LB-031
`
`Original: English
`
`Temporary Document LB-031
`
`ITU - Telecommunication Standardization Sector
`
`STUDY GROUP 15
`
`Leuven – 14-18 June 2004
`
`
`Question: 4/15
`
`
`SOURCE1: Texas Instruments, Inc.
`
`VDSL2 – Constraining the Interleaver Complexity
`TITLE:
`________________________________________________________
`
`Abstract
`This contribution proposes restrictions on the interleaver. The interleaver is a major source of complexity
`in VDSL2. We propose that the interleaver delay in time be restricted rather than restricting the depth as
`in ADSL2. This allows the following: 1) the flexibility of using shorter codewords to correct longer bursts,
`2) the capability to correct repetitive impulse noise, and 3) lower complexity implementations for profiles
`that do not require the full VDSL2 data rate. We propose also that the upper limit on the number of
`codewords in a DMT symbol (or per unit time) scale with the data rate so that more codewords are
`allowed at higher data rates.
`Introduction, Limits on Interleaver Complexity, Limits on the Number of Codewords, Repetitive Impulse
`Noise, Examples, Proposal, References
`
`
`Differences
`As a courtesy to those who may have read T1E1.4/2003-493, this section lists the differences between
`this contribution and that one.
`-
`generally, this contribution proposes that the number of codewords in a given amount of time and
`the interleaver complexity should both scale with the data rate
` the substance of the introduction has not changed
`section 2 (limits on interleaver complexity): an example is included to illustrate practically how this
`proposal would work in the recommendation
`section 3 (limits on the number of codewords): this section has been completely revised
`section 4 (repetitive impulse noise): this section has not changed
`section 5 (examples) the table has been revised
`section 6 (proposal) the proposals have been revised
`section 7 (references) the references have been updated
`
`-
`-
`-
`-
`-
`
`-
`-
`
`1. Introduction
`
`A convolutional interleaver was first described by Ramsey [1] and Forney [2]. In general, a convolutional
`interleaver imposes a different delay on each input symbol (normally an octet). If i denotes the octet index within a
`
`1 Contact: Cory Modlin
`
`Texas Instruments, Inc.
`
`
`
`T: +1 301 318 2679
`
`E: cmodlin@ti.com
`
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`LB-031
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`(1)
`
`group of I octets so that i = 0, 1, … I −1, octet i experiences a delay of i·(d −1) with d the interleaver depth. The
`deinterleaver performs the inverse operation delaying octet i by (I −i −1) ·(d −1). The overall delay of the
`interleaver/deinterleaver pair is
`interleaver delay (octets) = (I −1) ·(d −1) octets.
`This applies to all interleavers being considered for VDSL2.
`
`The smallest amount of memory required to build an interleaver/deinterleaver pair is equal to the total delay of the
`interleaver/deinterleaver [3]. Typically, for memory optimized interleavers, the interleaver and deinterleaver
`memory size is nearly the same. Therefore, the smallest possible memory for either the interleaver or deinterleaver is
`smallest possible (de)interleaver memory = (I −1) ·(d −1)/2 bytes.
`(2)
`In a typical implementation, slightly more memory is often required. The actual amount of required memory is
`implementation specific.
`
`The length of a burst that can be corrected by the combination of Reed-Solomon coding and
`interleaving/deinterleaving is dependent on the line data rate. We define ldr as the line data rate, the rate of the
`Reed-Solomon encoded bits. This is as opposed to the net data rate, ndr, the effective payload data rate as seen at the
`α(β) interface between the TPS-TC and the PMS-TC. We adopt the notation ldr_mbit_s or ldr_kbit_s to indicate
`whether the data rate is given in mbit/s or kbit/s respectively. The line data rate and net data rate are related by the
`equation
`ndr_kbit_s = ldr_kbit_s * (n-r)/n – overhead rate
`where the Reed-Solomon codeword size is n octets with r octets of redundancy.
`
`For a t error correcting (typically t = r/2) Reed-Solomon code of size n octets, and assuming n = I*q,2 the
`combination of coding and interleaving can correct a burst of
`INP_min = t*d/q octets => t*d/q*8/ldr_mbit_s μs.
