Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
  • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
  • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
  • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
  • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
  • G06F7/499—Denomination or exception handling, e.g. rounding or overflow
  • G06F7/49942—Significance control
  • G06F7/49947—Rounding
  • G06F7/49952—Sticky bit
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
  • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
  • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
  • G06F7/499—Denomination or exception handling, e.g. rounding or overflow
  • G06F7/49942—Significance control
  • G06F7/49947—Rounding
  • G06F7/49963—Rounding to nearest

Definitions

• the present invention relates to signal compression. More particularly, the present invention relates to a novel and improved method and apparatus for compressing a fixed point signal without introducing a bias.
• Floating point notation has no fixed decimal point. Numbers are represented in floating point by two components: a mantissa and an exponent.
• Fixed point is a format in which all numerical quantities are expressed by a predetermined number of digits, with the decimal point implicitly located at some predetermined position. Fixed point numbers are the subject of the current invention.
• Different signals within a digital system may have different dynamic range requirements. For instance, multiplication of an M-bit number with an N-bit number results in a product having M+N bits for full precision. However, the system may not require that the product signal have that high a dynamic range. It may, therefore, be desirable to discard bits from the signal (i.e., compress the signal).
• Truncation refers to simply dropping one or more of the least significant bits or digits in this case from a signal. Truncation, however, introduces a negative bias into the compressed signal because truncation always involves throwing away a positive quantity (the truncated bits). These biases accumulate as more truncation operations are performed. This accumulated bias can significantly degrade downstream performance, particularly in low signal level environments. Rounding performs better than truncation, but nevertheless introduces a bias that also can degrade downstream performance.
• the present invention is a novel and improved method and apparatus for compressing fixed point signals without introducing a bias.
• signals are compressed according to a dithered rounding approach wherein signal values are rounded up and rounded down with approximately equal probability, canceling the bias that would otherwise result from the rounding operation.
• the present invention exploits numerical properties of the input signal in order to determine whether the signal value should be rounded up or down.
• An advantage provided by the current invention is that signal compression is achieved without the introduction of a bias. Signal compression may, therefore, be introduced at multiple points within a system without accumulating a signal bias and degrading downstream performance.
• a feature of the present invention is that one bit signal compression in general may be achieved in a particularly efficient fashion with a minimal amount of hardware.
• FIG. 1 is a diagram illustrating signal compression by K bits
• FIG. 2A is a graph illustrating the input/output relationship of conventional truncation
• FIG. 2B is a graph illustrating the input /output relationship of conventional rounding
• FIG. 2C is a graph illustrating the input/output relationship of dithered rounding according to the present invention.
• FIG. 2D is a table comparing the average error produced by one bit conventional truncation, conventional rounding, and dithered rounding;
• FIG. 3 is a flowchart illustrating a K-bit dithered rounding method;
• FIG. 4 is a diagram illustrating a preferred embodiment of a circuit for performing K-bit dithered rounding;
• FIG. 5 is a diagram illustrating a preferred embodiment of a circuit for performing one bit dithered rounding.
• FIG. 1 depicts a signal compressor 106 that compresses an
• N-bit input signal 102 to an N-K bit output signal 104 (K-bit compression).
• K-bit compression in the present context refers to systematically reducing the number of bits used to represent a signal.
• signal compressor 106 reduces the number of bits representing input signal 102 by K bits, thereby forming output signal 104.
• bit 1 refers to the least significant bit
• bit K refers to the K th least significant bit
• bit N refers to the most significant bit of an N-bit number.
• Groups of bits are also referred to as, e.g., the N-K most significant bits (identifying bit N-K through bit N of an N-bit number) or the K least significant bits (identifying bit 1 through bit K of a number having at least K bits).
• input signal 102 and output signal 104 will be referred to as having an integer component (the N-K most significant bits) and a fractional component (the K least significant bits).
• signal compressor 106 Various embodiments of signal compressor 106 are described below.
• a signal compression method according to the present invention is first described with reference to FIGS. 2 and 3.
• a K-bit signal compressor embodiment is described with reference to FIG. 4.
• a one bit signal compressor embodiment is then described with reference to FIG. 5.
• FIGS. 2 A, 2B, and 2C depict the input /output relationship of three methods of one bit signal compression (as shown in graphs 200, 202, and 204). These graphs give the value output by signal compressor 106 over a given range of input values.
• the first two graphs (200 and 202) depict conventional signal compression methods, while the third (204) depicts a method according to the present invention. Note that both input and output values are shown in decimal format for convenience, though the values are represented in 2's complement binary format as signal input 102 and signal output 104.
