This is a purely informative rendering of an RFC that includes verified errata. This rendering may not be used as a reference.
The following 'Verified' errata have been incorporated in this document:
EID 365
Network Working Group S. Floyd
Request for Comments: 2883 ACIRI
Category: Standards Track J. Mahdavi
Novell
M. Mathis
Pittsburgh Supercomputing Center
M. Podolsky
UC Berkeley
July 2000
An Extension to the Selective Acknowledgement (SACK) Option for TCP
Status of this Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2000). All Rights Reserved.
Abstract
This note defines an extension of the Selective Acknowledgement
(SACK) Option [RFC2018] for TCP. RFC 2018 specified the use of the
SACK option for acknowledging out-of-sequence data not covered by
TCP's cumulative acknowledgement field. This note extends RFC 2018
by specifying the use of the SACK option for acknowledging duplicate
packets. This note suggests that when duplicate packets are
received, the first block of the SACK option field can be used to
report the sequence numbers of the packet that triggered the
acknowledgement. This extension to the SACK option allows the TCP
sender to infer the order of packets received at the receiver,
allowing the sender to infer when it has unnecessarily retransmitted
a packet. A TCP sender could then use this information for more
robust operation in an environment of reordered packets [BPS99], ACK
loss, packet replication, and/or early retransmit timeouts.
1. Conventions and Acronyms
The keywords MUST, MUST NOT, REQUIRED, SHALL, SHALL NOT, SHOULD,
SHOULD NOT, RECOMMENDED, MAY, and OPTIONAL, when they appear in this
document, are to be interpreted as described in [B97].
2. Introduction
The Selective Acknowledgement (SACK) option defined in RFC 2018 is
used by the TCP data receiver to acknowledge non-contiguous blocks of
data not covered by the Cumulative Acknowledgement field. However,
RFC 2018 does not specify the use of the SACK option when duplicate
segments are received. This note specifies the use of the SACK
option when acknowledging the receipt of a duplicate packet [F99].
We use the term D-SACK (for duplicate-SACK) to refer to a SACK block
that reports a duplicate segment.
This document does not make any changes to TCP's use of the
cumulative acknowledgement field, or to the TCP receiver's decision
of *when* to send an acknowledgement packet. This document only
concerns the contents of the SACK option when an acknowledgement is
sent.
This extension is compatible with current implementations of the SACK
option in TCP. That is, if one of the TCP end-nodes does not
implement this D-SACK extension and the other TCP end-node does, we
believe that this use of the D-SACK extension by one of the end nodes
will not introduce problems.
The use of D-SACK does not require separate negotiation between a TCP
sender and receiver that have already negotiated SACK capability.
The absence of separate negotiation for D-SACK means that the TCP
receiver could send D-SACK blocks when the TCP sender does not
understand this extension to SACK. In this case, the TCP sender will
simply discard any D-SACK blocks, and process the other SACK blocks
in the SACK option field as it normally would.
3. The Sack Option Format as defined in RFC 2018
The SACK option as defined in RFC 2018 is as follows:
+--------+--------+
| Kind=5 | Length |
+--------+--------+--------+--------+
| Left Edge of 1st Block |
+--------+--------+--------+--------+
| Right Edge of 1st Block |
+--------+--------+--------+--------+
| |
/ . . . /
| |
+--------+--------+--------+--------+
| Left Edge of nth Block |
+--------+--------+--------+--------+
| Right Edge of nth Block |
+--------+--------+--------+--------+
The Selective Acknowledgement (SACK) option in the TCP header
contains a number of SACK blocks, where each block specifies the left
and right edge of a block of data received at the TCP receiver. In
particular, a block represents a contiguous sequence space of data
received and queued at the receiver, where the "left edge" of the
block is the first sequence number of the block, and the "right edge"
is the sequence number immediately following the last sequence number
of the block.
RFC 2018 implies that the first SACK block specify the segment that
triggered the acknowledgement. From RFC 2018, when the data receiver
chooses to send a SACK option, "the first SACK block ... MUST specify
the contiguous block of data containing the segment which triggered
this ACK, unless that segment advanced the Acknowledgment Number
field in the header."
