US 6543021

I'll search for authoritative information on this patent number and check for any litigation.

Let me check for any litigation or CAFC docket activity involving this patent.

US Patent 6,543,021 — Analyst Summary

Caveat on scope of search: I searched for the exact number 6543021 (and US6543021B1). I found no CAFC 2026 docket, ITC proceeding, or district-court litigation specifically asserting or involving this patent. Canon is a frequent patent litigant (e.g., St. Clair, WSOU, Glory Licensing matters surfaced in results), but none of those hits cite 6543021. I therefore report no known litigation activity for this patent, without claiming that exhaustively negative result is authoritative.

Bibliographic Data (from the authoritative patent text)

Abstract (as issued): A method is provided for coding information representing a physical quantity and represented by first binary symbols, having an operation of calculating second binary symbols from the information, the second binary symbols being called calculated binary symbols and being provided in order to be disposed in a square table. For each calculated binary symbol, there exist at least three distinct diagonals in the table which contain this calculated binary symbol and which, deprived of this calculated binary symbol, still allow each one on its own to recalculate the calculated binary symbol. A coding device, a decoding method, a decoding device, a transmission method, and a transmission device are provided, as well as a camera, a facsimile machine, photographic apparatus, and a computer, implementing the invention.

Plain-Language Overview of the Independent Claims

The patent has 25 claims. Based on the claim text provided, the independent claims are claim 1, claim 13, and — arguably — claim 10 (a storage-medium claim that references the claim-1 method). Note: the claim listing in the source is truncated partway through claim 13, so I cannot confirm whether claims 14–25 contain further independent claims; treat that as an open uncertainty.

Claim 1 — Independent transmission method (the core claim).
A method of transmitting information that stands for a physical quantity, where the information is first binary symbols. Steps:

1. Coding: compute second ("calculated") binary symbols from the information, arranged in a square table.
2. Transfer: modulate the calculated symbols, then demodulate the modulated symbols into "received" symbols — and the demodulation must be a soft-decision method (i.e., it passes probabilistic/confidence values, not just hard 0/1 decisions).
3. Correct the received symbols into "corrected" symbols.
4. Decode the original information from the corrected symbols.

The defining limitation: for every calculated binary symbol, there must be at least three distinct diagonals in the table that (a) contain that symbol, and (b) if that symbol is removed, each diagonal by itself is still sufficient to recalculate the removed symbol. Additionally, the correction step must be performed iteratively over each of the distinct diagonals. (In this patent, "rows" are diagonals of gradient 0 and "columns" are diagonals of infinite gradient, so rows/columns count as diagonals.)

Claim 10 — Independent information-storage device. A computer/microprocessor-readable storage device storing program instructions that permit implementation of the claim-1 method. (Claim 11 depends on 10 and adds that the storage device may be partly or wholly removable.)

Claim 13 — Independent transmitting device. A device for transmitting information representing a physical quantity, expressed as first binary symbols, with coding means comprising means for calculating the second binary symbols … (the text supplied cuts off mid-claim, so the complete scope of claim 13 — and any independent claims after it — cannot be characterized from the provided material).

Dependent claims of note (not independent, but scope-defining):

• Claim 2 — the coding step works by defining several bivariable "information" polynomials (first binary symbols as coefficients) and summing products of each with a respective basis polynomial, where those basis polynomials form a basis of the set of all bivariable polynomials.
• Claim 3 — decoding by multiplying the corrected-symbol polynomial by each basis polynomial, then recovering the information coefficients from specific coefficients of those products.
• Claim 4 — the correction step computes a log-likelihood ratio, and corrected symbols are estimated from a sum of those ratios (the soft/turbo-decoding mechanic).
• Claim 5 — the table of calculated symbols is a word of an Abelian code.
• Claims 6–9 — structural families of the underlying code: diagonals of a given gradient are words of a BCH code (claim 6); of an (n,k) Hamming code with n = 2^m − 1, k = n − m (claim 7); of the same Hamming code for two different gradients (claim 8); or of the (n, n−1) parity code (claim 9).

Practical gist of claim 1: instead of an ordinary product code (which gives only three independent estimates per symbol — itself, its row, its column), the invention imposes redundancy on extra diagonal directions so that each symbol has ≥3 independently usable diagonals, enabling a turbo-style iterative soft-decision decoder that must cycle through those diagonals. The patent's worked example is a 49-bit (7×7) code carrying 10 information bits.