• the three graphs in FIG. 2 depict one bit compression of a four bit input signal to a three bit output signal.
• a four bit signal input 102 can represent integer signal values ranging from “7" to "-8", including "0".
• a three bit signal output 104 can represent integer signal values ranging from "3" to "-4", including "0".
• Truncation or rounding of an integer number of bits approximates the linear operation of division by a power of two. The average or expected deviation from this ideal is the bias.
• the linear operation of division by two is shown in graphs 200, 202, and 204 as a dotted line.
• FIG. 2A illustrates the input/output relationship of conventional one bit truncation.
• truncation refers to merely dropping the K least significant bits (the fractional component) from input signal 102 to form output signal 104. In other words, the output value is always rounded down.
• the solid line in FIG. 2A illustrates this relationship. For example, an input value of "5" (binary 0101) ideally compresses to a value of "2.5". Conventional truncation produces an output value of "2" (binary 010), the integer component of the input value.
• Conventional truncation produces an output value of "2" (binary 010), the integer component of the input value.
• FIG. 2B illustrates the input/output relationship of conventional one bit rounding.
• the output value is equal to the integer nearest the ideal value, with ideal values midway between two integers (i.e., any ideal value ending in a 0.5) always being rounded up.
• each of the odd input values is, therefore, rounded up (as shown by the solid line in FIG. 2B) as the ideal compressed value is midway between two integers.
• an input value of "5" which ideally compresses to a value of "2.5”
• the positive bias introduced by conventional rounding can be clearly seen in FIG.
• FIG. 2C illustrates the input/output relationship of a method of signal compression according to the present invention, called "dithered rounding.”
• Dithered rounding like conventional rounding, produces an output value that is equal to the integer nearest the ideal value.
• dithered rounding operates differently on those input values that result in ideal compressed values midway between two integers. Dithered rounding strives to round approximately half of these values up, and the other half down. This dither of the rounding cancels much of the bias introduced by conventional rounding.
• conventional one bit rounding introduces a positive bias to output signal 104 by always rounding up for each odd input value. Dithered one bit rounding, as shown in FIG.
• FIG. 2D is a table 206 comparing the average error for conventional truncation, conventional rounding, and dithered rounding.
• Table 206 depicts the results for one bit compression of a four bit number to a three bit number. The error is calculated for each input value, and a total average error for each of the three methods. As can be seen, conventional truncation results in the highest average error, conventional rounding has the next highest average error, and dithered rounding has a zero average error.
• edge effects errors are sometimes introduced for the most positive input values whenever 2's complement numbers are compressed. This is because, in some cases, it is not possible to represent the most positive compressed input value rounded to the next highest integer. For example, according to conventional rounding, an input value of "7” should result in an output value of "4". However, it is not possible to represent "4" using a 3 bit 2's complement format. An input value of "7” must, therefore, be represented as "3” in violation of conventional rounding rules.
• edge effects can be minimized by scaling the input signal such that input values rarely reach the most positive value. However these edge effects only appear for greater than one bit compression, i.e., one bit compression does not suffer from edge effects.
• FIG. 3 is a flowchart 300 depicting a dithered rounding method according to the current invention. This method compresses input signal 102 by K bits to form output signal 104 based on numerical characteristics of input signal 102.
• the following description assumes that input signal 102 and output signal 104 are represented in 2's complement format. Those skilled in the art will recognize that the ideas described below could be easily applied to binary numbers represented in other formats.
• step 302 the bits are checked to see if bit K of input signal 102 is "0".
• step 304 the N-K most significant bits of input signal 102 are output as an N- K bit output signal 104.
• Input values satisfying step 302 i.e., those values having a K th bit equal to "0" are those whose ideal compressed value is closest to the next lower output integer value, and are, therefore, rounded down. If bit K of input signal 102 is not a "0", then processing proceeds to step 306.
• step 306 the bits are checked to see if bit K of input signal 102 is " 1 ". If bit K of input signal 102 is "1", and if bits 1 through K-l are not all "0", then processing proceeds to step 308. In step 308, "1" is added to the N-K most significant bits of input signal 102 and the result is output as an N-K bit output signal 104. Input values satisfying the test for "1" in step 306 are those whose ideal compressed value is closest to the next higher output integer value, and are, therefore, rounded up.
• bit K of input signal 102 is "1", and bits 1 through K-l are all "0", then processing proceeds to step 310.
