mirror of https://github.com/saitohirga/WSJT-X.git
A few (last-minute?) edits and corrections.
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6444 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
This commit is contained in:
Joe Taylor
parent
a232d9da9d
commit
c00c0d1921
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@ -163,8 +163,8 @@ JT65 uses timed transmitting and receiving sequences one minute long.
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Messages are short and structured so as to streamline minimal exchanges
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between two amateur operators over potentially difficult radio paths.
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Most messages contain two callsigns and a grid locator, signal report,
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acknowledgment, or sign-off; one of the tokens ``CQ'', ``QRZ'', or ``DE''
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may be substituted for the first callsign.
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acknowledgment, or sign-off; one of the tokens CQ, QRZ, or DE may be substitute
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d for the first callsign.
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Alternatively, a message may contain up to 13 Latin characters of arbitrary
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text.
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All messages are efficiently compressed into exactly 72 bits of digital
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@ -182,7 +182,11 @@ key "jt65_protocol"
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.
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For a concise description of the overall process of transmitting and receiving
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a JT65 message, see the accompanying sidebar.
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a JT65 message, see the accompanying sidebar
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\series bold
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JT65 Message Processing
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\series default
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.
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\end_layout
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\begin_layout Standard
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@ -211,7 +215,8 @@ ly.
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The JT65 code is properly described as a short block-length, low-rate Reed-Solo
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mon code based on a 64-symbol
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\emph on
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alphabet
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alphabet.
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\emph default
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\begin_inset CommandInset nomenclature
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@ -221,7 +226,6 @@ description "A sequence of possible symbol values used for signaling. JT65 uses
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\end_inset
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.
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Characters in this alphabet are mapped onto 64 different frequencies for
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transmission.
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@ -230,8 +234,8 @@ description "A sequence of possible symbol values used for signaling. JT65 uses
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\begin_layout Standard
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Reed Solomon codes are widely used to ensure reliability in data transmission
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and storage.
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In hardware implementations, decoding is generally accomplished with an
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algorithm such as the Berlekamp-Massey (BM) algorithm, based on
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In hardware implementations, decoding is generally accomplished with a
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procedure such as the Berlekamp-Massey (BM) algorithm, based on
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\emph on
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hard decisions
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\emph default
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@ -299,7 +303,7 @@ MAP65
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WSJT-X
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\emph default
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, widely used for amateur weak-signal communication using JT65 and other
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specialized digital modes.
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specialized digital protocols.
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These programs are open-source, freely available
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\begin_inset CommandInset citation
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LatexCommand cite
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@ -313,13 +317,13 @@ key "wsjt"
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\begin_layout Standard
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The JT65 protocol specifies transmissions that start one second into a UTC
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minute and last for 46.8 seconds.
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Receiving software therefore has up to several seconds to decode a message
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before the start of the next minute, when the operator sends a reply.
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With today's personal computers, this relatively long available time encourages
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experimentation with decoders of high computational complexity.
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As a result, the FT algorithm can extend the decoding threshold on a typical
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fading channel by many dB over the hard-decision BM decoder, and by a meaningfu
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l amount over the KV decoder.
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Receiving software therefore has as much as ten seconds to decode a message
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before the start of the next minute, when the operator will send a reply.
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With today's personal computers, this relatively long time encourages experimen
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tation with decoders of high computational complexity.
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With time to spare, the FT algorithm lowers the decoding threshold on a
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typical fading channel by many dB over the hard-decision BM decoder, and
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by a meaningful amount over the KV decoder.
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In addition to its excellent performance, the new algorithm has other desirable
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properties, not least of which is its conceptual simplicity.
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Decoding performance and computational complexity scale in a convenient
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@ -339,13 +343,13 @@ The remainder of this paper is organized as follows.
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Section 3 provides statistical motivation for the FT algorithm, and Section
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4 describes the algorithm in full detail.
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Material in these two sections is important because it documents our approach
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and underlines its fundamental technical contribution.
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It is heavier in formal mathematics than common in
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and underlines its fundamental technical contributions.