Uncertainty Notes

• Litigation: No CAFC 2026 (or other) docket referencing 6543021 was found in my search. This is a "not found," not a verified absence.
• Claim 13 and claims 14–25: the claim text in the provided source is truncated mid-claim 13; I have not auto-filled the missing text. Any statement about the number or content of independent claims beyond claims 1, 10, and 13 would be speculative.
• Micro-level details (e.g., whether claim 12 counts as independent) were interpreted literally from the provided text: claim 12 is written as "A method according to claim 1," so it is dependent.

I'll search for litigation involving US patent 6,543,021 across patent litigation sources.

Let me search more targeted sources, including the Unified Patents litigation portal and RPX.

Litigation Search — US Patent No. 6,543,021

Bottom line: I found no litigation specifically involving US Patent No. 6,543,021.

Despite searching patent-litigation-oriented sources (including the specific number queries requested, RPX/insight, and general district-court docket coverage surfaced in results), no case — district court, CAFC, or ITC — identified this patent number as a patent-in-suit or otherwise referenced it. I could not retrieve a Unified Patents litigation caselist entry for 6543021; the portal query returned no matching result.

Results table

Important caveat on the search hits (do not be misled by "…654")

The searches returned several documents that contain a "654" string but are not this patent. I flag these explicitly because the instruction was not to return results for similar numbers:

• "the '654 patent" — Sansui / Orion display-products case. The RPX document (insight.rpxcorp.com) references a '654 patent asserted over digital televisions (Sansui SLED3900/SLED6520). That is a different patent (a display/TV patent), not US 6,543,021 (which is in H03M13/29 error-correcting-code art). Do not conflate them.
• WSOU Investments LLC v. Canon, Inc., 6:20-cv-00980 (W.D. Tex.). This is a real Canon patent action surfaced in results, but the patents asserted by WSOU (which commonly asserts former Nokia portfolio patents) are unrelated to Piret's coding patent; no result tied 6,543,021 to this docket. Note also that in this case Canon is the defendant, not the plaintiff — the opposite posture one would expect for enforcement of the Piret patent.
• The Air Measurement Technologies malpractice and PTAB/FIS materials returned are entirely unrelated numbers and subject matter.

None of the above cite US 6,543,021.

Context worth noting for an attorney's risk assessment

1. The patent is expired. US 6,543,021 lists an anticipated expiration of 2019-07-14 and legal status "Expired – Fee Related." An expired patent cannot support prospective injunctive relief, and any past-infringement claim would be time-barred well before the current date absent unusual tolling. This materially explains the absence of active litigation.
2. Enforcement posture of the assignee. The patent is assigned to Canon Inc. / Canon Kabushiki Kaisha. Canon is an active patent litigant generally (and is a frequent defendant against NPEs such as WSOU), but I found no indication that Canon ever asserted — or that any third party ever acquired for assertion — this particular coding patent.
3. No NPE transfer detected in results. I saw no evidence that 6,543,021 was ever assigned into a monetization vehicle, which is the typical path to a litigation campaign for a 1998-priority patent of this type.

Exhaustiveness disclaimer

This is a "no results found" conclusion, not a verified absence. My searches were constrained, and litigation databases (PACER, Darts-ip, Lex Machina, Unified Patents) are not exhaustively indexed by the open web. A definitive negative would require:

• a PACER docket search on the patent number across all districts,
• the Unified Patents litigation database and RPX by patent number,
• USPTO Assignment records (already partly indicated — single 1999 assignment from Piret to Canon), and
• a CAFC docket query by patent number.

If you need a court-admissible confirmation of no litigation, I recommend running those four database queries directly rather than relying on this web search.

Note on identifiers: I interpreted 6543021 and US6543021B1 literally per the operating rules and did not auto-correct them. If the intended target was actually a different number (e.g., another "654"-containing patent from the search hits), that would change the answer — please confirm the number.

I'll verify the structured data's "no proceedings" result against public sources before reporting.

Let me run additional targeted checks to confirm the negative result.

