2D-RS Schemes‎ > ‎


1. Executive Summary

High cost and wear-out characteristics of NAND Flash chips have limited sales of NAND Flash Solid State Disks. ECC Tek’s two dimensional Reed-Solomon error-correction system shown in Figure 1 solves these problems because lower-cost, lower-grade memory chips can be used in 2D-RS SSDs without decreasing reliability.

Figure 1 2D-RS SSD

2D arrays as shown in Figure 2 are written and read. The e’s in Figure 2 represent errors. Column 3 shows errors from a failed Flash chip.

Figure 2 2D Array

2D-RS SSDs should be developed into commercial products for the following reasons:

  • 2D-RS SSDs will solve the wear-out problem associated with NAND Flash chips by allowing blocks and chips to fail without the loss of data or performance. Failed blocks can be removed (mapped out) and replaced with new ones.
  • 2D-RS SSDs could also be designed so that failed chips could optionally be removed and replaced resulting in an indefinite SSD lifetime.
  • If MLC NAND Flash chips are designed so that all of the bits from one cell are adjacent and in one page (which is the way they should be designed), then the 2D-RS scheme can correct more cell failures than any binary BCH scheme with the same amount of redundancy. Correcting Cell Failures
  • 2D-RS SSDs eliminate the need for performance-robbing wear-leveling operations.
  • 2D-RS SSDs will have automatic, built-in backup.

2. Light Bulb, Razor Blade and Printer Cartridge Analogies

What if someone said light bulbs could not be used as a lighting source because of their limited lifetimes? Standard light bulbs last about 750 hours or 31 days and longer life ones last approximately 1500 hours or 62 days.

People who believe the above statement are in denial of reality because there are billions of light bulbs operating on planet earth every moment of every day. Burnt-out light bulbs are simply replaced with new ones.

The short lifetime of light bulbs is not a negative fact to light bulb manufacturers but a positive fact because it ensures a continuous demand for light bulbs.

Razor blades and printer cartridges are other examples of items that wear-out but are viable and profitable products.

3. 2D-RS SSDs Can Compete Against Hard Drives

ECC Tek’s 2D-RS ECC technology will enable 2D-RS SSDs to compete and win against hard disk drives.

The cost of a 2D-RS SSD will be much greater than the cost of a conventional hard drive initially, but the performance will be 100 to 1,000 times greater, it will only take a fraction of the power that an HDD consumes, it will be much more reliable and rugged and it will make no noise! 2D-RS SSDs will allow instant boot-up and will have low power consumption, high reliability, high performance and no noise!

The future could be very bright for NAND Flash hard drives, but ECC Tek believes they must have the ECC technology ECC Tek is offering in order to make them viable products.

4. Brief Description of the 2D-RS SSD ECC Technology

As shown in Figure 1, a number of conventional Reed-Solomon (RS) encoders and decoders are used in combination with a parallel RS (PRS) encoder and decoder. The idea is to view the data to be encoded and decoded as a 2D array or matrix as shown in Figure 2. Rows and columns are encoded and decoded separately and independently. RS symbol sizes for the rows are not necessarily the same as RS symbol sizes for the columns.

Each column of the array is stored in a separate Flash chip. The entire array would be written and read at one time so that N chips would be written and read simultaneously.

There would be a conventional RS encoding done on each column so that all of the symbols in error (shown as "e’s” in Figure 2) that are not too severe (such as in every column except column 3) would be corrected by the RS column decoders.

Each row would also be encoded with a single RS row encoder.

There would be two encodings and a variable number of decodings. A system with two pairs of pipelined decoders is shown in Figure 3. A very high throughput system can be implemented by duplicating the decoding pair circuits multiple times or repeated decodings can be accomplished by feeding the output from one pair of decoders back to the input and repeating the decoding that way as illustrated in Figure 4. With feedback, reading would be paused whenever the decodings are repeated.


Figure 3 2D-RS SSD with Two Pairs of Decoders




Figure 4 2D-RS SSD with One Decoding Pair and Feedback

When writing, all of the data in each row would be encoded using a single PRS encoder which will add additional columns. Then all of the columns would be encoded using a number of conventional RS encoders which will add additional rows. The entire array would be written to N Flash chips simultaneously.

When reading, columns are decoded first and then rows. Most of the errors, like those shown in Figure 2 except in column 3, will be corrected by the column decoders. For column 3, the column decoder will declare a failure. The failure indicator from the column 3 decoder will be used to tell the row decoder that all of the symbols in position 3 of each row are "erased". RS codes can correct twice as many “erasures” as “errors”.