• These input values are those whose ideal compressed value is midway between two integers. As described above, the dithered rounding method of the current invention strives to round approximately half of these values up, and the other half down. This is accomplished by determining whether the N-K most significant bits of input signal 102 (the integer component of input signal 102) are odd or even (i.e., whether the N-K most significant bits considered alone represent an odd or an even number), and rounding accordingly. Those skilled in the art will recognize that one half of the input values will have an odd integer component, and the other half will have an even integer component. In a preferred embodiment, those input values having an even integer component are rounded up, those having an odd integer component are rounded down.
• this rounding convention is reversed. That is, those input values having an odd integer component are rounded up, and those having an even integer component are rounded down.
• the oddness /evenness of input signal 102 is preferably determined by examining bit K+l of input signal 102. An odd integer component is indicated by "1" at bit K+l, whereas an even integer component is indicated by a "0". Those skilled in the art will recognize that oddness/evenness may be determined in other ways. If even, then processing proceeds to step 312 where "1" is added to the
• N-K most significant bits of input signal 102 and the result is output as an N- K bit output signal 104. If odd, then processing proceeds to step 314 where the N-K most significant bits of input signal 102 are output as an N-K bit output signal 104. As a result, approximately half of the input values tested in step 310 are rounded up, and the other half are rounded down.
• FIG. 4 depicts a K-bit dithered rounding signal compressor 402.
• Signal compressor 402 compresses N-bit input signal 102 by K bits, forming N-K bit output signal 104.
• the amount of compression K can vary from one bit to
• Signal compressor 402 preferably includes two OR gates (410 and
• Adder 406 selectively adds "1" to the integer component of input signal 102 (i.e., the N-K most significant bits), forming N-K bit output signal 104. The remainder of the components of signal compressor 402 determine whether or not "1" is added. As described above, "1" is added for those integer components that are to be rounded up.
• AND gate 408 only outputs "1" to adder 406 if both of its inputs are
• bit K of input signal 102 i.e., bit K of input signal 102 and the output of OR gate 410.
• bit K of input signal 102 is not "1"
• the integer component of input signal 102 will not be rounded up.
• OR gate 410 outputs "1" if either of its inputs are “1". Thus, one of its inputs must be “1” in order for the integer component of input signal 102 to be rounded up.
• OR gate 416 determines whether any of the K-l least significant bits of input signal 102 are “1". If any of these bits are "1", then
• OR gate 416 outputs "1", causing OR gate 410 to output "1" as well.
• NOR gate 412 is "1", causing OR gate 410 to output "1".
• Signal compressor 402 is a preferred embodiment for performing K-bit signal compression. The following section describes an alternative embodiment for one bit dithered rounding.
• FIG. 5 depicts a one bit dithered rounding signal compressor 502.
• Signal compressor 502 compresses N-bit input signal 102 by a single bit, forming N-1 bit output signal 104.
• Signal compressor 502 includes an OR gate 504. Those skilled in the art will recognize that significant savings in complexity are gained where only a single bit of compression is required. Thus, signal compressor 502 is a preferred embodiment in situations where one bit compression is required.
• OR gate 504 selectively adds "1" to the integer component of input signal 102 (i.e., the N-1 most significant bits) forming N-1 bit output signal
• OR gate 504 outputs "1" if either bit 1 or bit 2 of input signal 102 are “1 " .
• integer component of input signal 102 is rounded up if bit 2 is "0" and bit 1 is "1".

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• Pure & Applied Mathematics (AREA)
• General Engineering & Computer Science (AREA)
• Computational Mathematics (AREA)
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• 1998
  • 1998-08-14 US US09/134,248 patent/US6148317A/en not_active Expired - Lifetime
• 1999
  • 1999-08-13 CA CA002340421A patent/CA2340421A1/en not_active Abandoned
  • 1999-08-13 EP EP99941157A patent/EP1110325B1/en not_active Expired - Lifetime
  • 1999-08-13 KR KR1020017001935A patent/KR20010072504A/ko not_active Withdrawn
  • 1999-08-13 AT AT99941157T patent/ATE270009T1/de not_active IP Right Cessation
  • 1999-08-13 CN CN99811666A patent/CN1321269A/zh active Pending
  • 1999-08-13 DE DE69918313T patent/DE69918313T2/de not_active Expired - Fee Related
  • 1999-08-13 WO PCT/US1999/018546 patent/WO2000010253A2/en not_active Ceased
  • 1999-08-13 AU AU54866/99A patent/AU767325B2/en not_active Ceased
  • 1999-08-13 RU RU2001107011/09A patent/RU2233024C2/ru not_active IP Right Cessation
  • 1999-08-13 JP JP2000565606A patent/JP4354648B2/ja not_active Expired - Fee Related

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