Verification note before the findings

The canonical structured block provided in this prompt states: "The USPTO ODP API returns no AIA trial proceedings for this patent as of the most recent ingest." I ran four independent web searches (PTAB/Google Patents phrasing, exact-number queries 6543021 / US6,543,021 / US6543021B1 paired with IPR/PGR/CBM, and a Canon/inventor-name query). All returned zero patent-specific PTAB hits. The only results were generic PTAB-practice commentary and unrelated Canon matters (e.g., the 2014 Canon ITC/§337 toner-cartridge campaign over the '278 and '564 patents, which does not involve 6,543,021). I did not find a proceeding number to report, and I am not inventing one.

Proceedings overview

Total AIA trial proceedings on US 6,543,021: 0. Breakdown: 0 active, 0 with claims invalidated, 0 with claims sustained, 0 settled, 0 institution denials. The patent has never been challenged in an IPR, PGR, or CBM, so there is no post-issuance claim-level record to read against. For a defendant, the defensive posture is therefore not "hardened by surviving two IPRs" and not "claim 1 is dead" — it is simply "untested at the PTAB, and, more importantly, expired." The decisive fact is not a PTAB outcome but the bibliographic one from the authoritative patent text: anticipated expiration 2019-07-14, legal status Expired – Fee Related. A defendant receiving a demand letter citing this patent today should lead with expiration, not with an invalidity theory.

There are no per-proceeding entries to write, because there are no proceedings. The sections requested for each proceeding (panel, grounds, institution decision, FWD, settlement, appeal) are not applicable and I will not fabricate them.

Why the zero is the expected result here (and what it does not prove)

• Procedural availability window. The patent is pre-AIA (filed 1999-07-14, issued 2003-04-01). Post-Grant Review was unavailable — PGR reaches only patents with an effective filing date on or after 2013-03-16. CBM review likewise would not fit: this is an error-correcting-code patent (H03M13/29, H03M13/27xx), i.e., a "technological invention," not a covered business method. That leaves IPR as the only realistic AIA vehicle, available from 2012-09-16 onward.
• No commercial trigger. PTAB petitions cluster around asserted patents. Per the earlier-generated litigation section, no district-court or ITC assertion of 6,543,021 was located. Well-asserted patents attract IPRs; unasserted ones often never do. The zero-track record is consistent with a patent that was never a litigation weapon.
• The window was closing as the AIA trial regime opened. IPRs began 2012-09-16; the patent's term ran to 2019-07-14. There was only a ~7-year overlap, and no apparent assertion pressure during it.
• Scope of my negative. I can only confirm the USPTO ODP AIA-trial result and the absence of patent-specific web hits. I did not verify pre-AIA inter partes reexamination or ex parte reexamination records for 6,543,021, nor European opposition history. Those are separate channels and are outside this task's "AIA trial" scope. I am flagging them as unverified, not as absent.

Strategic summary

Claim status: entirely untested at the PTAB. No claim of 6,543,021 is canceled, none has been confirmed patentable in an AIA trial, and none has been construed by the Board. Any statement that a particular claim is "dead" or "survived" would be fabricated. The only narrowing of record is whatever occurred during original prosecution (1999–2003), which is not an AIA-trial narrowing. Distributionally, that is a weak defensive record to inherit — but it is moot, because of expiration.

Estoppel landscape: § 315(e)(2) is empty. With no IPR/PGR, there are no petitioner-side estoppels binding anyone, and no privity chains to trace. Conversely, there is no free-ride invalidity record to cite in a § 282 defense. For a defendant facing a hypothetical assertion, the full prior-art universe is still open (subject to § 102/§ 103 and the patent's 1998 priority date), and the strongest art-of-choice is likely the inventor's own academic corpus — the specification cites J. Lacan, "Diagonals of 2D-Abelian codes," 1998 Information Theory Workshop, and the Delsarte/Imai Abelian-code literature; those are exactly the printed publications an IPR petitioner would mine. That is theory, not a filed petition.

Pattern signals: none. No repeat petitioner, no defensive aggregator (Unified Patents or similar) in the chain, no PTAB-to-Federal-Circuit appeal trail involving this number. Canon has litigated aggressively on other patents (the 2014 ITC § 337 action and parallel SDNY suits over the '278/'564 families), but 6,543,021 is not among them. Inventor Philippe Piret is a coding theorist; the patent reads as a research-derived asset that was granted and left undisturbed rather than a licensing instrument.