The errors in the failed column 3 in the above example will not be corrected by the column 3 decoder but will be corrected by the single PRS row decoder.

It is possible to repeat the column and row decoders multiple times as illustrated in Figure 3. Additional errors will be corrected in each decoding iteration until all of the errors are corrected. If one of the row decodings fails, that row would be declared as "erased". In that case, the column decodings can be done a subsequent time and one of the symbols in each column corresponding to the failed row will be declared as "erased". Multiple decodings would probably require the use of RS codes both for the rows and columns rather than binary BCH codes on the columns because RS codes naturally correct “erasures” while binary BCH codes do not.

Normally the column and row decodings would not have to be repeated. However, repeating the decodings is an option that will extend the capability of the error correction system.

Probably the most important argument in favor of using ECC Tek’s advanced 2D-RS ECC in 2D-RS SSDs is that it would allow low grade chips to be used that otherwise would be discarded because of too many defects. The cost of low grade Flash chips could be a small fraction of the cost of high grade chips. That would allow 2D-RS SSDs to be developed that are cost competitive with hard drives! Then everyone would want one!

The PRS ECC designs ECC Tek is proposing are absolutely state-of-the-art, are patented and are not available from any other source in the world!

Figure 5 is an example of using the 2D ECC system with 4-bit row symbols and 12-bit column symbols. The row symbols are inside the red boxes, and the column symbols are inside the blue boxes.


Figure 5 Example 2D System Using 4-bit Row Symbols and 12-bit Column Symbols

5. 2D-RS SSD Pricing Strategy

The price of a 2D-RS SSD product should be based on its features and those features should be priced on a feature by feature basis.

For example, suppose you went to buy a new PC and were told about two PCs that had exactly the same performance but that one of the PCs took 1.5 minutes to boot-up and the other one took only 1 second to boot-up. What would the "fast boot-up feature" be worth? Most people would gladly pay $100 to $150 more to get the fast boot-up feature.

The fast boot-up PC should also be noticeably faster at running application programs – especially ones that require large file transfers like transferring pictures or video. A certain amount of money could be added to a price of a PC if it has a "fast file transfer feature".

Then there is the "automatic, built-in backup feature". That feature should be priced based upon the amount of backup that is built-in. For example, a 2D-RS SSD that allows one Flash chip to fail may add an additional $100 to the price, one that allows two Flash chips to fail might be priced at $200 more and one that tolerates three Flash chip failures might be priced at $300 more.

Pricing each feature individually makes good sense and is reasonable. That's what is done with automobiles. When you buy a car, you pay for each accessory or feature individually. When you buy a PC with a conventional HDD or SSD, you do not have the option of adding those features, but when you buy a PC with a 2D-RS HDD or a 2D-RS SSD you do.

It would be easy to justify a 2D-RS SSD price that is substantially higher than an equivalent capacity HDD or 2D-RS HDD price. The extra price is due to the added features.

Most people are alike, and many would gladly pay a significant premium to get the added features that only a 2D-RS SSD can provide and conventional HDDs, 2D-RS HDDs or SSDs cannot.

6. Today’s Buyers

It is important to realize that today's buyers are willing to pay whatever it costs to get what they want even if they can't afford it or if the items are overpriced.

Here are some examples:

The iPhone. The iPhone costs hundreds of dollars while low cost cell phones are available for less than $50.

The iPod. The iPod costs hundreds of dollars while low cost music players are available for less than $20, yet buyers buy them by the millions because they are cool. Even teenagers who can't afford them somehow scrape up the money to buy them.

Cell phones. The biggest market for cell phones is probably teenagers who can't afford them but must have them and find the money to buy them.

SUVs. SUVs are expensive items that the younger generation must have and are willing to buy even though they are expensive and the cost for gas is astronomical.

Coffee. People regularly pay more for a cup of coffee at coffee shops today than they used to pay for an entire pound of coffee that would probably have made a hundred cups of coffee. When I worked at Seagate, I bought a Mr. Coffee coffeemaker and charged 5 cents per cup. It was a profitable business at 5 cents a cup so you can imagine what the profit margin could be at Starbucks, Caribou Coffee, Dunn Brothers, etc. Those companies look at the fact that people are willing to pay a high price for coffee at a coffee shop as an opportunity for them to make large profits.

Rather than looking at the price of a 2D-RS SSD as a negative, it should be looked at as being a positive. It offers NAND Flash chip manufacturing companies the opportunity to price an item higher and make more profit.