However, RFC 2018 does not address the use of the SACK option when
acknowledging a duplicate segment. For example, RFC 2018 specifies
that "each block represents received bytes of data that are
contiguous and isolated". RFC 2018 further specifies that "if sent
at all, SACK options SHOULD be included in all ACKs which do not ACK
the highest sequence number in the data receiver's queue." RFC 2018
does not specify the use of the SACK option when a duplicate segment
is received, and the cumulative acknowledgement field in the ACK
acknowledges all of the data in the data receiver's queue.
4. Use of the SACK option for reporting a duplicate segment
This section specifies the use of SACK blocks when the SACK option is
used in reporting a duplicate segment. When D-SACK is used, the
first block of the SACK option should be a D-SACK block specifying
the sequence numbers for the duplicate segment that triggers the
acknowledgement. If the duplicate segment is part of a larger block
of non-contiguous data in the receiver's data queue, then the
following SACK block should be used to specify this larger block.
Additional SACK blocks can be used to specify additional non-
contiguous blocks of data, as specified in RFC 2018.
The guidelines for reporting duplicate segments are summarized below:
(1) A D-SACK block is only used to report a duplicate contiguous
sequence of data received by the receiver in the most recent packet.
(2) Each duplicate contiguous sequence of data received is reported
in at most one D-SACK block. (I.e., the receiver sends two identical
D-SACK blocks in subsequent packets only if the receiver receives two
duplicate segments.)
(3) The left edge of the D-SACK block specifies the first sequence
number of the duplicate contiguous sequence, and the right edge of
the D-SACK block specifies the sequence number immediately following
the last sequence in the duplicate contiguous sequence.
(4) If the D-SACK block reports a duplicate contiguous sequence from
a (possibly larger) block of data in the receiver's data queue above
the cumulative acknowledgement, then the second SACK block in that
SACK option should specify that (possibly larger) block of data.
(5) Following the SACK blocks described above for reporting duplicate
segments, additional SACK blocks can be used for reporting additional
blocks of data, as specified in RFC 2018.
Note that because each duplicate segment is reported in only one ACK
packet, information about that duplicate segment will be lost if that
ACK packet is dropped in the network.
4.1 Reporting Full Duplicate Segments
We illustrate these guidelines with three examples. In each example,
we assume that the data receiver has first received eight segments of
500 bytes each, and has sent an acknowledgement with the cumulative
acknowledgement field set to 4000 (assuming the first sequence number
is zero). The D-SACK block is underlined in each example.
4.1.1. Example 1: Reporting a duplicate segment.
Because several ACK packets are lost, the data sender retransmits
packet 3000-3499, and the data receiver subsequently receives a
duplicate segment with sequence numbers 3000-3499. The receiver
sends an acknowledgement with the cumulative acknowledgement field
set to 4000, and the first, D-SACK block specifying sequence numbers
3000-3500.
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
3000-3499 3000-3499 3500 (ACK dropped)
3500-3999 3500-3999 4000 (ACK dropped)
3000-3499 3000-3499 4000, SACK=3000-3500
---------
4.1.2. Example 2: Reporting an out-of-order segment and a duplicate
segment.
Following a lost data packet, the receiver receives an out-of-order
data segment, which triggers the SACK option as specified in RFC
2018. Because of several lost ACK packets, the sender then
retransmits a data packet. The receiver receives the duplicate
packet, and reports it in the first, D-SACK block:
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
3000-3499 3000-3499 3500 (ACK dropped)
3500-3999 3500-3999 4000 (ACK dropped)
4000-4499 (data packet dropped)
4500-4999 4500-4999 4000, SACK=4500-5000 (ACK dropped)
3000-3499 3000-3499 4000, SACK=3000-3500, 4500-5000
---------
4.1.3. Example 3: Reporting a duplicate of an out-of-order segment.
Because of a lost data packet, the receiver receives two out-of-order
segments. The receiver next receives a duplicate segment for one of
these out-of-order segments:
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
3500-3999 3500-3999 4000
4000-4499 (data packet dropped)
4500-4999 4500-4999 4000, SACK=4500-5000
5000-5499 5000-5499 4000, SACK=4500-5500
(duplicated packet)
5000-5499 4000, SACK=5000-5500, 4500-5500
---------
4.2. Reporting Partial Duplicate Segments
It may be possible that a sender transmits a packet that includes one
or more duplicate sub-segments--that is, only part but not all of the
transmitted packet has already arrived at the receiver. This can
occur when the size of the sender's transmitted segments increases,
which can occur when the PMTU increases in the middle of a TCP
session, for example. The guidelines in Section 4 above apply to
reporting partial as well as full duplicate segments. This section
gives examples of these guidelines when reporting partial duplicate
segments.
