<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-04-20</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001160958</issuerCik>
        <issuerName>INPHI Corp</issuerName>
        <issuerTradingSymbol>IPHI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001223721</rptOwnerCik>
            <rptOwnerName>EDMUNDS JOHN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>110 RIO ROBLES</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN JOSE</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>95134</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-04-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>27456</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>230921</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-04-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>162230</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>68691</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-04-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>68691</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>12.34</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-04-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common
Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>20000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>13.48</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-04-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>11000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common
Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>11000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On April 20, 2021, pursuant to the Agreement and Plan of Merger and Reorganization, dated as of October 29, 2020 (the &quot;Merger Agreement&quot;) by and among by and among Marvell Technology Group Ltd., a Bermuda exempted company (&quot;Marvell&quot;), Marvell Technology, Inc. (f/k/a Maui HoldCo, Inc.), a Delaware corporation and a wholly owned subsidiary of Marvell (&quot;HoldCo&quot;), Maui Acquisition Company Ltd, a Bermuda exempted company and a wholly owned subsidiary of HoldCo (&quot;Bermuda Merger Sub&quot;), Indigo Acquisition Corp., a Delaware corporation and a wholly owned subsidiary of HoldCo (&quot;Delaware Merger Sub&quot;), and Inphi Corporation, a Delaware corporation (&quot;Inphi&quot;), Bermuda Merger Sub merged with and into Marvell with Marvell as the surviving corporation and a wholly owned subsidiary of Holdco (the &quot;Bermuda Merger&quot;),</footnote>
        <footnote id="F2">(continued from footnote 1) and Delaware Merger Sub merged with and into Inphi with Inphi as the surviving corporation and a wholly owned subsidiary of Holdco (the &quot;Delaware Merger&quot; and, together with the Bermuda Merger, the &quot;Mergers&quot;). At the effective time of the Mergers, the restricted stock units that vest based on the per share market value of the shares of Inphi Common Stock (the &quot;Inphi Common Stock&quot;) exceeding certain relative performance target levels (a &quot;MVSU&quot;) were vested in full on April 20, 2020. The holder of such vested MVSUs became entitled to receive (subject to applicable withholding or other taxes) (i) an amount in cash equal to the product of (A) $66.00, multiplied by (B) the total number of shares of Inphi Common Stock subject to such vested MVSU, and (ii) a number of shares of HoldCo Common Stock equal to the product of (A) 2.323, multiplied by (B) the total number of shares of Inphi Common Stock subject to such vested MVSU.</footnote>
        <footnote id="F3">Disposed pursuant to the Merger Agreement, whereby at the effective time of the Mergers, the outstanding Inphi Common Stock was automatically converted into the right to receive 2.323 shares of HoldCo Common Stock and $66.00 in cash, without interest (in addition to cash in lieu of fractional shares).</footnote>
        <footnote id="F4">Per the terms of the Merger Agreement, (a) 50,160 RSUs that were outstanding and vested immediately prior to the effective time of the Mergers (including 41,410 RSUs that only vest subject to delivery of an effective release) were cancelled in exchange for (subject to applicable withholding or other taxes), (i) an amount of cash equal to the product of (A) $66.00, multiplied by (B) the total number of shares of Inphi Common Stock subject to such RSU, (ii) a number of shares of HoldCo Common Stock equal to the product of (a) 2.323, multiplied by (B) the total number of shares of Inphi Common Stock subject to such RSU, and (b) 18,531 RSUs were forfeited.</footnote>
        <footnote id="F5">At the effective time of the Mergers, options to purchase shares of Inphi Common Stock (an &quot;Option&quot;) were canceled in exchange for payment (subject to applicable withholding or taxes) of an amount in cash equal to the product of (i) the number of shares of Inphi Common Stock subject to such option, multiplied by (ii) the excess of (A) the Equity Award Cash Consideration Amount over (B) the exercise price applicable to such Option. &quot;Equity Award Cash Consideration Amount&quot; refers to an amount in cash equal to the sum of (i) $66.00, plus (ii) the product of (A) 2.323, multiplied by (B) the volume weighted average trading price of a share of HoldCo Common Stock for the five consecutive trading days ending on the trading day immediately preceding the Closing Date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ford Tamer, attorney-in-fact</signatureName>
        <signatureDate>2021-04-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