If cost was the only factor involved in making buying decisions, there would be no market for Lamborghinis, Ferraris, Rolls-Royces, multi-million dollar houses, leather coats, jewelry, etc. and on and on. Many buyers are willing to pay high prices for those items because of the perceived benefits of owning those things. The same will be true of 2D-RS SSD products.

2D-RS SSDs should initially be thought about more as luxury items than as commodities.

7. The 2D-RS SSD Downward Cost Spiral

There is a cause and effect cycle as follows: Once 2D-RS SSD products start to sell, there will be a large increase in the manufacturing volume of NAND Flash chips, which will cause the costs of Flash chips to go down, which will allow the price of 2D-RS SSDs to be reduced, which will cause more 2D-RS SSDs to be sold.

This cycle will repeat with time and can be thought of as a downward spiral.

As manufacturing volumes of 2D-RS SSDs increase, costs and prices will continually decrease.

One factor that affects the extent of the cost and price drops is the number of Flash chips that are in a 2D-RS SSD. A high number of Flash chips in a 2D-RS SSD will cause a fast downward cost spiral with a very large cost and price drop.

The most important thing to see is that the early adopters will pay the highest prices for 2D-RS SSDs, but, once they start to take off in the market place, prices will drop very rapidly and potentially very far. Nobody knows how far, but it is possible that prices could drop as low as conventional HDD prices – or even lower than conventional HDD prices given enough time and high enough volumes.

It is very important to take the 2D-RS SSD downward cost spiral into consideration when deciding whether or not to develop a 2D-RS SSD product. In other words, NAND Flash chip manufacturers must think about what will happen in the future if large numbers of 2D-RS SSDs start selling.

8. Could a 2D-RS SSD Ever Cost Less Than an HDD?

Yes, it's possible.

Consider a 2D-RS SSD with many Flash chips as components and a fair amount of fault tolerance.

Flash chips that do not pass the tests for use in conventional SSDs because of too many errors can be used in 2D-RS SSDs. The cost of the Flash chips could be 0 or even a negative number if it currently costs Flash chip manufacturers to dispose of unusable Flash chips.

Flash chips do not have to be tested before installing them in 2D-RS SSDs because 2D-RS SSDs will automatically know which ones are bad and which ones have lots of errors. The 2D-RS SSD controller chip can have built-in logic to test untested Flash chips. The cost of testing Flash chips can be eliminated.

Once 2D-RS SSDs with a large number of Flash chips start selling in large volumes, Flash chip volumes will be many times 2D-RS SSD volumes and costs will start to come down very rapidly due to the downward cost spiral.

Because of these factors, it is possible that 2D-RS SSDs could one day cost less than HDDs. When and if that happens, HDDs will become obsolete because there would be no valid reason to buy an HDD over a 2D-RS SSD.

9. Are Buyers Willing to Pay a Premium for a 2D-RS SSD?

All of the people I have asked have said they would gladly pay a few hundred dollars extra to get a fail-safe hard drive with automatic, built-in backup. Many of those people would probably also be willing to pay an extra fee to buy a 2D-RS SSD. A survey of potential buyers should be done to see what they say. It is almost certain that many people would gladly pay a significant premium to get a fail-safe hard drive or a 2D-RS SSD.

10. Human Factors

It is important to take into consideration a number of human factors when trying to determine whether or not it makes sense to develop a 2D-RS SSD product.

When Carl Ledbetter was the CEO of the supercomputer company ETA in St. Paul, MN, he spoke at the University of Minnesota and said he bought a printer for his grandmother, and she was amazed at how fast it could print. Two weeks later, she was complaining about how slow it was. That’s the way people are. There is a never ending desire for more and more speed and higher and higher performance like that provided by 2D-RS SSD products.

There was a famous author who lost the entire manuscript of her book because she had it saved on a hard drive and it crashed. She did not know that data loss was possible. Some people have lost entire picture albums because of hard drive failures. These types of people would greatly benefit from using a 2D-RS SSD product.

Most normal human beings want automatic, built-in features. They don’t want to have to spend time and money and effort to get RAID controller boards, extra drives or special software and then have to learn how to use all of them. Some people who need backups the most would not know how to do those things. They just want to buy a computer, take it home, plug it in and starting using it without having to worry about losing their data or without having to go do a bunch of other stuff. There is no doubt that most of them would gladly pay a significant premium to get automatic, built-in backup.