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These sections are heavier in formal mathematics than common in
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\emph on
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QEX
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\emph default
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; for this reason, some readers may choose to skip or skim sections 3 and
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4 and proceed more quickly to the results.
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; for this reason, some readers may choose to skip or skim them and proceed
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more quickly to the results.
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Most readers will benefit by reviewing the original paper on the JT65 protocol
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\begin_inset CommandInset citation
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@ -377,8 +381,11 @@ WSJT-X
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\emph default
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.
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Section 7 summarizes some on-the-air experiences with the new decoder.
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You may Refer to the sidebar Glossary for brief definitions of some specialized
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terms.
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Refer to the sidebar
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\series bold
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Glossary
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\series default
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for brief definitions of some specialized terms.
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\end_layout
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\begin_layout Section
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@ -427,7 +434,7 @@ description "For the JT65 code, a vector of 63 symbol values each in the range 0
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\end_inset
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, the number of message symbols conveyed by the codeword; and the transmission
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alphabet or number of possible values for each symbol in the codewords.
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alphabet, or number of possible values for each symbol in the codewords.
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The codeword length and the number of message symbols are specified with
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the notation
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\begin_inset Formula $(n,k)$
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@ -474,8 +481,8 @@ description "The Hamming distance between two codewords, or between a received w
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\end_inset
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is used as a measure of the lack of agreement between different codewords,
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or between a received word
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is used as a measure of disagreement between different codewords, or between
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a received word
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\begin_inset CommandInset nomenclature
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LatexCommand nomenclature
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symbol "{\\bf Received word: }"
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@ -486,7 +493,7 @@ description "A vector of symbol values, possibly accompanied by soft information
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and a codeword.
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Hamming distance is the number of code symbols that differ in two words
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being compared.
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Reed-Solomon codes have minimum Hamming distance
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Reed-Solomon codes have guaranteed minimum Hamming distance
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\begin_inset Formula $d$
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\end_inset
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@ -513,7 +520,7 @@ With
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.
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With 72 information bits in each message, JT65 can transmit any one of
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\begin_inset Formula $2^{72}$
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\begin_inset Formula $2^{72}\approx4.7\times10^{21}$
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\end_inset
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possible messages.
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@ -522,8 +529,12 @@ With
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\end_layout
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\begin_layout Standard
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A received word containing some incorrect symbols (errors) can be decoded
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into the correct codeword using a deterministic
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A received word containing some
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\emph on
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errors
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\emph default
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(incorrect symbols) can be decoded into the correct codeword using a determinis
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tic,
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\begin_inset CommandInset nomenclature
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LatexCommand nomenclature
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symbol "{\\bf Deterministic algorithm: }"
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@ -531,7 +542,7 @@ description "A series of computational steps that for the same input always prod
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\end_inset
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, algebraic algorithm provided that no more than
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algebraic algorithm provided that no more than
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\begin_inset Formula $t$
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\end_inset
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@ -561,7 +572,7 @@ For the JT65 code
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\end_inset
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errors.
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In the unlikely event that the location of every error is known and if
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In the unlikely event that the location of every error is known, and if
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no correct symbols are accidentally labeled as errors, the BM algorithm
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can correct up to
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\begin_inset Formula $d-1=n-k$
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@ -801,9 +812,9 @@ GNU Octave
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\emph default
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as function
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\family typewriter
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hygepdf
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hygepdf(x,N,X,s)
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\family default
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(x,N,X,s).
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.
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The cumulative probability that at least
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\begin_inset Formula $\epsilon$
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\end_inset
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@ -979,7 +990,7 @@ Examples 1 and 2 show that a random strategy for selecting symbols to erase
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\begin_inset Formula $N=53$
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\end_inset
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less reliable symbols.
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less reliable ones.
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If
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\begin_inset Formula $s=45$
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\end_inset
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@ -1075,8 +1086,8 @@ Example 3 shows how statistical information about symbol quality should
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Once erasure probabilities have been assigned to each of the 63 received
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symbols, the FT algorithm uses a random number generator to decide whether
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or not to erase each symbol, according to its assigned erasure probability.
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The list of erased symbols is then submitted to the BM decoder which either
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produces a codeword or fails to decode.