When the SACK option is used for reporting partial duplicate
segments, the first D-SACK block reports the first duplicate sub-
segment. If the data packet being acknowledged contains multiple
partial duplicate sub-segments, then only the first such duplicate
sub-segment is reported in the SACK option. We illustrate this with
the examples below.
4.2.1. Example 4: Reporting a single duplicate subsegment.
The sender increases the packet size from 500 bytes to 1000 bytes.
The receiver subsequently receives a 1000-byte packet containing one
500-byte subsegment that has already been received and one which has
not. The receiver reports only the already received subsegment using
a single D-SACK block.
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
500-999 500-999 1000
1000-1499 (delayed)
1500-1999 (data packet dropped)
2000-2499 2000-2499 1000, SACK=2000-2500
1000-2000 1000-1499 1500, SACK=2000-2500
1000-2000 2500, SACK=1000-1500
---------
4.2.2. Example 5: Two non-contiguous duplicate subsegments covered by
the cumulative acknowledgement.
After the sender increases its packet size from 500 bytes to 1500
bytes, the receiver receives a packet containing two non-contiguous
duplicate 500-byte subsegments which are less than the cumulative
acknowledgement field. The receiver reports the first such duplicate
segment in a single D-SACK block.
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
500-999 500-999 1000
1000-1499 (delayed)
1500-1999 (data packet dropped)
2000-2499 (delayed)
2500-2999 (data packet dropped)
3000-3499 3000-3499 1000, SACK=3000-3500
1000-2499 1000-1499 1500, SACK=3000-3500
2000-2499 1500, SACK=2000-2500, 3000-3500
1000-2499 2500, SACK=1000-1500, 3000-3500
---------
4.2.3. Example 6: Two non-contiguous duplicate subsegments not covered
by the cumulative acknowledgement.
This example is similar to Example 5, except that after the sender
increases the packet size, the receiver receives a packet containing
two non-contiguous duplicate subsegments which are above the
cumulative acknowledgement field, rather than below. The first, D-
SACK block reports the first duplicate subsegment, and the second,
SACK block reports the larger block of non-contiguous data that it
belongs to.
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
500-999 500-999 1000
1000-1499 (data packet dropped)
1500-1999 (delayed)
2000-2499 (data packet dropped)
2500-2999 (delayed)
3000-3499 (data packet dropped)
3500-3999 3500-3999 1000, SACK=3500-4000
1000-1499 (data packet dropped)
1500-2999 1500-1999 1000, SACK=1500-2000, 3500-4000
2500-2999 1000, SACK=2500-3000, 1500-2000,
3500-4000
1500-2999 1000, SACK=1500-2000, 1500-3000,
---------
3500-4000
4.3. Interaction Between D-SACK and PAWS
RFC 1323 [RFC1323] specifies an algorithm for Protection Against
Wrapped Sequence Numbers (PAWS). PAWS gives a method for
distinguishing between sequence numbers for new data, and sequence
numbers from a previous cycle through the sequence number space.
Duplicate segments might be detected by PAWS as belonging to a
previous cycle through the sequence number space.
RFC 1323 specifies that for such packets, the receiver should do the
following:
Send an acknowledgement in reply as specified in RFC 793 page 69,
and drop the segment.
Since PAWS still requires sending an ACK, there is no harmful
interaction between PAWS and the use of D-SACK. The D-SACK block can
be included in the SACK option of the ACK, as outlined in Section 4,
independently of the use of PAWS by the TCP receiver, and
independently of the determination by PAWS of the validity or
invalidity of the data segment.