11. The Value of Data or Content

In most cases, the data or content created by computer users is much more valuable than the computer hardware and software used to create it. Users may spend hundreds and hundreds of hours to create content and they would be extremely shocked, sad, sorry, unhappy, perplexed, troubled, disappointed, angry, and on and on if they suddenly lose everything because of a hard drive failure.

12. Performance Reasons for Developing 2D-RS SSD Products

Today's hard disk drives are the only components in a modern computer that operate on data one bit at a time! Think of it! Processors in modern PCs can operate on 32‑bit or 64‑bit chunks of data at a rate of up to 3 GigaHertz, yet conventional HDDs read and write data one bit at a time!

2D-RS SDDs can be designed to allow high I/O data rates to match the data transfer rates of other parallel-transfer components such as microprocessor chips and main memories.

2D-RS SSDs can be made fault-tolerant with an arbitrary level of built-in fault-tolerance.

13. Failure and Fault Tolerance Reasons for Developing 2D-RS SSD Products

With R redundant chips in each 2D-RS SSD, up to R chips can fail with no loss of data or performance. In addition, the raw error rates of each component Flash chip can be relatively high because the 2D-RS system can correct random errors that the conventional RS Flash decoder does not correct.

14. Reasons for Developing 2D-RS SSD Products Based on More Effective Use of Manufactured Flash Chips and More Profit Potential

ECC Tek is proposing that 2D-RS SSD products be developed that could use Flash chips that have been rejected as “unusable” in conventional SSDs because of too many errors and/or defects. Selling 2D-RS SSDs which use lower grade Flash chips at normal price levels instead of deeply discounted prices could enable all NAND Flash manufacturing companies to make more effective use of manufactured Flash chips and to realize millions of dollars in revenue that otherwise would not exist.

2D-RS SSD products which use low grade NAND Flash chips will, most likely, be much more reliable than standard SSDs because a “lateral”, “horizontal” or “parallel” ECC coding scheme is used in combination with the conventional, “longitudinal”, “vertical” or “serial” ECC scheme that is used in conventional SSDs. The horizontal ECC literally opens up an entirely “new dimension” to the problem of correcting errors because now ECC can be applied to a two‑dimensional array of data items instead of just a one‑dimensional array as is currently being done in conventional SSDs. No one will be able to legitimately claim that 2D-RS SSD products which use low grade Flash chips are in any way inferior to standard SSDs. In fact, those types of 2D-RS SSD products will, most likely, be highly superior in performance and reliability to conventional SSDs.

With a number of NAND Flash chips ganged together, the parallel RS decoder and the improved serial RS decoders will have information from multiple, statistically independent sources and the resulting random distribution of errors will be ideally suited for correction using RS codes. The law of large numbers (from statistics) applies to 2D-RS SSDs , and the result is that the statistical or probabilistic behavior of the system will closely follow probabilistic models so the behavior of 2D-RS SSD systems will be very predictable.

15. Reasons for Developing 2D-RS SSD Products Related to Users’ Experience

Many users of desktop and laptop computer systems will be willing to pay a premium for a PC or Mac if it has an ultra-fast, failure-tolerant hard drive in it. If a system already costs over a thousand dollars, many users will be willing to pay an additional premium to get a super-duper, ultra-high-performance, fail-safe hard drive or SSD in the same way that users are willing to pay a premium to get Intel's fastest and most powerful processors.

Once users use a Pentium PC operating at 3 GHz, they will never be willing to go back to a Pentium PC operating at 250 MHz! There is a market for faster processors because users like them, get used to using them and don't want anything slower once they use them.

The same thing clearly will be true for systems which contain 2D-RS SSDs in place of conventional HDDs. Users will buy them because they will only cost a little more than systems that contain conventional HDDs, but they will be much faster, consume much less power and will have automatic, built-in backup. In a PC, 2D-RS SSDs will accelerate boot up, accelerate all OS operations and accelerate application programs. Once users get used to using systems which contain 2D-RS SSDs, they will never go back to systems that use conventional HDDs.

One major impact to users of PCs which contain a 2D-RS SSD instead of a conventional HDD would be that, on power up, the operating system would load into memory almost instantaneously – like an "instant on" computer. Most PC users would love that.

Another impact on computer users would be the increased level of comfort and security a user would feel knowing that, if one or more Flash chip components fail, no data will be lost.

Any application programs that do a lot of I/O would also see a significant performance boost – such as programs that download music, movies or pictures.