Recommended next steps

1. If you are a defendant: the operative fact is expiration. Anticipated expiration 2019-07-14; legal status Expired – Fee Related (source: the authoritative patent text at https://patents.google.com/patent/US6543021/en). An expired patent cannot be enforced for post-expiration conduct, and a demand citing an expired, never-asserted patent is a red flag worth documenting. Do not represent to a court that any claim was "canceled" — no PTAB proceeding exists to have canceled it.
2. Confirm the expiration mechanism with the USPTO directly before relying on it — the record shows "Expired – Fee Related" (failure to pay maintenance fees) with an anticipated 20-year expiration of 2019-07-14, which is the full term from the 1999-07-14 filing. Either path ends enforceability, but the distinction matters for any pre-lapse damages theory. Check the USPTO Patent Center maintenance-fee history for 6,543,021.
3. Close the reexamination gap I could not close. Pull the patent's full file wrapper / reexamination tab on Patent Center and PTAB E2E (https://ptab.uspto.gov) to confirm there is no inter partes or ex parte reexamination history, which is a pre-AIA channel my searches did not clear.
4. There is nothing to do at the PTAB. No pending milestone to track, no FWD to link, no appeal on the Federal Circuit docket (and none on CourtListener) to cite. If you nonetheless want an invalidity record for defensive-use purposes, note that any IPR you file today would be filed on an expired patent, where the Board's practice on expired-claim construction (Phillips-style, not BRI) and on claim-cancellation mootness concerns would seriously reduce the practical value of a win.
5. If you need an authoritative negative for a filing or opinion: cite (a) the USPTO Open Data Portal "no AIA trial proceedings" result, and (b) a fresh PTAB E2E party/patent search on 6543021. Both, together, support the statement that no AIA trial proceeding has ever been instituted against US 6,543,021.

I'll research the assignment record for US 6,543,021 across USPTO Assignment Center, Google Patents legal events, and NPE directories.

Let me dig into the Google Patents legal events for this specific patent and the USPTO assignment records.

Assignment & Ownership Analysis — US 6,543,021 B1

Search-scope caveat up front: I could not pull the live USPTO Assignment Center detail page (assignmentcenter.uspto.gov) or a reel/frame image for this specific patent within the tool budget. The authoritative patent text supplies the existence and date of a reassignment but not a reel/frame number. Everything below is grounded in the authoritative Google Patents text in the user message plus the corroborating hits I retrieved, and I explicitly flag one near-miss that must not be misattributed to this patent.

Inventors

Pattern note: A single sole inventor is normal here and shows no fire-sale precursor. The classic "all inventors depart within 12 months" tell is not applicable to a one-inventor case, and there is no evidence of departure. Piret has a long publication record (1978–2006), consistent with a career researcher rather than a founder-inventor positioning a portfolio for sale.

Original assignee

Canon Kabushiki Kaisha (Canon Inc.) is the assignee on the issued patent (assignment recorded 1999-10-06; see the "reassignment" event in the authoritative text). Canon is a large, publicly traded Japanese imaging/optics/electronics manufacturer — primary line of business is cameras, printers, copiers, semiconductor lithography, and medical/optical equipment.

• Product embodying the claims? Canon ships communications/imaging products and has a large internal channel-coding research program (this patent's whole family — algebraic-geometric codes, Reed-Solomon, product/Abelian codes — is Canon R&D). I found no evidence that this specific coding scheme was productized as a named feature; it reads as defensive, in-house error-correction IP.
• Current status: Operating, not acquired, not dissolved, not in bankruptcy. The patent itself is Expired – Fee Related (anticipated expiration 2019-07-14 per the authoritative text), and Canon did not transfer it to any third party before expiry.

Assignment timeline

Only one recorded assignment exists in the chain.

• 1999-10-06 (recorded; execution date not separately surfaced in the authoritative text) — Reel/Frame: not surfaced in accessible sources
  • Conveyance: Assignment ("ASSIGNMENT OF ASSIGNORS INTEREST")
  • Assignor: Piret, Philippe (the sole inventor)
  • Assignee: Canon Kabushiki Kaisha
  • Correspondent: not surfaced in the sources I could access — I will not fabricate a name or firm. (The Assignment Center record should carry the correspondent; I could not render it.)
  • Context: original inventor→corporate assignment at filing — not a sale, not a reorg, not a securitization.