TCP senders receiving D-SACK blocks should be aware that a segment
reported as a duplicate segment could possibly have been from a prior
cycle through the sequence number space. This is independent of the
use of PAWS by the TCP data receiver. We do not anticipate that this
will present significant problems for senders using D-SACK
information.
5. Detection of Duplicate Packets
This extension to the SACK option enables the receiver to accurately
report the reception of duplicate data. Because each receipt of a
duplicate packet is reported in only one ACK packet, the loss of a
single ACK can prevent this information from reaching the sender. In
addition, we note that the sender can not necessarily trust the
receiver to send it accurate information [SCWA99].
In order for the sender to check that the first (D)SACK block of an
acknowledgement in fact acknowledges duplicate data, the sender
should compare the sequence space in the first SACK block to the
cumulative ACK which is carried IN THE SAME PACKET. If the SACK
sequence space is less than this cumulative ACK, it is an indication
that the segment identified by the SACK block has been received more
than once by the receiver. An implementation MUST NOT compare the
sequence space in the SACK block to the TCP state variable snd.una
(which carries the total cumulative ACK), as this may result in the
wrong conclusion if ACK packets are reordered.
If the sequence space in the first SACK block is greater than the
cumulative ACK, then the sender next compares the sequence space in
the first SACK block with the sequence space in the second SACK
block, if there is one. This comparison can determine if the first
SACK block is reporting duplicate data that lies above the cumulative
ACK.
TCP implementations which follow RFC 2581 [RFC2581] could see
duplicate packets in each of the following four situations. This
document does not specify what action a TCP implementation should
take in these cases. The extension to the SACK option simply enables
the sender to detect each of these cases. Note that these four
conditions are not an exhaustive list of possible cases for duplicate
packets, but are representative of the most common/likely cases.
Subsequent documents will describe experimental proposals for sender
responses to the detection of unnecessary retransmits due to
reordering, lost ACKS, or early retransmit timeouts.
5.1. Replication by the network
If a packet is replicated in the network, this extension to the SACK
option can identify this. For example:
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
500-999 500-999 1000
1000-1499 1000-1499 1500
(replicated)
1000-1499 1500, SACK=1000-1500
---------
In this case, the second packet was replicated in the network. An
ACK containing a D-SACK block which is lower than its ACK field and
is not identical to a previously retransmitted segment is indicative
of a replication by the network.
WITHOUT D-SACK:
If D-SACK was not used and the last ACK was piggybacked on a data
packet, the sender would not know that a packet had been replicated
in the network. If D-SACK was not used and neither of the last two
ACKs was piggybacked on a data packet, then the sender could
reasonably infer that either some data packet *or* the final ACK
packet had been replicated in the network. The receipt of the D-SACK
packet gives the sender positive knowledge that this data packet was
replicated in the network (assuming that the receiver is not lying).
RESEARCH ISSUES:
The current SACK option already allows the sender to identify
duplicate ACKs that do not acknowledge new data, but the D-SACK
option gives the sender a stronger basis for inferring that a
duplicate ACK does not acknowledge new data. The knowledge that a
duplicate ACK does not acknowledge new data allows the sender to
refrain from using that duplicate ACKs to infer packet loss (e.g.,
Fast Retransmit) or to send more data (e.g., Fast Recovery).
5.2. False retransmit due to reordering
If packets are reordered in the network such that a segment arrives
more than 3 packets out of order, TCP's Fast Retransmit algorithm
will retransmit the out-of-order packet. An example of this is shown
below:
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
500-999 500-999 1000
1000-1499 (delayed)
1500-1999 1500-1999 1000, SACK=1500-2000
2000-2499 2000-2499 1000, SACK=1500-2500
2500-2999 2500-2999 1000, SACK=1500-3000
1000-1499 1000-1499 3000
1000-1499 3000, SACK=1000-1500
---------
In this case, an ACK containing a SACK block which is lower than its
ACK field and identical to a previously retransmitted segment is
indicative of a significant reordering followed by a false
(unnecessary) retransmission.
WITHOUT D-SACK:
With the use of D-SACK illustrated above, the sender knows that
either the first transmission of segment 1000-1499 was delayed in the
network, or the first transmission of segment 1000-1499 was dropped
and the second transmission of segment 1000-1499 was duplicated.