16. Legal Issues

ECC Tek will do everything within its power to avoid any involvement with lawyers or lawsuits. Getting involved with lawyers and lawsuits is the very last thing ECC Tek wants. ECC Tek personnel have read several books on patents and intellectual property issues, have written the PRS Patent (except the claims) and have written and negotiated all of ECC Tek's Agreements with little help from lawyers. ECC Tek has no intention of suing any other party and wants to avoid litigation at all costs because ECC Tek has seen first hand what extended litigation with an uncertain outcome is like in the case of Rodime’s 7-year litigation with Seagate. ECC Tek does not want that and will do everything it can to avoid that type of a situation.

The wisest thing for any NAND Flash chip manufacturing company to do in situations where advanced technology and IP is involved is to immediately acquire any IP that they think they may have an interest in because then they would own the IP and could completely avoid any possible future litigation regarding that IP. It is the wisest thing to do because the outcome is known. Nobody can ever know the outcome of litigation and how long the litigation will take in advanced technology cases. For example, in the case of Rodime, Seagate spent 7 years in litigation and ended up paying a $45 million settlement. In hindsight, it clearly would have been a much better strategy for Seagate to acquire or license Rodime's patents upfront even if they were overpriced rather than spend 7 years in litigation with an unknown outcome. Nobody can know the outcome of that type of litigation because judges and juries cannot understand advanced technology, and they might as well flip a coin to make their decision as listen to arguments. No judges or juries would understand the PRS technology and patent.

A NAND Flash chip manufacturer could avoid any possible litigation and avoid any possible legal fees regarding the PRS patent and regarding ECC Tek by offering to either license the PRS patent or acquire ECC Tek. There are all kinds of different acquisition scenarios that would guarantee a NAND Flash chip manufacturing company a desirable outcome with no uncertainty at a reasonable cost.

ECC Tek is open to any kind of reasonable offer from any NAND Flash company to acquire the PRS patent or acquire ECC Tek.

ECC Tek believes now is the right time for the 2D-RS SSD technology to get implemented and will do whatever it takes to make that happen.

Probably all of the money spent by Seagate and Rodime in their IP litigation went to the lawyers – all of it! Think of it. If we could negotiate a deal with no lawyers involved on either side until the last minute, we could prevent all of that money going to lawyers.

17. IP Landmines

It is appropriate to use military analogies to get an understanding of certain business situations in highly competitive industries.

If there is a war and the military wants to move into an area that has previously been occupied by the enemy, they must first do their best to detonate or disarm all of the landmines. It takes time, money, and effort and possibly the loss of equipment and lives to do it, but there is no other choice. If they don't do it, they risk a much larger loss of time, money, equipment and life later on.

The landmine analogy applies to today’s high tech businesses. IP owned by competitors are the landmines that can potentially result in expensive and extended IP litigation with uncertain outcomes. If potential competitors have been in a technology area before you decide to go into that area, you may come across some IP landmines that lead to lawsuits. The only reasonable thing to do in that situation is to sweep the area of IP landmines before you enter that area. IP landmines are detonated or disarmed by acquiring the IP so you own it. If you own it, it can't hurt you later on. You might suffer some small losses in the process, but it is much better than risking much larger losses later on.

ECC Tek has been in the 2D-RS SSD and RAID areas since 1982. ECC Tek conceived of fault-tolerance HDDs idea 5 years before the influential 1987 RAID paper entitled "The Case for Redundant Arrays of Independent Disks" was written at the U of CA in Berkeley by Randy Katz, David Patterson and some graduate students. ECC Tek knows the history and details of RAID and the RAID issues.

ECC Tek has no intention of suing any other party and will do everything within its power to avoid lawyers and any type of litigation. However, that might not be the case if some other parry owns ECC Tek's IP.

18. PRS Patent

ECC Tek patented the PRS system more than 20 years ago so no third party can claim that anyone is infringing their IP.

19. ECC Tek Has Set the Standard in Space

I think it is fair to say that ECC Tek has set the de facto standard for the use of PRS with synchronous DRAM memories in space.

ECC Tek is well positioned to set the standard for 2D-RS SSDs also, but we need a NAND Flash chip manufacturer to partner with us to make it happen!

20. Endorsements for ECC Tek

"QSS Group, Inc. (QSS – a major subcontractor to NASA Goddard Space Flight Center) and NASA GSFC licensed parallel Reed-Solomon (PRS) encoder and decoder designs, written in synthesizable Verilog, from ECC Technologies, Inc. (ECC Tek) for possible use in NASA's next-generation space telescope project recently renamed to the James Webb Space Telescope (JWST). ECC Tek delivered the PRS designs to QSS and NASA GSFC in a timely fashion and the performance of the PRS designs met JWST project requirements. QSS and NASA GSFC would recommend to any company with a need for PRS ECC to consider licensing PRS designs from ECC Tek.

