the presence of d-1 link failures, when d is a prime power and the network contains d/sup n/ nodes. The latter is accomplished by constructing d-1 edge-disjoint cycles each of length d/sup n/-1. A modification of the graph that allows it to admit a Hamiltonian cycle in the event of d-1 edge failures is also discussed. >

On balanced codes

In a balanced code each codeword contains equally many 1s and 0s. Parallel decoding balanced codes with 2/sup r/ (or 2/sup r/-1) information bits are presented, where r is the number of check bits. The 2/sup 2/-r-1 construction given by D.E. Knuth (ibid., vol.32, no.1, p.51-3, 1986) is improved. The new codes are shown to be optimal when Knuths complementation method is used. >

Systematic, Single Limited Magnitude Error Correcting Codes for Flash Memories

A relatively new model of error correction is the limited magnitude error model. That is, it is assumed that the absolute difference between the sent and received symbols is bounded above by a certain value l. In this paper, we propose systematic codes for asymmetric limited magnitude channels that are able to correct a single error. We also show how this construction can be slightly modified to design codes that can correct a single symmetric error of limited magnitude. The designed codes achieve higher code rates than single error correcting codes previously given in the literature.

Transmission time analysis for the parallel asynchronous communication scheme

In asynchronous systems, the sender encodes a data word with a code word from an unordered code and transmits the code word on the parallel bus lines. In this paper, a transmission time analysis for the above parallel asynchronous communication scheme is presented. It is proven that the average transmission time for a code word is a strictly increasing function of the weight of the code word and it approaches the worst transmission time possible when the weight goes to infinity. This implies that fast parallel asynchronous systems can be designed using low weight codes. This paper also analyzes the transmission time performances of the proximity detecting codes and gives some efficient low constant weight code designs.