Given that no other segments have been duplicated in the network,
this second option can be considered unlikely.
Without the use of D-SACK, the sender would only know that either the
first transmission of segment 1000-1499 was delayed in the network,
or that either one of the data segments or the final ACK was
duplicated in the network. Thus, the use of D-SACK allows the sender
to more reliably infer that the first transmission of segment
1000-1499 was not dropped.
[AP99], [L99], and [LK00] note that the sender could unambiguously
detect an unnecessary retransmit with the use of the timestamp
option. [LK00] proposes a timestamp-based algorithm that minimizes
the penalty for an unnecessary retransmit. [AP99] proposes a
heuristic for detecting an unnecessary retransmit in an environment
with neither timestamps nor SACK. [L99] also proposes a two-bit
field as an alternate to the timestamp option for unambiguously
marking the first three retransmissions of a packet. A similar idea
was proposed in [ISO8073].
RESEARCH ISSUES:
The use of D-SACK allows the sender to detect some cases (e.g., when
no ACK packets have been lost) when a a Fast Retransmit was due to
packet reordering instead of packet loss. This allows the TCP sender
to adjust the duplicate acknowledgment threshold, to prevent such
unnecessary Fast Retransmits in the future. Coupled with this, when
the sender determines, after the fact, that it has made an
unnecessary window reduction, the sender has the option of "undoing"
that reduction in the congestion window by resetting ssthresh to the
value of the old congestion window, and slow-starting until the
congestion window has reached that point.
Any proposal for "undoing" a reduction in the congestion window would
have to address the possibility that the TCP receiver could be lying
in its reports of received packets [SCWA99].
5.3. Retransmit Timeout Due to ACK Loss
If an entire window of ACKs is lost, a timeout will result. An
example of this is given below:
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
500-999 500-999 1000 (ACK dropped)
1000-1499 1000-1499 1500 (ACK dropped)
1500-1999 1500-1999 2000 (ACK dropped)
2000-2499 2000-2499 2500 (ACK dropped)
(timeout)
500-999 500-999 2500, SACK=500-1000
--------
In this case, all of the ACKs are dropped, resulting in a timeout.
This condition can be identified because the first ACK received
following the timeout carries a D-SACK block indicating duplicate
data was received.
WITHOUT D-SACK:
Without the use of D-SACK, the sender in this case would be unable to
decide that no data packets has been dropped.
RESEARCH ISSUES:
For a TCP that implements some form of ACK congestion control
[BPK97], this ability to distinguish between dropped data packets and
dropped ACK packets would be particularly useful. In this case, the
connection could implement congestion control for the return (ACK)
path independently from the congestion control on the forward (data)
path.
5.4. Early Retransmit Timeout
If the sender's RTO is too short, an early retransmission timeout can
occur when no packets have in fact been dropped in the network. An
example of this is given below:
Transmitted Received ACK Sent
Segment Segment (Including SACK Blocks)
500-999 (delayed)
1000-1499 (delayed)
1500-1999 (delayed)
2000-2499 (delayed)
(timeout)
500-999 (delayed)
500-999 1000
1000-1499 (delayed)
1000-1499 1500
...
1500-1999 2000
2000-2499 2500
500-999 2500, SACK=500-1000
--------
1000-1499 2500, SACK=1000-1500
---------
...
In this case, the first packet is retransmitted following the
timeout. Subsequently, the original window of packets arrives at the
receiver, resulting in ACKs for these segments. Following this, the
retransmissions of these segments arrive, resulting in ACKs carrying
SACK blocks which identify the duplicate segments.
This can be identified as an early retransmission timeout because the
ACK for byte 1000 is received after the timeout with no SACK
information, followed by an ACK which carries SACK information (500-
999) indicating that the retransmitted segment had already been
received.
WITHOUT D-SACK:
If D-SACK was not used and one of the duplicate ACKs was piggybacked
on a data packet, the sender would not know how many duplicate
packets had been received. If D-SACK was not used and none of the
duplicate ACKs were piggybacked on a data packet, then the sender
would have sent N duplicate packets, for some N, and received N
duplicate ACKs. In this case, the sender could reasonably infer that
some data or ACK packet had been replicated in the network, or that
an early retransmission timeout had occurred (or that the receiver is
lying).