The following four NASA missions are using ECC Tek's PRS Designs:
  • JWST (James Webb Space Telescope)
  • SDO (Solar Dynamic Observatory)
  • LRO (Lunar Reconnaissance Orbiter)
  • GPM (Global Precipitation Measurement)

NASA GSFC is also using ECC Tek's conventional RS designs in the Magnetospheric MultiScale (MMS) mission."

Alex Kisin
Sr. Staff Electrical Engineer

"Raytheon Space and Airborne Systems has licensed parallel Reed-Solomon (PRS) encoder and decoder designs written in synthesizable Verilog from ECC Technologies (ECC Tek) for use in a space based product. The PRS designs licensed from ECC Tek are working and ECC Tek has provided Raytheon SAS with the necessary support to ensure our success."

Mark Gordon
Raytheon Space and Airborne Systems
El Segundo, CA 90245

"Provigent licensed Reed-Solomon encoder and decoder designs from ECC Technologies, Inc. (ECC Tek), for use in Provigent's broadband [IEEE 802.16] wireless transceiver chip. The modules were designed for ultra-high speed applications, requiring high programmability, and minimal decoder latency. ECC Tek delivered the designs to Provigent on schedule, meeting all of these requirements, and achieving modules optimized for the above constraints. The modules were written in synthesizable Verilog, maintaining Provigent's methodologies, and were easily integrated into the chip. Provigent would highly recommend to any company with a need for ECC IP to consider licensing IP from ECC Tek. ECC Tek proved a reliable source of licensed software, highly capable and responsive."

Michal Katzir
VLSI Manager

"NxtWave Communications has licensed a Reed-Solomon decoder core from ECC Technologies, Inc. ECC performed the modeling, design and implementation of the core with a high degree of professionalism. The deliverables in the form of system model, synthesizable Verilog source code, test benches and design documentation exceeded our expectations. The project was executed on schedule and within budget. We highly recommend ECC as a source for this technology."

Bernardo Paratore
VP I.C.Product Development
NxtWave Communications
Langhorne, PA 19047

"Telegrid Technologies, Inc. licensed Reed-Solomon decoder software from ECC Technologies, Inc. On this task, ECC performed the design and implementation of the software with a high degree of professionalism. The final product met our specifications and exceeded our performance requirements. Before starting, ECC made sure they understood our application and as a result, required very little support from our technical personnel. The final product was delivered on schedule and within budget. We highly recommend ECC as a capable and responsive source of licensed software."

Igal Sharret
Telegrid Technologies, Inc.
Eatontown, NJ

21. Endorsements for Phil White

"Phil was always a conscientious and capable worker, and was well-liked and respected by his management and co-workers. He made a number of contributions to the development of error-control methods, primarily for mass storage (disc, tape) products, and understands this technology well. I would have no qualms in recommending him for engineering and research work in this field."

Dr. Donald B. Bonstrom (retired)
Former VP & Director of Central Research Labs
Control Data Corporation

"Mr. White is among the most loyal and conscientious employees that I have had the opportunity to supervise at Control Data. I can recommend Mr. White without reservation on both a personal and a professional basis, and I would not hesitate to enlist his help in the future, if the occasion should arise."

Dr. Robert W. Johnson (retired)
Former General Manager of Research Division
Control Data Corporation

"I have known Phil White for more than [thirty] years. During that time I have never known or been told of any event which would contradict my firmly held opinion of him. He is an unusually sincere and forthright individual without any symptoms of guile or deceit. I would trust him far beyond the limits that would be set for an average individual. His introspective nature and basic honesty are refreshing characteristics in the modern world."

Dr. Meredith (Matt) S. Ulstad (retired)
Former CDC Research Scientist and Part-time Professor

"Phil specializes in logic design, especially on the design of error-correction codes and appropriate hardware. He understands this subject and is a great specialist in this area."

Dr. Vadim Minuhin (retired)
Sr. Consulting Research Scientist
Seagate Technology

22. Endorsements for 2D-RS SSD Concept

"This is definitely exciting technology that I could see SGI being an OEM for.... I could definitely see SGI selling this storage technology."

Raj Das
Former Vice President - Storage