Preceding/following administrative events (not conveyances, listed for completeness): filed by Canon 1999-07-14; granted 2003-04-01; anticipated expiration 2019-07-14; status now Expired – Fee Related.

⚠️ Misattribution trap to flag: A search hit surfaced a recorded assignment — Reel 019492/0045, effective 2006-02-24, "ASSIGNMENT OF ASSIGNORS INTEREST; ASSIGNORS: PIRET, PHILIPPE; LEBARS, PHILIPPE A." — but that block belongs to US 8,132,078 (Decoding method for algebraic geometric codes and associated device), whose Google Patents page merely cites US 6,543,021. Do not enter 019492/0045 into this patent's chain. US 6,543,021 has no post-1999 assignments.

Since the Assignment Center contains only the original inventor→Canon assignment for this patent, there is no post-issuance chain to reconstruct. That is itself the finding: the original assignee retained ownership through expiry.

Timeline diagram

timeline
    title Ownership of US 6543021
    1998 : Priority date 16 July
    1999 : Application filed by Canon
         : Inventor Piret assigns to Canon KK
    2003 : Patent granted
    2019 : Anticipated expiration
    2020 : Expired for fee non-payment

NPE / troll-pattern signals

Verdict

Insufficient data (only the original assignment). The record contains exactly one conveyance — inventor Philippe Piret → Canon Kabushiki Kaisha, recorded 1999-10-06 — with no reel/frame or correspondent recoverable from the sources I could reach, and no post-issuance assignments. No NPE signal is present on any of the eight criteria: no shell LLC, no known asserter, no cascade, no pre-suit transfer, no bankruptcy, no privateering, and no defensive-aggregator endpoint.

Substantively, this is an operating-company-held, never-asserted, now-expired asset retained by Canon through its 2019 anticipated expiration — not an NPE chain. Verify against USPTO Assignment Center and the Assignment Search by patent number 6543021, which should return the single 1999-10-06 Canon record and confirm the absence of any later reel/frame.

I'll research the prior art citations for US 6,543,021, focusing on the specific patent number and its cited references.

Let me pull the specific "References Cited" (prior art) section from the patent's front page.

Let me search specifically for the patent citation list on the Google Patents front page for this exact patent.

Prior-Art Analysis — US Patent 6,543,021 (Piret, Canon)

Scope note up front (important, read this before the tables): The authoritative patent text you supplied contains the description and claims, but it does not reproduce the front-page "References Cited / U.S. Patent Documents" block. I attempted to retrieve that specific back-citation list via search and could not pull the front-page citation table for US6543021B1 itself. What the searches predominantly returned was the reverse relationship — i.e., later patents that cite 6543021 (forward citations), e.g. US8132078, US20050138533A1, FR2863794A1, US11515897B2 (Google Patents). I did not auto-substitute any of those for the actual prior-art citations of 6543021, and I am not going to fabricate a "U.S. Patent Documents" list I could not verify.

What I can ground with high confidence is the prior art the patent itself identifies and discusses in its specification (the authoritative text you supplied). That is the defensible prior-art set for this document, and I analyze it below.

A. Prior art expressly cited/discussed in the 6543021 specification (non-patent literature)

These are the references the applicant put in the record as the state of the art; they are the "most relevant prior art" for 6543021 in a literal, document-grounded sense.

B. The strongest § 102 combinations and why full anticipation fails

Working through the claim limitations against the above:

• Claim 1 requires the conjunction of (i) a square table with ≥3 distinct diagonals per symbol, each independently sufficient to recompute it; (ii) soft-decision demodulation; and (iii) iterative correction over the diagonals. No single reference above discloses all three. Lacan (1998) discloses the diagonal redundancy but on a hard-decision basis — so it does not anticipate claim 1; it is the most dangerous § 103 reference, especially combined with Pyndiah (1994) or Hagenauer et al. (1996) (which supply the soft/iterative element). This is precisely the "genus" the contested claims were drawn to carve out of the ordinary product code, and the applicant cites Lacan expressly to distinguish it.
• Claim 4 (l.l.r. summation) is the most exposed to § 102 by Hagenauer et al. (1996) standing alone — that is essentially the standard turbo/iterative soft-decoding metric. Its saving limitation is the tie to the diagonal structure of claim 1.
• Claims 6–9 (code-family limitations) are the most exposed to § 102 by Peterson & Weldon / Peterson (1961) / Lin & Costello, in the sense that the Hamming (2^m−1, 2^m−1−m), BCH, and parity (n, n−1) code definitions are textbook. Their patentability rides entirely on the requirement that the diagonals be words of those codes.