RESEARCH ISSUES:
After the sender determines that an unnecessary (i.e., early)
retransmit timeout has occurred, the sender could adjust parameters
for setting the RTO, to prevent more unnecessary retransmit timeouts.
Coupled with this, when the sender determines, after the fact, that
it has made an unnecessary window reduction, the sender has the
option of "undoing" that reduction in the congestion window.
6. Security Considerations
This document neither strengthens nor weakens TCP's current security
properties.
7. Acknowledgements
We would like to thank Mark Handley, Reiner Ludwig, and Venkat
Padmanabhan for conversations on these issues, and to thank Mark
Allman for helpful feedback on this document.
8. References
[AP99] Mark Allman and Vern Paxson, On Estimating End-to-End
Network Path Properties, SIGCOMM 99, August 1999. URL
"http://www.acm.org/sigcomm/sigcomm99/papers/session7-
3.html".
[BPS99] J.C.R. Bennett, C. Partridge, and N. Shectman, Packet
Reordering is Not Pathological Network Behavior, IEEE/ACM
Transactions on Networking, Vol. 7, No. 6, December 1999,
pp. 789-798.
[BPK97] Hari Balakrishnan, Venkata Padmanabhan, and Randy H. Katz,
The Effects of Asymmetry on TCP Performance, Third ACM/IEEE
Mobicom Conference, Budapest, Hungary, Sep 1997. URL
"http://www.cs.berkeley.edu/~padmanab/
index.html#Publications".
[F99] Floyd, S., Re: TCP and out-of-order delivery, Message ID
<199902030027.QAA06775@owl.ee.lbl.gov> to the end-to-end-
interest mailing list, February 1999. URL
"http://www.aciri.org/floyd/notes/TCP_Feb99.email".
[ISO8073] ISO/IEC, Information-processing systems - Open Systems
Interconnection - Connection Oriented Transport Protocol
Specification, Internation Standard ISO/IEC 8073, December
1988.
[L99] Reiner Ludwig, A Case for Flow Adaptive Wireless links,
Technical Report UCB//CSD-99-1053, May 1999. URL
"http://iceberg.cs.berkeley.edu/papers/Ludwig-
FlowAdaptive/".
[LK00] Reiner Ludwig and Randy H. Katz, The Eifel Algorithm:
Making TCP Robust Against Spurious Retransmissions, SIGCOMM
Computer Communication Review, V. 30, N. 1, January 2000.
URL "http://www.acm.org/sigcomm/ccr/archive/ccr-toc/ccr-
toc-2000.html".
[RFC1323] Jacobson, V., Braden, R. and D. Borman, "TCP Extensions for
High Performance", RFC 1323, May 1992.
[RFC2018] Mathis, M., Mahdavi, J., Floyd, S. and A. Romanow, "TCP
Selective Acknowledgement Options", RFC 2018, April 1996.
[RFC2581] Allman, M., Paxson,V. and W. Stevens, "TCP Congestion
Control", RFC 2581, April 1999.
[SCWA99] Stefan Savage, Neal Cardwell, David Wetherall, Tom
Anderson, TCP Congestion Control with a Misbehaving
Receiver, ACM Computer Communications Review, pp. 71-78, V.
29, N. 5, October, 1999. URL
"http://www.acm.org/sigcomm/ccr/archive/ccr-toc/ccr-toc-
99.html".
Authors' Addresses
Sally Floyd
AT&T Center for Internet Research at ICSI (ACIRI)
Phone: +1 510-666-6989
EMail: floyd@aciri.org
URL: http://www.aciri.org/floyd/
Jamshid Mahdavi
Novell
Phone: 1-408-967-3806
EMail: mahdavi@novell.com
Matt Mathis
Pittsburgh Supercomputing Center
Phone: 412 268-3319
EMail: mathis@psc.edu
URL: http://www.psc.edu/~mathis/
Matthew Podolsky
UC Berkeley Electrical Engineering & Computer Science Dept.
Phone: 510-649-8914
EMail: podolsky@eecs.berkeley.edu
URL: http://www.eecs.berkeley.edu/~podolsky
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