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Compute number of bit errors and bit error rate (BER)

`[number,ratio] = biterr(x,y) `

[number,ratio] = biterr(x,y,k)

[number,ratio] = biterr(x,y,k,* flg*)

[number,ratio,individual] = biterr(...)

The `biterr`

function compares unsigned binary
representations of elements in `x`

with those in `y`

.
The schematics below illustrate how the shapes of `x`

and `y`

determine
which elements `biterr`

compares.

Each element of `x`

and `y`

must
be a nonnegative decimal integer; `biterr`

converts
each element into its natural unsigned binary representation. `number`

is
a scalar or vector that indicates the number of bits that differ. `ratio`

is `number`

divided
by the *total number of bits*. The total number
of bits, the size of `number`

, and the elements that `biterr`

compares
are determined by the dimensions of `x`

and `y`

and
by the optional parameters.

`[number,ratio] = biterr(x,y) `

compares
the elements in `x`

and `y`

. If
the largest among all elements of `x`

and `y`

has
exactly k bits in its simplest binary representation, the total number
of bits is k times the number of entries in the *smaller* input.
The sizes of `x`

and `y`

determine
which elements are compared:

If

`x`

and`y`

are matrices of the same dimensions, then`biterr`

compares`x`

and`y`

element by element.`number`

is a scalar. See schematic (a) in the preceding figure.If one is a row (respectively, column) vector and the other is a two-dimensional matrix, then

`biterr`

compares the vector element by element with*each row (resp., column)*of the matrix. The length of the vector must equal the number of columns (resp., rows) in the matrix.`number`

is a column (resp., row) vector whose mth entry indicates the number of bits that differ when comparing the vector with the mth row (resp., column) of the matrix. See schematics (b) and (c) in the figure.

`[number,ratio] = biterr(x,y,k) `

is
the same as the first syntax, except that it considers each entry
in `x`

and `y`

to have `k`

bits.
The total number of bits is `k`

times the number
of entries of the smaller of `x`

and `y`

.
An error occurs if the binary representation of an element of `x`

or `y`

would
require more than `k`

digits.

`[number,ratio] = biterr(x,y,k,`

is
similar to the previous syntaxes, except that * flg*)

`flg`

`biterr`

compares
and how `biterr`

computes the outputs. The possible
values of `flg`

`'`

`row-wise`

`'`

, `'`

`column-wise`

`'`

,
and `'`

`overall`

`'`

.
The table below describes the differences that result from various
combinations of inputs. As always, `ratio`

is `number`

divided
by the total number of bits. If you do not provide `k`

as
an input argument, the function defines it internally as the number
of bits in the simplest binary representation of the largest among
all elements of `x`

and `y`

.

**Comparing a Two-Dimensional Matrix x with Another
Input y**

Shape of y | flg | Type of Comparison | number | Total Number of Bits |
---|---|---|---|---|

2-D matrix | `'` `overall` `'` (default) | Element by element | Total number of bit errors | `k` times number of entries of `y` |

`'` `row-wise` `'` | mth row of `x` vs. mth row of `y` | Column vector whose entries count bit errors in each row | `k` times number of entries of `y` | |

`'` `column-wise` `'` | mth column of `x` vs. mth column of `y` | Row vector whose entries count bit errors in each column | `k` times number of entries of `y` | |

Row vector | `'` `overall` `'` | `y` vs. each row of `x` | Total number of bit errors | `k` times number of entries of `x` |

`'` `row-wise` `'` (default) | `y` vs. each row of `x` | Column vector whose entries count bit errors in each row of `x` | `k` times size of `y` | |

Column vector | `'` `overall` `'` | `y` vs. each column of `x` | Total number of bit errors | `k` times number of entries of `x` |

`'` `column-wise` `'` (default) | `y` vs. each column of `x` | Row vector whose entries count bit errors in each column of `x` | `k` times size of `y` |

`[number,ratio,individual] = biterr(...)`

returns
a matrix `individual`

whose dimensions are those
of the larger of `x`

and `y`

. Each
entry of `individual`

corresponds to a comparison
between a pair of elements of `x`

and `y`

,
and specifies the number of bits by which the elements in the pair
differ.

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