C. Patent citations — what I could and could not confirm

• Backward (prior-art) patent citations: Not retrieved. I could not obtain the front-page "U.S. Patent Documents" list for US6543021B1 from the searches performed. Per your strict rule, I will not fill this in from memory or from similar-number hits.
• Forward citations (context only — not prior art): Search results confirm US6543021B1 is cited by later Canon and third-party patents, e.g.:
  • US8132078, US20050138533A1 — https://patents.google.com/patent/US8132078#7
  • FR2863794A1 — https://patents.google.com/patent/FR2863794A1/en
  • US11515897B2 — https://patents.google.com/patent/US11515897B2/en
  • Also cited alongside US5942005A (IBM, filed 1997-04-08) and EP0884879A3 (Canon) in other citation tables. These are not prior art against 6543021 and must not be treated as such.

D. Honest limitations (do not over-read the above)

1. The definitive USPTO "References Cited" list for US6543021B1 was not obtained. To make the § 102 mapping exhaustive you would need the front page of the granted patent (or the file wrapper / PatentCenter for application 09/353,155) listing the U.S. patent documents and any foreign references cited. My analysis rests on the specification's own citations, which is a defensible but incomplete proxy.
2. The priority document is a French application (priority 1998-07-16; U.S. filing 1999-07-14, app. no. 09/353,155). I could not retrieve its number; it should be pulled to confirm whether any French search-report citations (which often differ from the U.S. list) were carried over.
3. Publication-date caution: Lin & Costello (1983), Imai (1977), Sakata (1981), Peterson (1961), Delsarte (1970), Gallager (1963) all pre-date the 1998 priority and are properly § 102(b) art. Hagenauer (1996) and Pyndiah (1994) also pre-date. Lacan (1998) is the closest in time and should have its exact publication date verified against the 1998-07-16 priority.

Bottom line: On the record I can verify, the most relevant prior art for 6543021 is the set of non-patent references the patent itself cites — Lacan (1998) (diagonals of 2D-Abelian codes, hard-decision) as the closest structural art, Pyndiah (1994) and Hagenauer et al. (1996) as the soft-decision/iterative-decoding art, and Peterson & Weldon / Imai / Sakata / Delsarte / Lin & Costello for the underlying code families. None of them, singly, anticipates claim 1 as issued; the obtainable rejections are § 103 combinations (Lacan + Hagenauer/Pyndiah). The front-page U.S. patent citations for 6543021 remain unretrieved and are flagged as an open item rather than filled in.

Obviousness Analysis — US 6,543,021 under 35 U.S.C. § 103

0. Scope, sources, and caveats

Which "prior art" I am permitted to use. The task directs me to the prior art identified in this patent's own background/"Prior Art" section. The fetched page (Google Patents) does not include the front-page "References Cited" list of U.S. patent documents and foreign documents; that portion was truncated. I therefore analyze only the non-patent references that the patent itself cites in its Background and Detailed Description.

The references on the record, as cited in the patent:

Caveats I must state up front:

1. I cannot verify the actual USPTO-cited references; my analysis rests on the self-cited background art in the authoritative text.
2. No litigation/objective-indicia evidence exists on the record (per the earlier litigation section). I therefore cannot credit secondary considerations either way.
3. The claim listing in the source is truncated mid-claim 13; I analyze claims 1–12 fully and treat claim 13+ as unknowable beyond its opening words.

The governing legal rubric: KSR Int'l Co. v. Teleflex Inc., 550 U.S. 398 (2007) — a claimed combination is obvious where the elements are individually known and a person of ordinary skill (PHOSITA) had a reason, a motivation, or a predictable path to combine them, especially where the combination does no more than yield predictable results from the known functions of known elements. Graham v. John Deere supplies the four-factor frame.

1. Claim 1 — the core claim

Claim 1 requires four things beyond generic transmission: (a) coding into a square table; (b) a soft-decision demodulation; (c) iterative correction with respect to each distinct diagonal; and (d) the structural limitation that for every calculated symbol there are ≥3 distinct diagonals that contain it and that, each individually, can recalculate it.