`(4)
`In ADSL2 and ADSL2+, q = 1, t is up to 8 (assuming erasure decoding is not used), n is up to 255 and d can be up
`to 64 downstream and 8 upstream. In ADSL2+, the maximum line data rate is 24.48 Mbps. At this rate the coding
`plus interleaving can correct up to 8*64/1*8/24.48 = 167μs.
`
`The end-to-end delay of the interleaver/deinterleaver in ms is
`delay (ms) = (I −1) ·(d −1)·8/ldr_kbit_s
`and for ADSL2+, the delay at the maximum line data rate is (255 – 1)*(64 – 1)*8/24480 = 5.23 ms.
`
`Error bursts must be separated in time so that each codeword corrects only one burst. The span of a codeword of size
`n octets and an interleaver depth, d, is
`span (ms) = n·d/q·8/ldr_kbit_s
`(6)
`The time spacing between codewords in equation (6) is nearly identical to the interleaver delay in equation (5) for
`large codeword size and depth since n = I*q.
`At the maximum codeword size, interleaver depth, and line data rate in ADSL2+, the codeword spans
`(255)*(64)*8/24480 = 5.33 ms. At the maximum line data rate and codeword size, the ADSL2+ coding + interleaver
`can correct a 167μs burst every 5.33 ms.
`Equations (2), (4), (5), and (6) illustrate trade-offs between interleaver memory, error correction capability, delay,
`and burst separation. More interleaver memory normally allows more error correction but leads to higher delays and
`
`(3)
`
`(5)
`
`
`
`
`2 Here, “q” is assumed to be an integer. This is not the same q used to describe the DMT tone spacing.
`2
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`a longer separation between error bursts. Significant error correction can be achieved by using shorter codewords
`requiring less memory, less delay, and shorter time between bursts. However, small codewords typically have lower
`net coding gain and higher computation requirements since there are more decoder operations required in the same
`amount of time. Therefore, we make a trade-off between complexity, capability, and performance.
`
`2. Limits on Interleaver Complexity
`
`The size of the interleaver memory will be a major source of complexity in VDSL2. 100 Mbit/s symmetric has been
`an often stated goal for VDSL2. However, a number of operators have stated their requirements at well below 100
`Mbit/s. See for example [4] or [5].
`Therefore, it seems prudent to define the interleaver complexity requirements in a way that will allow those who
`want to deploy VDSL2 at lower speeds to do so at a reduced complexity with respect to higher speed
`implementations.
`The way to do this and to guarantee some minimum level of performance is to specify the interleaver complexity in
`terms of the delay in time. From equation (5), we see that the delay in time (ms) is proportional to the interleaver
`depth and to the codeword size and inversely proportional to the data rate.
`ADSL2 instead specifies the smallest maximum interleaver depth and the maximum number of codewords allowed
`in a DMT symbol. There are two problems with this approach. The first is that it removes the flexibility of trading
`codeword size and interleaver depth to allow more error correction with the same amount of memory. The second
`problem is that as the data rate increases, the interleaver delay decreases and with it, the error correction capability
`decreases also.
`One possible way to specify the smallest maximum supported delay is to start with ADSL2+ and require that
`VDSL2 interleavers support at least 5.23ms delay. This maintains a level of impulse noise protection as the data rate
`increases and still allows lower speed implementations to save complexity.
`For interoperability reasons, the VTU-O and VTU-R must exchange the interleaver delay in terms of octets. The
`requirement is that the interleaver delay in octets be sufficient to satisfy the smallest maximum delay even at the
`highest supported data rate. If a VDSL2 implementation supports a larger interleaver memory than is required, it
`should be free to specify the larger value. The VTU-O and VTU-R would then select the smaller of the transmitter
`and receiver capabilities, in each direction, as the end-to-end capabilities.
`Again, the actual amount of memory required is implementation specific.
`
`3
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`Example:
`
`Suppose a VDSL2 transceiver supports up to 44.5 Mbit/s as a line data rate. If the minimum interleaver delay
`requirement were 5.23ms, then, from equation (5) and equation (1), this transceiver must support a delay of at
`least 29092 octets which corresponds to having an interleaver memory of at least 14546 octets according to
`equation (2) (although this is actually implementation specific). During initialization, the VDSL2 transceiver
`would indicate that it could support up to 44.5 Mbit/s and 29092 or more octets of interleaver delay. The actual
`interleaver delay could be considerably higher than 5.23ms, in this example, if the actual connection data rate is
`below 44.5 Mbit/s. For example, if the actual connection line rate were 5 Mbit/s, the interleaver delay could be
`as high as 47 ms using 14546 octets of interleaver memory. This is why the maximum delay is still needed.