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The list of erased symbols is then submitted to the BM decoder, which produces
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either a codeword or a flag indicating failure to decode.
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\end_layout
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@ -1091,20 +1102,16 @@ candidate
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\emph default
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.
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Our next task is to find a metric that can reliably select one of many
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proffered candidates as the codeword actually transmitted.
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proffered candidates as the codeword that was actually transmitted.
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\end_layout
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\begin_layout Standard
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The FT algorithm uses quality indices made available by a noncoherent 64-FSK
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demodulator (see the sidebar
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\begin_inset Quotes eld
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\end_inset
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JT65 Information Processing
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\begin_inset Quotes erd
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\end_inset
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\series bold
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JT65 Message Processing
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\series default
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).
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The demodulator computes binned power spectra for each signaling interval;
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the result is a two-dimensional array
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@ -1149,7 +1156,7 @@ JT65 Information Processing
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\begin_inset Formula $p_{1}$
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\end_inset
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-rank, the rank
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-rank (the rank
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\begin_inset Formula $\{1,2,\ldots,63\}$
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\end_inset
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@ -1161,13 +1168,14 @@ JT65 Information Processing
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\begin_inset Formula $p_{1}$
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\end_inset
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values, and the ratio
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values) and the ratio
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\begin_inset Formula $p_{2}/p_{1}$
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\end_inset
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.
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Note that high ranking symbols have larger signal-to-noise ratio than those
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with lower rank; and when
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High ranking symbols have larger signal-to-noise ratio than those with
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lower rank.
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When
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\begin_inset Formula $p_{2}/p_{1}$
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\end_inset
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@ -1176,13 +1184,21 @@ JT65 Information Processing
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\end_layout
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\begin_layout Standard
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We use 3-bit quantization of these two metrics to index the entries in an
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We use 3-bit quantization of the metrics
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\begin_inset Formula $p_{1}$
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\end_inset
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-rank and
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\begin_inset Formula $p_{2}/p_{1}$
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\end_inset
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to index the entries in an
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\begin_inset Formula $8\times8$
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\end_inset
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table of symbol error probabilities derived empirically from a large data
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set of received words that were successfully decoded.
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table of symbol error probabilities.
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The probabilities were derived empirically from a large data set of received
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words that were successfully decoded.
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The table provides an estimate of the
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\emph on
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a priori
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@ -1196,7 +1212,7 @@ a priori
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\end_inset
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.
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This table is a key element of the algorithm, as it will define which symbols
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This table is a key element of the algorithm, as it determines which symbols
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are effectively protected from erasure.
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The
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\emph on
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@ -1296,8 +1312,8 @@ In practice we find that
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\begin_inset Formula $u$
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\end_inset
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, the average signal-plus-noise power in all symbols according to a candidate
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codeword's symbol values:
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, the average signal-plus-noise power in all received symbols according
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to a candidate codeword's symbol values:
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\end_layout
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\begin_layout Standard
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@ -1345,7 +1361,7 @@ The correct JT65 codeword produces a value for
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\end_inset
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for the correct codeword has expectation value (average over many random
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realizations)
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realizations) given by
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\end_layout
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\begin_layout Standard
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@ -1422,11 +1438,7 @@ i.e.
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\end_inset
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where the subscript
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\begin_inset Quotes eld
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\end_inset
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i
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\begin_inset Quotes erd
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\begin_inset Formula $i$
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\end_inset
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is an abbreviation for
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|
@ -1480,7 +1492,7 @@ If
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\begin_inset Formula $y$
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\end_inset
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is too small for decoding to be possible, or the correct codeword is never
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is too small for decoding to be possible or the correct codeword is never
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presented as a candidate, the ratio
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\begin_inset Formula $r=u_{2}/u_{1}$
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\end_inset
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@ -1547,9 +1559,9 @@ As with all decoding algorithms that generate a list of possible codewords,
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\begin_inset Formula $r<R_{1}$
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\end_inset
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are used to validate additional codewords that did not pass the first test.