1.1 What each reference teaches

• [Lacan] — the patent itself concedes: "A hard iterative decoding method based on hard demodulation is considered in the article 'Diagonals of 2D-Abelian codes' by J. Lacan." The title and the patent's own characterization establish that Lacan works with 2D-Abelian codes whose words are square tables, using redundancy along diagonals, and decodes iteratively over those diagonals. This is the single most damaging reference: it supplies the square-table + diagonal-redundancy + diagonal-iteration architecture (claim elements a, c, and the diagonal premise of d).

• [Hagenauer] and [Pyndiah] — teach soft-decision demodulation/decoding of block and product codes with log-likelihood ratios, extrinsic information, and iterated passes alternating among the two code directions, with markedly better performance than hard decision (element b, plus the LLR-based "iterative correction" quality). The patent's own Background reproduces this framework: the LLR matrix, the alternating row/column steps, and the sum Σ = Λ + Λ′ + K used to decide each symbol.

• [Delsarte], [Imai], [Sakata] — supply the algebraic substrate: Abelian codes, ideals, idempotent-generator decomposition, the "basis" of minimal idempotents, and systematic two-dimensional encoding. These are what claim 2 (basis polynomials), claim 3 (product polynomials), and claim 5 (Abelian code) map onto.

• [Peterson&Weldon], [Lin&Costello], [Peterson] — textbook-level knowledge that BCH, Hamming, and parity codes are standard cyclic codes and implementable on diagonals (claims 6–9).

1.2 The combination and the motivation

The obviousness thesis is straightforward and, notably, is stated almost verbatim by the applicant's own background section:

Primary reference: [Lacan] (diagonal-based 2D-Abelian code structure, hard iterative decoding)
+ Secondary: [Hagenauer]/[Pyndiah] (replace hard decisions with soft, LLR-based iterative decoding)
+ optionally [Delsarte]/[Imai]/[Sakata] (algebraic construction of the diagonal-constrained code)

Motivation to combine, articulated as a PHOSITA would:

1. Same field, same problem, same channel model. Both references address combatting errors in transmission over noisy channels (the patent's own stated object). KSR permits combination of references in the same field directed to the same problem.
2. The patent itself frames the combination as the invention. The Background presents [Lacan] (diagonals, hard) and [Hagenauer]/[Pyndiah] (soft iterative) back-to-back, then states the aim is "explicitly implementing coding methods using codes for which it is possible to obtain more than three independent sets of symbols." The stated deltas over the art are (i) use diagonals in addition to rows/columns, and (ii) use soft iteration. Each delta is a known technique, and the motivation to take the second step (soft) is explicitly supplied by [Hagenauer], which the patent says proves product-code decoding "particularly efficient" when soft.
3. Predictable result. Under KSR, "a combination of familiar elements according to known methods is likely to be obvious when it does no more than yield predictable results." Replacing hard-likelihood iteration with soft-LLR iteration in a diagonal-based code is the routine, expected improvement [Hagenauer] teaches for the analogous row/column case. Combining a diagonal-constrained code structure [Lacan] with soft iterative decoding [Hagenauer] yields the predictable benefit of better error correction — the very benefit the patent claims.

1.3 The weak point in the obviousness case on claim 1

The strongest non-obviousness argument (and the one the specification half-concedes) targets element (d) and the quality of iteration:

• The patent argues: "the quantities (Λ′)s,t and (K)s,t introduced above become more and more correlated at each iteration," and that having more than three disjoint estimate sets is needed to break the correlation. A PHOSITA combining hard [Lacan] with soft [Hagenauer] might arrive at three estimate sets (row, column, one diagonal) — i.e., exactly the pre-existing product-code situation — without appreciating that ≥3 diagonals per symbol are needed for the soft iteration to decorrelate. That is a genuine "recognition of the problem," not just mechanical substitution, and it is the kind of insight KSR still respects where the improvement is unpredictable.
• For claim 1 to fall, the Office would need [Lacan] to teach enough diagonal redundancy that a third independent estimate per symbol is available or obvious, not merely that diagonals exist. Lacan's abstract/title suggests diagonals are studied, but whether it discloses ≥3 recalculating diagonals per symbol is a factual question I cannot resolve from the truncated text. I flag this as the pivotal fact.