`Transceiver capabilities exchanged during initialization for this example:
`
` maximum data rate = 44.5 Mbit/s
` minimum data rate = any value at or below the maximum data rate
` maximum delay supported ≥ 29092 octets
`o meets 5.23 ms example minimum requirement
`o minimum amount of memory required for (de)interleaver is 14546 octets
`
` maximum delay = any valid value as in ADSL2 today §
`
`3. Limits on the Number of Codewords
`
`Similar to the interleaver delay, we propose that the maximum number of codewords in a DMT symbol (or per unit
`time) also scale with the data rate. The higher the data rate, the more DMT codewords there can be in a fixed length
`DMT symbol.
`In ADSL2+, 5.23ms delay allows correction of an impulse burst of only 167μs. This is because the (de)interleaver
`depth is limited to 64. By removing the depth restriction, the correction capability can be increased without
`increasing the delay in ms or the size of the (de)interleaver.
`The correction capability can be enhanced by using smaller codewords. This implies there are more codewords in
`each DMT symbol and a larger interleaver depth. Typically the complexity increase from adding interleaver
`memory is considerably higher than the complexity from decoding small codewords.
`Small codewords with the codeword size, n, less than 255 can lead to slightly lower net coding gain depending on
`the situation. As the codeword size decreases, the gross coding gain increases since a higher percentage of errors are
`corrected. However, at the same time, there is more overhead. Typically for very small codeword sizes, the penalty
`from the overhead starts to outweigh the added benefits from more error correction capability and we see a net
`coding gain loss. A trade-off needs to be made between performance, delay, and complexity. This trade-off needs
`to take into account that a majority of lines are not afflicted by large impulse noise.
`At a given interleaver delay expressed in time and a given amount of impulse noise protection, the maximum
`codeword size allowed is fixed. To see this, we re-write equation (4) as
`
`(7)
`
`4
`
`
`
`8
`
`
`
`qd
`
`t
`
`
`
`ldr
`
`_
`
`mbit
`
`_
`
`s
`
`
`
`INP_min
`_
`s
`and then insert this into equation (5) and find
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`LB-031
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`
`
`
`
`qn
`
`
`
`
`delay
`
`(
`
`ms
`
`)
`
`
`
`
`
`1
`81
`d
`
`
`
`
`NP_min_
`ms
`
`8I
`
`
`
`qd
`
`t
`
`
`
`
`
`(8)
`
`
`
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`
`8
`
`
`
`
`
`INP_min_
`ms
`
`8
`
`
`
`qd
`
`t
`
`
`
`qn
`
`
`
`n
`
`
`
`
`
`INP_min_
`ms
`t
`where in the second line we assume that n/q and d >> 1 and we have substituted I = n/q. As we see, at a fixed error
`correction capability, t, and a fixed impulse noise correction requirement, INP_min_ms, the codeword size n is
`constrained by the delay.
`With a fixed codeword size, the number of codewords in a fixed time period or in a DMT symbol will scale with the
`data rate. Therefore, we propose that the constraint on the number of codewords per unit time (or for a DMT
`symbol) scale with data rate.
`For example, to achieve INP_min_μs = 500 (2 DMT symbols if the DMT symbol rate is 4000) at t = 8 and a delay
`constraint of 5.23ms, we need n ≈ 85. The number of codewords in a 4 kHz DMT symbol is
`
`octet 1
`codeword 1
`
`
`
` octets n
`
` bits 8
`
`
`
`codewords 4per kHz symbolDMT
`
`
`
`
`
`
`
`ldr
`
`_
`
`kbit
`
`_
`
`s
`
`
`
`
`
`
`
` 1
`s
`
`
`
`
` k 4 symbols DMT
`
`_
`
`s
`
`_
`
`s
`
`. (9)
`
`_
`
`kbit
`2
`n
`
`kbit
`2720
`
`_3
`
`ldr
`
`ldr
`
`
`
`
`
`
`
`
`
`
`
`
`At a line data rate of 30 mbit/s (30000 kbit/s), for example, the number of codewords per 4 kHz DMT symbol is
`30000
`03.11
`12
`
`
`2720
`Putting this in ADSL2 terms with S defined as the number of DMT symbols per codeword, we would say
`720
`_
`ldr
`kbit
`s
`where n = 85 and t = 8 was used to constrain S. For the example at 30 Mbit/s, this would be S ≥ 1/12.