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A timeout is used to limit the algorithm's execution time if no acceptable
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codeword is found in a reasonable number of trials,
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are used to validate additional codewords that fail the first test.
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A timeout is used to limit execution time if no acceptable codeword is
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found in a reasonable number of trials,
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\begin_inset Formula $T$
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\end_inset
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|
|
@ -1563,8 +1575,11 @@ As with all decoding algorithms that generate a list of possible codewords,
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\end_inset
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or even higher.
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Pseudo-code for the FT algorithm is presented in an accompanying box as
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Algorithm 1.
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Pseudo-code for the FT algorithm is presented in an accompanying box,
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\series bold
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Algorithm 1
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\series default
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.
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\end_layout
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\begin_layout Standard
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||||
|
|
@ -1661,7 +1676,7 @@ If
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\begin_inset Formula $d_{1}=d_{s},$
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\end_inset
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and
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\begin_inset Formula $X_{1}=X,$
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\end_inset
|
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|
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|
|
@ -1744,15 +1759,8 @@ key "lc2004"
|
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.
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After developing this algorithm, we became aware that our approach is conceptua
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lly similar to a
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\begin_inset Quotes eld
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\end_inset
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stochastic erasures-only list decoding algorithm
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\begin_inset Quotes erd
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\end_inset
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described in reference
|
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lly similar to the stochastic, erasures-only list decoding algorithm described
|
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in reference
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\begin_inset CommandInset citation
|
||||
LatexCommand cite
|
||||
key "ls2009"
|
||||
|
|
@ -1767,11 +1775,11 @@ key "ls2009"
|
|||
|
||||
\end_inset
|
||||
|
||||
is applied to higher-rate Reed-Solomon codes on a symmetric channel with
|
||||
is applied to higher-rate Reed-Solomon codes on a symmetric channel using
|
||||
binary phase-shift keying (BPSK).
|
||||
Our 64-ary input channel with 64-FSK modulation required us to develop
|
||||
unique methods for assigning erasure probabilities and for defining acceptance
|
||||
criteria to select the best codeword from the list of candidates.
|
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criteria to select the best codeword from the list of tested candidates.
|
||||
|
||||
\end_layout
|
||||
|
||||
|
|
@ -1870,11 +1878,11 @@ not
|
|||
\end_inset
|
||||
|
||||
possible messages.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
Pseudo-code for the hinted decode or Deep Search algorithm is presented
|
||||
as Algorithm 2.
|
||||
Pseudo-code for the hinted-decoding algorithm is presented as
|
||||
\series bold
|
||||
Algorithm 2
|
||||
\series default
|
||||
.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
|
@ -1958,18 +1966,17 @@ Otherwise, declare decoding failure and exit.
|
|||
\end_layout
|
||||
|
||||
\begin_layout Enumerate
|
||||
An acceptable hinted decode has been found.
|
||||
Declare a successful result and return the saved codeword and the value
|
||||
|
||||
An acceptable codeword has been found.
|
||||
Declare a successful result and return the codeword and the value
|
||||
\begin_inset Formula $q=100\,(u_{1}-bu_{2})$
|
||||
\end_inset
|
||||
|
||||
as a confidence indicator.
|
||||
By default we use the value
|
||||
(By default we use the value
|
||||
\begin_inset Formula $b=1.12$
|
||||
\end_inset
|
||||
|
||||
for submode JT65A.
|
||||
for submode JT65A.)
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
|
@ -2095,16 +2102,16 @@ sync losses
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
As expected, the soft-decision algorithms FT and KV are about 2 dB better
|
||||
than the hard-decision BM algorithm on the AWGN channel.
|
||||
As expected, on the AWGN channel the soft-decision algorithms FT and KV
|
||||
are about 2 dB better than the hard-decision BM algorithm.
|
||||
In addition, FT has an edge over KV that increases from about 0.2 dB at
|
||||
higher SNRs to nearly 0.5 dB at low SNR.
|
||||
Execution time for FT with timeout parameter
|
||||
With timeout parameter
|
||||
\begin_inset Formula $T=10^{5}$
|
||||
\end_inset
|
||||
|
||||
is longer than that for the KV algorithm, but still small enough to be
|
||||
practical on today's home computers.