Net on claim 1: prima facie obvious over [Lacan] + [Hagenauer] (with [Pyndiah]), with the entire contest turning on the three-independently-recalculating-diagonals requirement (d) and whether the claimed "iterative over each distinct diagonal" reads on a predictable soft-decoding extension. On the record as cited, I would expect a strong § 103 rejection with the burden shifting to the applicant to show the coding gain was unpredictable.

2. Dependent claims — secondary combinations

Observation: the specification largely maps its own claims onto the cited literature. Claims 5–9 are explicitly framed as "using an Abelian code," "diagonal… is a word of a BCH code," "Hamming code," "parity code" — each backed in the background by an identified textbook or article. This is the classic pattern that invites a § 103 rejection, because the claim limitations are the known properties of the cited codes applied to the [Lacan]/[Hagenauer] architecture.

3. The KSR "design incentives / market pressure" overlay

• Design incentives: Increasing error-correction performance at bounded redundancy/complexity is the constant driver of the coding field; [Hagenauer]'s soft iterative decoding and [Lacan]'s diagonal Abelian codes are two known levers. A PHOSITA facing a noisy wireless channel had ample incentive to combine levers.
• Known techniques, finite predictable options: BCH/Hamming/parity-diagonal choices (claims 6–9) are the enumerated, predictable design options for "make the diagonal a cyclic code." KSR treats selection among a finite set of known, predictable options as obvious.
• No teaching away on the record: I see nothing in the cited art that discourages soft-decoding diagonals; if anything, [Hagenauer] and [Pyndiah] urge soft iteration.

4. Weaknesses I must candidly flag (both directions)

1. Unverifiable front-page art. I could not inspect the USPTO "References Cited"; a real § 103 analysis should include those (they often contain closer U.S. patents than the naked NPL cites here).
2. The pivotal factual gap. Whether [Lacan] alone discloses or renders obvious three independently-recalculating diagonals per symbol is unresolved from the truncated text. If Lacan only hints at a single extra diagonal family, the Office's case weakens and the applicant's "correlation-reduction insight" argument (spec: the Λ′/K correlation discussion) gains traction.
3. Predictability contest. The decisive Graham factual question is whether moving from hard diagonal iteration to soft diagonal iteration produced predictable or unexpected coding gain. The applicant can argue the ≥3-diagonal requirement is the discovered condition that makes the soft iteration work — a classic "recognition of the problem" non-obviousness position (In re Omeprazole line). Without experimental data (the patent supplies a worked (49,10) example but no comparative BER curves vs. [Lacan]/[Hagenauer]), the record is thin on both sides.
4. Objective indicia absent. No commercial-success, licensing, copying, or long-felt-need evidence is on the record (and the earlier litigation search found no enforcement activity on this expired patent), so secondary considerations cannot tip the balance toward non-obviousness here.

5. Bottom line

Likely § 103 rejection grounded in two combinations:

• Claims 1, 4, 5 (and 12): obvious over [Lacan] in view of [Hagenauer] (optionally [Pyndiah]). Rationale: same field/problem; [Lacan] supplies square-table diagonal redundancy with diagonal iteration; [Hagenauer]/[Pyndiah] supply the soft-decision/LLR iterative decoding that the patent concedes is "particularly efficient" for such codes. The contested element is the ≥3-recalculating-diagonals limitation — a factual dispute on the content of [Lacan].

• Claims 2, 3, 6–9: obvious over the above plus [Imai], [Delsarte], [Sakata], [Peterson&Weldon], [Lin&Costello], [Peterson]. Rationale: the algebraic-basis construction and the BCH/Hamming/parity diagonal codewords are textbook-known, predictable design options explicitly linked by the patent's own background to the claimed features.

Claims 10–11 rise or fall with claim 1 (known storage media performing their known function).

My confidence: moderate for claims 4, 5, 6–9 (the art maps cleanly and the combinations are textbook); lower/moderate for the full scope of claim 1, which turns on (i) exactly what [Lacan] teaches about multiple recalculating diagonals and (ii) whether the soft-iteration coding gain was predictable over the [Lacan]/[Hagenauer] baseline. Both are factual questions I cannot close from the available text, and I state that rather than assert a conclusion the record does not support.