`Since variable tone spacing and a variable cyclic extension length will cause the DMT symbol period to vary from
`4000 Hz, this rule on the number of codewords per DMT symbol needs to be specified in a way that allows a
`variable DMT symbol period. We leave this for a future meeting.
`This does not mean that n = 85 would be the largest or smallest codeword size allowed, it is simply used to
`guarantee a certain minimum level of impulse noise protection at a given minimum interleaver delay at a given
`maximum data rate. If the actual interleaver delay is higher or the data rate lower or the impulse noise protection
`lower, larger codewords can be used. The proposal is that Smin scale with the data rate. In ADSL2, Smin is fixed at
`½ and in ADSL2+, Smin is fixed at 1/3.
`
`.
`
`
`
`_2
`
`S
`
`
`
`(10)
`
`5
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`LB-031
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`4. Repetitive Impulse Noise
`
`Recently, impulse noise measurements taken by BT [6] have shown that some faulty or poorly designed consumer
`electronic equipment can emit 100 Hz noise pulses. Presumably, in North America, we would find similar 120 Hz
`noise sources although we are not aware of a comparable study. If 120 Hz noise sources exist, the period of the
`disturbance would be 8.33ms. To correct an impulse that occurs every 8.33ms, each Reed-Solomon codeword must
`span no more than 8.33ms or be designed so that each codeword can correct multiple bursts.
`Noting the similarity between equations (5) and (6), as long as the length of each impulse falls within the correction
`capability of the Reed-Solomon code plus interleaver, the impulse train can be corrected as long as the interleaver
`delay is less than about 8.33ms in regions with 60Hz power transmission or 10ms in regions that use 50Hz power
`transmission.
`
`5. Examples
`
`net data rate
`(ndr_mbit_s)
`
`line data rate
`(ldr_mbit_s)
`
`delay(ms)
`
`interleaver
`depth (d)
`for q = 1
`
`966
`5.18
`123.5
`100
`348
`5.17
`44.5
`36
`242
`5.17
`30.1
`25
`191
`5.23
`24.4
`20
`* ADSL2/2+ minimum memory requirement.
`
`6. Proposal
`
`number of
`codewords
`per 4000Hz
`DMT symbol
`(1/S)
`46
`17
`12
`9
`
`optimal
`(de)interleaver
`memory size (octets)
` [(I – 1)*(d – 1)/2]
`
`impulse
`noise
`protection
`
`40048
`14400
`10002
`8001*
`
`500 μs
`500 μs
`500 μs
`500 μs
`
`This contribution addresses
`
`
`What shall be the mandatory interleaver capabilities?
`
`MC-086, D1060
`
`11.4
`
`Open
`
`
`and proposes:
`
`interleaver complexity should be specified in terms of a time delay (ms), not in terms of an amount of
`memory or an interleaver depth
`interleaver delay in terms of octets should be exchanged between the VTU-O and VTU-R; the delay in
`octets should meet the minimum requirements in terms of the delay in time
`the upper limit on the number of codewords per unit time should be constrained and should scale with
`the data rate so that as the data rates increase, this upper limit on the number of codewords is also
`higher
`
`
`
`
`
`7. References
`
`[1] Ramsey, J.L., “Realization of Optimum Interleavers”, in IEEE Trans Info Theory, Vol IT-16, No. 3, May 1970,
`pp. 338-345.
`[2] Forney, G.D., “Burst-Correcting Codes for the Classic Bursty Channel”, IEEE Trans Communications
`Technology, Vol COM-19, October 1971, pp. 772-781.
`[3] Heegard, C. and Wicker, S.B., “Turbo Coding,” Kluwer Academic Publishers, Boston, MA, 1999.
`
`6
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`[4] Foster, K., “VDSL2 Requirements,” ITU Temporary Document SS-058, January 2004.
`[5] Starr, T. and Wei, D., “VDSL2 Rate and Reach Goals,” ITU Delayed Contribution 1045, April 2004.
`[6] Foster, K., “Improved Impulse Noise Modelling for xDSL Modem Testing,” ITU Delayed Contribution 1251,
`April 2004.
`
`LB-031
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