|
||||
execution time for FT is longer than that for the KV algorithm, but still
|
||||
small enough to be fully practical on today's home computers.
|
||||
|
||||
\end_layout
|
||||
|
||||
|
|
@ -2197,7 +2204,7 @@ reference "fig:WER2"
|
|||
|
||||
\end_inset
|
||||
|
||||
shows the FT and KV results from Figure
|
||||
replots the FT and KV results from Figure
|
||||
\begin_inset CommandInset ref
|
||||
LatexCommand ref
|
||||
reference "fig:bodide"
|
||||
|
|
@ -2235,8 +2242,12 @@ reference "fig:bodide"
|
|||
\end_inset
|
||||
|
||||
dB gain over KV at low SNR.
|
||||
It also provides very significant gains over the hard-decision BM decoder
|
||||
even when limited to very small numbers of trials.
|
||||
It also provides very significant gains over the hard-decision BM decoder,
|
||||
even when limited to very small
|
||||
\begin_inset Formula $T$
|
||||
\end_inset
|
||||
|
||||
.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
|
@ -2312,7 +2323,7 @@ reference "fig:N_vs_X"
|
|||
\end_inset
|
||||
|
||||
shows the number of stochastic erasure trials required to find the correct
|
||||
codeword as a function of
|
||||
codeword plotted as a function of
|
||||
\begin_inset Formula $X,$
|
||||
\end_inset
|
||||
|
||||
|
|
@ -2440,13 +2451,26 @@ reference "fig:Psuccess"
|
|||
Hz.
|
||||
These simulated Doppler spreads are comparable to those encountered on
|
||||
HF ionospheric paths and also for EME at VHF and the lower UHF bands.
|
||||
For comparison we note that the JT65 symbol rate is about 2.7 Hz.
|
||||
For comparison we note that the JT65 symbol rate is about
|
||||
\begin_inset ERT
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
|
||||
|
||||
\backslash
|
||||
linebreak
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
2.7 Hz.
|
||||
It is interesting to note that while Rayleigh fading severely degrades
|
||||
the success rate of the BM decoder, the penalties are much smaller with
|
||||
both FT and Deep Search (DS) decoding.
|
||||
Simulated Doppler spreads of 0.2 Hz actually increased the FT decoding rate
|
||||
slightly at SNRs close to the decoding threshold, presumably because with
|
||||
the low-rate JT65 code signal peaks provide the information needed for
|
||||
the low-rate JT65 code, signal peaks provide the information needed for
|
||||
good copy.
|
||||
\end_layout
|
||||
|
||||
|
|
@ -2486,10 +2510,10 @@ Percentage of JT65 messages successfully decoded as a function of
|
|||
Franke-Taylor (FT) decoding algorithms.
|
||||
Curves labeled DS correspond to the hinted-decode (Deep Search) algorithm
|
||||
with a codeword list of length
|
||||
\begin_inset Formula $L=5850$
|
||||
\begin_inset Formula $L\,$
|
||||
\end_inset
|
||||
|
||||
.
|
||||
= 5850.
|
||||
Numbers adjacent to the curves are simulated Doppler spreads in Hz.
|
||||
In the current version of
|
||||
\emph on
|
||||
|
|
@ -2523,12 +2547,16 @@ The JT65 protocol has proven remarkably versatile.
|
|||
Today the mode is used by thousands of amateurs around the world, communicating
|
||||
over terrestrial paths on the MF and HF bands and over terrestrial as well
|
||||
as EME paths from 50 MHz through 10 GHz.
|
||||
Three submodes are in use, together accommodating a wide range of Doppler
|
||||
spreads and potential instrumental instabilities.
|
||||
Three
|
||||
\emph on
|
||||
submodes
|
||||
\emph default
|
||||
are in use, together accommodating a wide range of Doppler spreads and
|
||||
potential instrumental instabilities.
|
||||
All three submodes transmit the 63 data symbols interspersed with 63 synchroniz
|
||||
ation symbols at keying rate 11025/4096 = 2.69 baud.
