arXiv subjects

Ratko V. Tomic

Publications and source records attributed to Ratko V. Tomic.

3 recordsLinked to original sources

arXiv2013

Optimal Networks from Error Correcting Codes

To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times fewer cables, have 1.2-2 times lower latency and correspondingly lower congestion and packet losses than the best present or proposed networks providing the same number of ports at the same total bisection. These advantage ratios increase with network size. The key new ingredient is the exact equivalence discovered between the problem of maximizing network bisection for large classes of practically interesting Cayley graphs and the problem of maximizing codeword distance for linear error correcting codes. Resulting translation recipe converts existent optimal error correcting codes into optimal throughput networks.

cs.IT↗

arXiv2013

Network Throughput Optimization via Error Correcting Codes

A new network construction method is presented for building of scalable, high throughput, low latency networks. The method is based on the exact equivalence discovered between the problem of maximizing network throughput (measured as bisection bandwidth) for a large class of practically interesting Cayley graphs and the problem of maximizing codeword distance for linear error correcting codes. Since the latter problem belongs to a more mature research field with large collections of optimal solutions available, a simple translation recipe is provided for converting the existent optimal error correcting codes into optimal throughput networks. The resulting networks, called here Long Hop networks, require 1.5-5 times fewer switches, 2-6 times fewer internal cables and 1.2-2 times fewer `average hops' than the best presently known networks for the same number of ports provided and the same total throughput. These advantage ratios increase with the network size and switch radix. Independently interesting byproduct of the discovered equivalence is an efficient O(n*log(n)) algorithm based on Walsh-Hadamard transform for computing exact bisections of this class of Cayley graphs (this is NP complete problem for general graphs).

cs.IT↗

arXiv2005

Quantized Indexing: Beyond Arithmetic Coding

Quantized Indexing is a fast and space-efficient form of enumerative (combinatorial) coding, the strongest among asymptotically optimal universal entropy coding algorithms. The present advance in enumerative coding is similar to that made by arithmetic coding with respect to its unlimited precision predecessor, Elias coding. The arithmetic precision, execution time, table sizes and coding delay are all reduced by a factor O(n) at a redundancy below 2*log(e)/2^g bits/symbol (for n input symbols and g-bit QI precision). Due to its tighter enumeration, QI output redundancy is below that of arithmetic coding (which can be derived as a lower accuracy approximation of QI). The relative compression gain vanishes in large n and in high entropy limits and increases for shorter outputs and for less predictable data. QI is significantly faster than the fastest arithmetic coders, from factor 6 in high entropy limit to over 100 in low entropy limit (`typically' 10-20 times faster). These speedups are result of using only 3 adds, 1 shift and 2 array lookups (all in 32 bit precision) per less probable symbol and no coding operations for the most probable symbol . Further, the exact enumeration algorithm is sharpened and its lattice walks formulation is generalized. A new numeric type with a broader applicability, sliding window integer, is introduced.

cs.IT↗