|
||||
Submode JT65A uses tone spacing equal to the symbol rate, so its total
|
||||
occupied bandwidth is
|
||||
Submode JT65A uses tone spacing equal to the symbol rate; its total occupied
|
||||
bandwidth is
|
||||
\begin_inset Formula $66\times2.69=177.6$
|
||||
\end_inset
|
||||
|
||||
|
|
@ -2602,7 +2630,7 @@ name "fig:JT65B_EME"
|
|||
|
||||
Examples of JT65B EME signals recorded at K1JT.
|
||||
Numbers above the spectrogram are audio frequencies in Hz, and the spectrogram'
|
||||
s vertical direction is one minute of time.
|
||||
s vertical span is one minute of time.
|
||||
The horizontal green bar on the frequency axis indicates the bandwidth
|
||||
occupied by the second decoded signal, a reply from SP6GWB.
|
||||
See text for additional details.
|
||||
|
|
@ -2629,7 +2657,7 @@ reference "fig:spectrogram"
|
|||
shows activity in submode JT65A during a single minute on the 20 m amateur
|
||||
band.
|
||||
At this time the band was crowded with overlapping signals.
|
||||
You can probably count at least 19 distinct synchronizing tones (the speckled
|
||||
With care you can count at least 19 distinct synchronizing tones (the speckled
|
||||
vertical lines in the figure), and can see that in some places as many
|
||||
as four signals overlap.
|
||||
After signal processing to demodulate the signals and produce soft-symbol
|
||||
|
|
@ -2679,8 +2707,12 @@ name "fig:spectrogram"
|
|||
|
||||
\end_inset
|
||||
|
||||
Spectrogram showing one minute of data collected under crowded band conditions
|
||||
on the 20 m band.
|
||||
Spectrogram from
|
||||
\emph on
|
||||
WSJT-X
|
||||
\emph default
|
||||
showing one minute of data collected under crowded band conditions on the
|
||||
20 m band.
|
||||
Numbers on the scale are frequencies (in Hz) above 14.076 MHz.
|
||||
|
||||
\end_layout
|
||||
|
|
@ -2849,7 +2881,7 @@ key "lhmg2010"
|
|||
|
||||
\end_inset
|
||||
|
||||
"Stochastic Chase Decoding of Reed-Solomon Codes", Camille Leroux, Saied
|
||||
``Stochastic Chase Decoding of Reed-Solomon Codes'', Camille Leroux, Saied
|
||||
Hemati, Shie Mannor, Warren J.
|
||||
Gross,
|
||||
\emph on
|
||||
|
|
@ -2868,8 +2900,8 @@ key "lk2008"
|
|||
|
||||
\end_inset
|
||||
|
||||
"Soft-Decision Decoding of Reed-Solomon Codes Using Successive Error-and-Erasure
|
||||
Decoding," Soo-Woong Lee and B.
|
||||
``Soft-Decision Decoding of Reed-Solomon Codes Using Successive Error-and-Erasur
|
||||
e Decoding,'' Soo-Woong Lee and B.
|
||||
V.
|
||||
K.
|
||||
Vijaya Kumar,
|
||||
|
|
@ -2893,11 +2925,7 @@ key "ls2009"
|
|||
|
||||
\end_inset
|
||||
|
||||
|
||||
\begin_inset Quotes erd
|
||||
\end_inset
|
||||
|
||||
Stochastic Erasure-Only List Decoding Algorithms for Reed-Solomon Codes,
|
||||
``Stochastic Erasure-Only List Decoding Algorithms for Reed-Solomon Codes,
|
||||
\begin_inset Quotes erd
|
||||
\end_inset
|
||||
|
||||
|
|
@ -3122,7 +3150,9 @@ height_special "totalheight"
|
|||
status open
|
||||
|
||||
\begin_layout Paragraph
|
||||
Sidebar: JT65 Information Processing
|
||||
|
||||
\size large
|
||||
Sidebar: JT65 Message Processing
|
||||
\end_layout
|
||||
|
||||
\begin_layout Enumerate
|
||||
|
|
|
|||
Loading…
Reference in New Issue